Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6003,2,Mod(1,6003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6003, 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("6003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6003 = 3^{2} \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6003.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: | \(47.9341963334\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 2 x^{19} - 33 x^{18} + 64 x^{17} + 453 x^{16} - 846 x^{15} - 3353 x^{14} + 5985 x^{13} + \cdots - 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | no (minimal twist has level 2001) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Root | \(-0.852674\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6003.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.852674 | 0.602932 | 0.301466 | − | 0.953477i | \(-0.402524\pi\) | ||||
0.301466 | + | 0.953477i | \(0.402524\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.27295 | −0.636473 | ||||||||
\(5\) | 0.278169 | 0.124401 | 0.0622006 | − | 0.998064i | \(-0.480188\pi\) | ||||
0.0622006 | + | 0.998064i | \(0.480188\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.70488 | 1.02235 | 0.511175 | − | 0.859477i | \(-0.329211\pi\) | ||||
0.511175 | + | 0.859477i | \(0.329211\pi\) | |||||||
\(8\) | −2.79076 | −0.986682 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.237188 | 0.0750054 | ||||||||
\(11\) | −5.07059 | −1.52884 | −0.764420 | − | 0.644718i | \(-0.776975\pi\) | ||||
−0.764420 | + | 0.644718i | \(0.776975\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.519860 | −0.144183 | −0.0720916 | − | 0.997398i | \(-0.522967\pi\) | ||||
−0.0720916 | + | 0.997398i | \(0.522967\pi\) | |||||||
\(14\) | 2.30638 | 0.616407 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.166287 | 0.0415717 | ||||||||
\(17\) | −2.19587 | −0.532576 | −0.266288 | − | 0.963894i | \(-0.585797\pi\) | ||||
−0.266288 | + | 0.963894i | \(0.585797\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.104552 | −0.0239860 | −0.0119930 | − | 0.999928i | \(-0.503818\pi\) | ||||
−0.0119930 | + | 0.999928i | \(0.503818\pi\) | |||||||
\(20\) | −0.354095 | −0.0791780 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.32356 | −0.921786 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.92262 | −0.984524 | ||||||||
\(26\) | −0.443271 | −0.0869326 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.44317 | −0.650698 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.35747 | 1.32144 | 0.660720 | − | 0.750632i | \(-0.270251\pi\) | ||||
0.660720 | + | 0.750632i | \(0.270251\pi\) | |||||||
\(32\) | 5.72330 | 1.01175 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.87236 | −0.321107 | ||||||||
\(35\) | 0.752416 | 0.127181 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.259721 | −0.0426979 | −0.0213490 | − | 0.999772i | \(-0.506796\pi\) | ||||
−0.0213490 | + | 0.999772i | \(0.506796\pi\) | |||||||
\(38\) | −0.0891492 | −0.0144619 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.776303 | −0.122744 | ||||||||
\(41\) | −0.509113 | −0.0795101 | −0.0397551 | − | 0.999209i | \(-0.512658\pi\) | ||||
−0.0397551 | + | 0.999209i | \(0.512658\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.63055 | 0.706152 | 0.353076 | − | 0.935595i | \(-0.385136\pi\) | ||||
0.353076 | + | 0.935595i | \(0.385136\pi\) | |||||||
\(44\) | 6.45459 | 0.973066 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.852674 | −0.125720 | ||||||||
\(47\) | 12.4082 | 1.80992 | 0.904959 | − | 0.425499i | \(-0.139902\pi\) | ||||
0.904959 | + | 0.425499i | \(0.139902\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.316385 | 0.0451979 | ||||||||
\(50\) | −4.19739 | −0.593601 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.661754 | 0.0917687 | ||||||||
\(53\) | −1.04291 | −0.143255 | −0.0716274 | − | 0.997431i | \(-0.522819\pi\) | ||||
−0.0716274 | + | 0.997431i | \(0.522819\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.41048 | −0.190189 | ||||||||
\(56\) | −7.54867 | −1.00873 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.852674 | −0.111962 | ||||||||
\(59\) | −0.323984 | −0.0421792 | −0.0210896 | − | 0.999778i | \(-0.506714\pi\) | ||||
−0.0210896 | + | 0.999778i | \(0.506714\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.63178 | 1.10519 | 0.552593 | − | 0.833451i | \(-0.313638\pi\) | ||||
0.552593 | + | 0.833451i | \(0.313638\pi\) | |||||||
\(62\) | 6.27352 | 0.796738 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.54754 | 0.568442 | ||||||||
\(65\) | −0.144609 | −0.0179366 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.31184 | −0.404605 | −0.202303 | − | 0.979323i | \(-0.564842\pi\) | ||||
−0.202303 | + | 0.979323i | \(0.564842\pi\) | |||||||
\(68\) | 2.79522 | 0.338970 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.641565 | 0.0766817 | ||||||||
\(71\) | 14.1260 | 1.67645 | 0.838226 | − | 0.545323i | \(-0.183593\pi\) | ||||
0.838226 | + | 0.545323i | \(0.183593\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.479599 | −0.0561328 | −0.0280664 | − | 0.999606i | \(-0.508935\pi\) | ||||
−0.0280664 | + | 0.999606i | \(0.508935\pi\) | |||||||
\(74\) | −0.221458 | −0.0257439 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.133090 | 0.0152664 | ||||||||
\(77\) | −13.7153 | −1.56301 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.38238 | 1.05560 | 0.527800 | − | 0.849369i | \(-0.323017\pi\) | ||||
0.527800 | + | 0.849369i | \(0.323017\pi\) | |||||||
\(80\) | 0.0462559 | 0.00517156 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.434108 | −0.0479392 | ||||||||
\(83\) | 6.67576 | 0.732759 | 0.366380 | − | 0.930465i | \(-0.380597\pi\) | ||||
0.366380 | + | 0.930465i | \(0.380597\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.610823 | −0.0662531 | ||||||||
\(86\) | 3.94835 | 0.425761 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 14.1508 | 1.50848 | ||||||||
\(89\) | −5.52034 | −0.585155 | −0.292577 | − | 0.956242i | \(-0.594513\pi\) | ||||
−0.292577 | + | 0.956242i | \(0.594513\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.40616 | −0.147406 | ||||||||
\(92\) | 1.27295 | 0.132714 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 10.5801 | 1.09126 | ||||||||
\(95\) | −0.0290833 | −0.00298388 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.587030 | 0.0596038 | 0.0298019 | − | 0.999556i | \(-0.490512\pi\) | ||||
0.0298019 | + | 0.999556i | \(0.490512\pi\) | |||||||
\(98\) | 0.269774 | 0.0272513 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 6.26624 | 0.626624 | ||||||||
\(101\) | −12.3741 | −1.23127 | −0.615634 | − | 0.788033i | \(-0.711100\pi\) | ||||
−0.615634 | + | 0.788033i | \(0.711100\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.6687 | 1.34681 | 0.673407 | − | 0.739272i | \(-0.264830\pi\) | ||||
0.673407 | + | 0.739272i | \(0.264830\pi\) | |||||||
\(104\) | 1.45080 | 0.142263 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.889263 | −0.0863728 | ||||||||
\(107\) | 4.99088 | 0.482487 | 0.241243 | − | 0.970465i | \(-0.422445\pi\) | ||||
0.241243 | + | 0.970465i | \(0.422445\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.14915 | 0.780547 | 0.390274 | − | 0.920699i | \(-0.372380\pi\) | ||||
0.390274 | + | 0.920699i | \(0.372380\pi\) | |||||||
\(110\) | −1.20268 | −0.114671 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.449786 | 0.0425008 | ||||||||
\(113\) | −14.9087 | −1.40250 | −0.701248 | − | 0.712917i | \(-0.747373\pi\) | ||||
−0.701248 | + | 0.712917i | \(0.747373\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.278169 | −0.0259394 | ||||||||
\(116\) | 1.27295 | 0.118190 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.276253 | −0.0254312 | ||||||||
\(119\) | −5.93956 | −0.544479 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14.7109 | 1.33735 | ||||||||
\(122\) | 7.36010 | 0.666352 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −9.36566 | −0.841062 | ||||||||
\(125\) | −2.76017 | −0.246877 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.41334 | −0.835299 | −0.417649 | − | 0.908608i | \(-0.637146\pi\) | ||||
−0.417649 | + | 0.908608i | \(0.637146\pi\) | |||||||
\(128\) | −7.56904 | −0.669015 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.123304 | −0.0108145 | ||||||||
\(131\) | −2.66337 | −0.232700 | −0.116350 | − | 0.993208i | \(-0.537119\pi\) | ||||
−0.116350 | + | 0.993208i | \(0.537119\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.282802 | −0.0245220 | ||||||||
\(134\) | −2.82392 | −0.243949 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.12813 | 0.525483 | ||||||||
\(137\) | 11.4148 | 0.975233 | 0.487617 | − | 0.873058i | \(-0.337866\pi\) | ||||
0.487617 | + | 0.873058i | \(0.337866\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.6211 | 1.07051 | 0.535254 | − | 0.844691i | \(-0.320216\pi\) | ||||
0.535254 | + | 0.844691i | \(0.320216\pi\) | |||||||
\(140\) | −0.957785 | −0.0809476 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 12.0449 | 1.01079 | ||||||||
\(143\) | 2.63600 | 0.220433 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.278169 | −0.0231007 | ||||||||
\(146\) | −0.408941 | −0.0338442 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.330611 | 0.0271761 | ||||||||
\(149\) | −10.6883 | −0.875616 | −0.437808 | − | 0.899068i | \(-0.644245\pi\) | ||||
−0.437808 | + | 0.899068i | \(0.644245\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.96037 | −0.647806 | −0.323903 | − | 0.946090i | \(-0.604995\pi\) | ||||
−0.323903 | + | 0.946090i | \(0.604995\pi\) | |||||||
\(152\) | 0.291780 | 0.0236665 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −11.6947 | −0.942387 | ||||||||
\(155\) | 2.04662 | 0.164389 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.59115 | 0.526031 | 0.263015 | − | 0.964792i | \(-0.415283\pi\) | ||||
0.263015 | + | 0.964792i | \(0.415283\pi\) | |||||||
\(158\) | 8.00011 | 0.636455 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.59205 | 0.125862 | ||||||||
\(161\) | −2.70488 | −0.213175 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 21.2877 | 1.66738 | 0.833691 | − | 0.552232i | \(-0.186224\pi\) | ||||
0.833691 | + | 0.552232i | \(0.186224\pi\) | |||||||
\(164\) | 0.648074 | 0.0506061 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.69225 | 0.441804 | ||||||||
\(167\) | −18.6280 | −1.44148 | −0.720739 | − | 0.693207i | \(-0.756197\pi\) | ||||
−0.720739 | + | 0.693207i | \(0.756197\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.7297 | −0.979211 | ||||||||
\(170\) | −0.520833 | −0.0399461 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −5.89444 | −0.449447 | ||||||||
\(173\) | 10.1837 | 0.774251 | 0.387125 | − | 0.922027i | \(-0.373468\pi\) | ||||
0.387125 | + | 0.922027i | \(0.373468\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −13.3151 | −1.00653 | ||||||||
\(176\) | −0.843171 | −0.0635564 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −4.70705 | −0.352808 | ||||||||
\(179\) | 5.18551 | 0.387583 | 0.193792 | − | 0.981043i | \(-0.437921\pi\) | ||||
0.193792 | + | 0.981043i | \(0.437921\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.3310 | 0.842224 | 0.421112 | − | 0.907009i | \(-0.361640\pi\) | ||||
0.421112 | + | 0.907009i | \(0.361640\pi\) | |||||||
\(182\) | −1.19900 | −0.0888755 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.79076 | 0.205737 | ||||||||
\(185\) | −0.0722466 | −0.00531167 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.1343 | 0.814224 | ||||||||
\(188\) | −15.7949 | −1.15196 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.0247986 | −0.00179908 | ||||||||
\(191\) | 15.0350 | 1.08789 | 0.543947 | − | 0.839119i | \(-0.316929\pi\) | ||||
0.543947 | + | 0.839119i | \(0.316929\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.4680 | 0.825487 | 0.412743 | − | 0.910847i | \(-0.364571\pi\) | ||||
0.412743 | + | 0.910847i | \(0.364571\pi\) | |||||||
\(194\) | 0.500545 | 0.0359370 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.402742 | −0.0287673 | ||||||||
\(197\) | 25.0347 | 1.78365 | 0.891826 | − | 0.452379i | \(-0.149425\pi\) | ||||
0.891826 | + | 0.452379i | \(0.149425\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.75281 | −0.407806 | −0.203903 | − | 0.978991i | \(-0.565363\pi\) | ||||
−0.203903 | + | 0.978991i | \(0.565363\pi\) | |||||||
\(200\) | 13.7378 | 0.971412 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −10.5511 | −0.742370 | ||||||||
\(203\) | −2.70488 | −0.189845 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.141620 | −0.00989115 | ||||||||
\(206\) | 11.6549 | 0.812037 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.0864458 | −0.00599393 | ||||||||
\(209\) | 0.530143 | 0.0366707 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.52515 | 0.242682 | 0.121341 | − | 0.992611i | \(-0.461281\pi\) | ||||
0.121341 | + | 0.992611i | \(0.461281\pi\) | |||||||
\(212\) | 1.32757 | 0.0911778 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.25560 | 0.290907 | ||||||||
\(215\) | 1.28808 | 0.0878461 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 19.9011 | 1.35097 | ||||||||
\(218\) | 6.94857 | 0.470617 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.79547 | 0.121051 | ||||||||
\(221\) | 1.14154 | 0.0767885 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −22.4725 | −1.50487 | −0.752436 | − | 0.658665i | \(-0.771121\pi\) | ||||
−0.752436 | + | 0.658665i | \(0.771121\pi\) | |||||||
\(224\) | 15.4809 | 1.03436 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −12.7123 | −0.845609 | ||||||||
\(227\) | 13.5150 | 0.897023 | 0.448511 | − | 0.893777i | \(-0.351954\pi\) | ||||
0.448511 | + | 0.893777i | \(0.351954\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.11059 | −0.403799 | −0.201900 | − | 0.979406i | \(-0.564711\pi\) | ||||
−0.201900 | + | 0.979406i | \(0.564711\pi\) | |||||||
\(230\) | −0.237188 | −0.0156397 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.79076 | 0.183222 | ||||||||
\(233\) | 17.3863 | 1.13902 | 0.569509 | − | 0.821985i | \(-0.307133\pi\) | ||||
0.569509 | + | 0.821985i | \(0.307133\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.45157 | 0.225156 | ||||||||
\(236\) | 0.412415 | 0.0268459 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −5.06451 | −0.328283 | ||||||||
\(239\) | −1.65727 | −0.107200 | −0.0535998 | − | 0.998562i | \(-0.517070\pi\) | ||||
−0.0535998 | + | 0.998562i | \(0.517070\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.8147 | 1.27637 | 0.638187 | − | 0.769881i | \(-0.279685\pi\) | ||||
0.638187 | + | 0.769881i | \(0.279685\pi\) | |||||||
\(242\) | 12.5436 | 0.806332 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −10.9878 | −0.703422 | ||||||||
\(245\) | 0.0880088 | 0.00562267 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.0543526 | 0.00345837 | ||||||||
\(248\) | −20.5329 | −1.30384 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2.35353 | −0.148850 | ||||||||
\(251\) | 9.99777 | 0.631054 | 0.315527 | − | 0.948917i | \(-0.397819\pi\) | ||||
0.315527 | + | 0.948917i | \(0.397819\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.07059 | 0.318785 | ||||||||
\(254\) | −8.02651 | −0.503628 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.5490 | −0.971813 | ||||||||
\(257\) | 2.47265 | 0.154239 | 0.0771197 | − | 0.997022i | \(-0.475428\pi\) | ||||
0.0771197 | + | 0.997022i | \(0.475428\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.702516 | −0.0436522 | ||||||||
\(260\) | 0.184080 | 0.0114161 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.27099 | −0.140302 | ||||||||
\(263\) | −23.9486 | −1.47673 | −0.738367 | − | 0.674399i | \(-0.764403\pi\) | ||||
−0.738367 | + | 0.674399i | \(0.764403\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.290106 | −0.0178211 | ||||||||
\(266\) | −0.241138 | −0.0147851 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.21579 | 0.257521 | ||||||||
\(269\) | 17.5956 | 1.07282 | 0.536412 | − | 0.843956i | \(-0.319779\pi\) | ||||
0.536412 | + | 0.843956i | \(0.319779\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.5307 | 0.761183 | 0.380591 | − | 0.924743i | \(-0.375720\pi\) | ||||
0.380591 | + | 0.924743i | \(0.375720\pi\) | |||||||
\(272\) | −0.365143 | −0.0221401 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9.73312 | 0.587999 | ||||||||
\(275\) | 24.9606 | 1.50518 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.17339 | 0.431007 | 0.215504 | − | 0.976503i | \(-0.430861\pi\) | ||||
0.215504 | + | 0.976503i | \(0.430861\pi\) | |||||||
\(278\) | 10.7617 | 0.645443 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.09981 | −0.125488 | ||||||||
\(281\) | 3.53636 | 0.210961 | 0.105481 | − | 0.994421i | \(-0.466362\pi\) | ||||
0.105481 | + | 0.994421i | \(0.466362\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.19773 | −0.130642 | −0.0653208 | − | 0.997864i | \(-0.520807\pi\) | ||||
−0.0653208 | + | 0.997864i | \(0.520807\pi\) | |||||||
\(284\) | −17.9817 | −1.06702 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.24765 | 0.132906 | ||||||||
\(287\) | −1.37709 | −0.0812871 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.1782 | −0.716363 | ||||||||
\(290\) | −0.237188 | −0.0139282 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.610504 | 0.0357270 | ||||||||
\(293\) | 3.48709 | 0.203718 | 0.101859 | − | 0.994799i | \(-0.467521\pi\) | ||||
0.101859 | + | 0.994799i | \(0.467521\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.0901226 | −0.00524714 | ||||||||
\(296\) | 0.724819 | 0.0421293 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −9.11360 | −0.527937 | ||||||||
\(299\) | 0.519860 | 0.0300643 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.5251 | 0.721934 | ||||||||
\(302\) | −6.78761 | −0.390583 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.0173857 | −0.000997137 0 | ||||||||
\(305\) | 2.40110 | 0.137487 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.3415 | −0.590222 | −0.295111 | − | 0.955463i | \(-0.595357\pi\) | ||||
−0.295111 | + | 0.955463i | \(0.595357\pi\) | |||||||
\(308\) | 17.4589 | 0.994813 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.74510 | 0.0991152 | ||||||||
\(311\) | 3.44449 | 0.195319 | 0.0976595 | − | 0.995220i | \(-0.468864\pi\) | ||||
0.0976595 | + | 0.995220i | \(0.468864\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.39424 | 0.530994 | 0.265497 | − | 0.964112i | \(-0.414464\pi\) | ||||
0.265497 | + | 0.964112i | \(0.414464\pi\) | |||||||
\(314\) | 5.62010 | 0.317161 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −11.9433 | −0.671861 | ||||||||
\(317\) | −20.4150 | −1.14662 | −0.573310 | − | 0.819338i | \(-0.694341\pi\) | ||||
−0.573310 | + | 0.819338i | \(0.694341\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.07059 | 0.283898 | ||||||||
\(320\) | 1.26499 | 0.0707149 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.30638 | −0.128530 | ||||||||
\(323\) | 0.229583 | 0.0127744 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.55907 | 0.141952 | ||||||||
\(326\) | 18.1515 | 1.00532 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.42081 | 0.0784512 | ||||||||
\(329\) | 33.5626 | 1.85037 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.63941 | −0.0901101 | −0.0450551 | − | 0.998985i | \(-0.514346\pi\) | ||||
−0.0450551 | + | 0.998985i | \(0.514346\pi\) | |||||||
\(332\) | −8.49788 | −0.466382 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −15.8836 | −0.869113 | ||||||||
\(335\) | −0.921252 | −0.0503334 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 25.4684 | 1.38735 | 0.693677 | − | 0.720286i | \(-0.255990\pi\) | ||||
0.693677 | + | 0.720286i | \(0.255990\pi\) | |||||||
\(338\) | −10.8543 | −0.590397 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.777545 | 0.0421683 | ||||||||
\(341\) | −37.3067 | −2.02027 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.0784 | −0.976141 | ||||||||
\(344\) | −12.9227 | −0.696747 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8.68336 | 0.466820 | ||||||||
\(347\) | 30.8489 | 1.65606 | 0.828029 | − | 0.560686i | \(-0.189462\pi\) | ||||
0.828029 | + | 0.560686i | \(0.189462\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.05975 | 0.377900 | 0.188950 | − | 0.981987i | \(-0.439492\pi\) | ||||
0.188950 | + | 0.981987i | \(0.439492\pi\) | |||||||
\(350\) | −11.3535 | −0.606867 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −29.0205 | −1.54680 | ||||||||
\(353\) | −16.3887 | −0.872282 | −0.436141 | − | 0.899878i | \(-0.643655\pi\) | ||||
−0.436141 | + | 0.899878i | \(0.643655\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.92943 | 0.208553 | ||||||||
\(356\) | 7.02710 | 0.372435 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.42155 | 0.233686 | ||||||||
\(359\) | −24.2910 | −1.28203 | −0.641014 | − | 0.767529i | \(-0.721486\pi\) | ||||
−0.641014 | + | 0.767529i | \(0.721486\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9891 | −0.999425 | ||||||||
\(362\) | 9.66162 | 0.507803 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.78997 | 0.0938197 | ||||||||
\(365\) | −0.133410 | −0.00698298 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 20.9932 | 1.09583 | 0.547917 | − | 0.836532i | \(-0.315421\pi\) | ||||
0.547917 | + | 0.836532i | \(0.315421\pi\) | |||||||
\(368\) | −0.166287 | −0.00866829 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.0616028 | −0.00320258 | ||||||||
\(371\) | −2.82095 | −0.146456 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.86668 | 0.459099 | 0.229550 | − | 0.973297i | \(-0.426275\pi\) | ||||
0.229550 | + | 0.973297i | \(0.426275\pi\) | |||||||
\(374\) | 9.49396 | 0.490921 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −34.6282 | −1.78581 | ||||||||
\(377\) | 0.519860 | 0.0267741 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.0116 | −0.925195 | −0.462597 | − | 0.886568i | \(-0.653082\pi\) | ||||
−0.462597 | + | 0.886568i | \(0.653082\pi\) | |||||||
\(380\) | 0.0370215 | 0.00189916 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 12.8200 | 0.655926 | ||||||||
\(383\) | −23.2088 | −1.18591 | −0.592957 | − | 0.805234i | \(-0.702039\pi\) | ||||
−0.592957 | + | 0.805234i | \(0.702039\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.81519 | −0.194440 | ||||||||
\(386\) | 9.77849 | 0.497712 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.747258 | −0.0379363 | ||||||||
\(389\) | 12.7471 | 0.646306 | 0.323153 | − | 0.946347i | \(-0.395257\pi\) | ||||
0.323153 | + | 0.946347i | \(0.395257\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.19587 | 0.111050 | ||||||||
\(392\) | −0.882955 | −0.0445960 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 21.3465 | 1.07542 | ||||||||
\(395\) | 2.60989 | 0.131318 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.267573 | 0.0134291 | 0.00671456 | − | 0.999977i | \(-0.497863\pi\) | ||||
0.00671456 | + | 0.999977i | \(0.497863\pi\) | |||||||
\(398\) | −4.90528 | −0.245879 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.818566 | −0.0409283 | ||||||||
\(401\) | 25.0956 | 1.25321 | 0.626607 | − | 0.779335i | \(-0.284443\pi\) | ||||
0.626607 | + | 0.779335i | \(0.284443\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.82485 | −0.190529 | ||||||||
\(404\) | 15.7515 | 0.783669 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.30638 | −0.114464 | ||||||||
\(407\) | 1.31694 | 0.0652783 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −24.7033 | −1.22150 | −0.610750 | − | 0.791823i | \(-0.709132\pi\) | ||||
−0.610750 | + | 0.791823i | \(0.709132\pi\) | |||||||
\(410\) | −0.120755 | −0.00596369 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −17.3995 | −0.857211 | ||||||||
\(413\) | −0.876339 | −0.0431218 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.85699 | 0.0911561 | ||||||||
\(416\) | −2.97532 | −0.145877 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.452039 | 0.0221099 | ||||||||
\(419\) | 14.0991 | 0.688786 | 0.344393 | − | 0.938826i | \(-0.388085\pi\) | ||||
0.344393 | + | 0.938826i | \(0.388085\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.9132 | 0.921772 | 0.460886 | − | 0.887459i | \(-0.347532\pi\) | ||||
0.460886 | + | 0.887459i | \(0.347532\pi\) | |||||||
\(422\) | 3.00581 | 0.146320 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.91051 | 0.141347 | ||||||||
\(425\) | 10.8094 | 0.524334 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 23.3480 | 1.12989 | ||||||||
\(428\) | −6.35313 | −0.307090 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.09831 | 0.0529652 | ||||||||
\(431\) | 7.03206 | 0.338722 | 0.169361 | − | 0.985554i | \(-0.445830\pi\) | ||||
0.169361 | + | 0.985554i | \(0.445830\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −20.4589 | −0.983192 | −0.491596 | − | 0.870823i | \(-0.663586\pi\) | ||||
−0.491596 | + | 0.870823i | \(0.663586\pi\) | |||||||
\(434\) | 16.9691 | 0.814545 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −10.3734 | −0.496798 | ||||||||
\(437\) | 0.104552 | 0.00500142 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −28.6535 | −1.36756 | −0.683778 | − | 0.729690i | \(-0.739664\pi\) | ||||
−0.683778 | + | 0.729690i | \(0.739664\pi\) | |||||||
\(440\) | 3.93632 | 0.187656 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.973364 | 0.0462982 | ||||||||
\(443\) | 37.4338 | 1.77854 | 0.889268 | − | 0.457387i | \(-0.151214\pi\) | ||||
0.889268 | + | 0.457387i | \(0.151214\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.53559 | −0.0727939 | ||||||||
\(446\) | −19.1617 | −0.907335 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 12.3006 | 0.581147 | ||||||||
\(449\) | −4.16541 | −0.196578 | −0.0982889 | − | 0.995158i | \(-0.531337\pi\) | ||||
−0.0982889 | + | 0.995158i | \(0.531337\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.58150 | 0.121558 | ||||||||
\(452\) | 18.9780 | 0.892651 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 11.5239 | 0.540843 | ||||||||
\(455\) | −0.391151 | −0.0183374 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.6569 | 0.732399 | 0.366200 | − | 0.930536i | \(-0.380659\pi\) | ||||
0.366200 | + | 0.930536i | \(0.380659\pi\) | |||||||
\(458\) | −5.21035 | −0.243463 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.354095 | 0.0165098 | ||||||||
\(461\) | 22.6379 | 1.05435 | 0.527177 | − | 0.849756i | \(-0.323251\pi\) | ||||
0.527177 | + | 0.849756i | \(0.323251\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.04786 | −0.188120 | −0.0940599 | − | 0.995567i | \(-0.529985\pi\) | ||||
−0.0940599 | + | 0.995567i | \(0.529985\pi\) | |||||||
\(464\) | −0.166287 | −0.00771966 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 14.8249 | 0.686750 | ||||||||
\(467\) | 2.50969 | 0.116135 | 0.0580673 | − | 0.998313i | \(-0.481506\pi\) | ||||
0.0580673 | + | 0.998313i | \(0.481506\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.95813 | −0.413648 | ||||||||
\(470\) | 2.94307 | 0.135754 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0.904162 | 0.0416174 | ||||||||
\(473\) | −23.4796 | −1.07959 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.514672 | 0.0236148 | ||||||||
\(476\) | 7.56074 | 0.346546 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.41311 | −0.0646341 | ||||||||
\(479\) | −15.3017 | −0.699154 | −0.349577 | − | 0.936908i | \(-0.613675\pi\) | ||||
−0.349577 | + | 0.936908i | \(0.613675\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.135019 | 0.00615632 | ||||||||
\(482\) | 16.8954 | 0.769566 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −18.7262 | −0.851189 | ||||||||
\(485\) | 0.163294 | 0.00741479 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.4632 | −0.564760 | −0.282380 | − | 0.959303i | \(-0.591124\pi\) | ||||
−0.282380 | + | 0.959303i | \(0.591124\pi\) | |||||||
\(488\) | −24.0892 | −1.09047 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.0750428 | 0.00339009 | ||||||||
\(491\) | −6.93040 | −0.312764 | −0.156382 | − | 0.987697i | \(-0.549983\pi\) | ||||
−0.156382 | + | 0.987697i | \(0.549983\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.19587 | 0.0988969 | ||||||||
\(494\) | 0.0463451 | 0.00208516 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.22345 | 0.0549345 | ||||||||
\(497\) | 38.2093 | 1.71392 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 27.5543 | 1.23350 | 0.616749 | − | 0.787160i | \(-0.288449\pi\) | ||||
0.616749 | + | 0.787160i | \(0.288449\pi\) | |||||||
\(500\) | 3.51355 | 0.157131 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 8.52484 | 0.380482 | ||||||||
\(503\) | 7.21927 | 0.321891 | 0.160946 | − | 0.986963i | \(-0.448546\pi\) | ||||
0.160946 | + | 0.986963i | \(0.448546\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.44209 | −0.153171 | ||||||||
\(506\) | 4.32356 | 0.192206 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 11.9827 | 0.531645 | ||||||||
\(509\) | 30.1844 | 1.33790 | 0.668950 | − | 0.743308i | \(-0.266744\pi\) | ||||
0.668950 | + | 0.743308i | \(0.266744\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.29726 | −0.0573873 | ||||||||
\(512\) | 1.87984 | 0.0830780 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.10836 | 0.0929958 | ||||||||
\(515\) | 3.80221 | 0.167545 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −62.9167 | −2.76707 | ||||||||
\(518\) | −0.599017 | −0.0263193 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.403569 | 0.0176977 | ||||||||
\(521\) | 10.4106 | 0.456096 | 0.228048 | − | 0.973650i | \(-0.426766\pi\) | ||||
0.228048 | + | 0.973650i | \(0.426766\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −30.7711 | −1.34552 | −0.672762 | − | 0.739859i | \(-0.734892\pi\) | ||||
−0.672762 | + | 0.739859i | \(0.734892\pi\) | |||||||
\(524\) | 3.39033 | 0.148107 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −20.4203 | −0.890369 | ||||||||
\(527\) | −16.1560 | −0.703767 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −0.247366 | −0.0107449 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.359992 | 0.0156076 | ||||||||
\(533\) | 0.264667 | 0.0114640 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.38831 | 0.0600219 | ||||||||
\(536\) | 9.24254 | 0.399217 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 15.0033 | 0.646840 | ||||||||
\(539\) | −1.60426 | −0.0691004 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 24.0739 | 1.03502 | 0.517509 | − | 0.855678i | \(-0.326860\pi\) | ||||
0.517509 | + | 0.855678i | \(0.326860\pi\) | |||||||
\(542\) | 10.6846 | 0.458941 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −12.5676 | −0.538832 | ||||||||
\(545\) | 2.26685 | 0.0971010 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.60380 | −0.111330 | −0.0556652 | − | 0.998449i | \(-0.517728\pi\) | ||||
−0.0556652 | + | 0.998449i | \(0.517728\pi\) | |||||||
\(548\) | −14.5304 | −0.620710 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 21.2833 | 0.907521 | ||||||||
\(551\) | 0.104552 | 0.00445408 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 25.3782 | 1.07919 | ||||||||
\(554\) | 6.11656 | 0.259868 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −16.0660 | −0.681349 | ||||||||
\(557\) | −16.5729 | −0.702215 | −0.351108 | − | 0.936335i | \(-0.614195\pi\) | ||||
−0.351108 | + | 0.936335i | \(0.614195\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.40724 | −0.101815 | ||||||||
\(560\) | 0.125117 | 0.00528714 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3.01536 | 0.127195 | ||||||||
\(563\) | 4.71445 | 0.198690 | 0.0993452 | − | 0.995053i | \(-0.468325\pi\) | ||||
0.0993452 | + | 0.995053i | \(0.468325\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.14716 | −0.174472 | ||||||||
\(566\) | −1.87395 | −0.0787680 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −39.4223 | −1.65412 | ||||||||
\(569\) | −2.24239 | −0.0940058 | −0.0470029 | − | 0.998895i | \(-0.514967\pi\) | ||||
−0.0470029 | + | 0.998895i | \(0.514967\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 38.4824 | 1.61044 | 0.805220 | − | 0.592977i | \(-0.202047\pi\) | ||||
0.805220 | + | 0.592977i | \(0.202047\pi\) | |||||||
\(572\) | −3.35548 | −0.140300 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.17421 | −0.0490106 | ||||||||
\(575\) | 4.92262 | 0.205288 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −31.8247 | −1.32488 | −0.662439 | − | 0.749116i | \(-0.730479\pi\) | ||||
−0.662439 | + | 0.749116i | \(0.730479\pi\) | |||||||
\(578\) | −10.3840 | −0.431918 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.354095 | 0.0147030 | ||||||||
\(581\) | 18.0571 | 0.749136 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.28817 | 0.219014 | ||||||||
\(584\) | 1.33844 | 0.0553852 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.97335 | 0.122828 | ||||||||
\(587\) | 35.1398 | 1.45038 | 0.725188 | − | 0.688551i | \(-0.241753\pi\) | ||||
0.725188 | + | 0.688551i | \(0.241753\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.769241 | −0.0316960 | ||||||||
\(590\) | −0.0768452 | −0.00316367 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.0431882 | −0.00177502 | ||||||||
\(593\) | −13.1988 | −0.542009 | −0.271004 | − | 0.962578i | \(-0.587356\pi\) | ||||
−0.271004 | + | 0.962578i | \(0.587356\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.65220 | −0.0677338 | ||||||||
\(596\) | 13.6056 | 0.557306 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.443271 | 0.0181267 | ||||||||
\(599\) | 42.6629 | 1.74316 | 0.871579 | − | 0.490254i | \(-0.163096\pi\) | ||||
0.871579 | + | 0.490254i | \(0.163096\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.17667 | −0.170370 | −0.0851850 | − | 0.996365i | \(-0.527148\pi\) | ||||
−0.0851850 | + | 0.996365i | \(0.527148\pi\) | |||||||
\(602\) | 10.6798 | 0.435277 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 10.1331 | 0.412311 | ||||||||
\(605\) | 4.09212 | 0.166368 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −19.0944 | −0.775017 | −0.387508 | − | 0.921866i | \(-0.626664\pi\) | ||||
−0.387508 | + | 0.921866i | \(0.626664\pi\) | |||||||
\(608\) | −0.598385 | −0.0242677 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.04736 | 0.0828950 | ||||||||
\(611\) | −6.45051 | −0.260960 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18.3726 | 0.742062 | 0.371031 | − | 0.928620i | \(-0.379004\pi\) | ||||
0.371031 | + | 0.928620i | \(0.379004\pi\) | |||||||
\(614\) | −8.81795 | −0.355864 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 38.2762 | 1.54219 | ||||||||
\(617\) | 36.9471 | 1.48743 | 0.743716 | − | 0.668495i | \(-0.233061\pi\) | ||||
0.743716 | + | 0.668495i | \(0.233061\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −35.4201 | −1.42365 | −0.711827 | − | 0.702355i | \(-0.752132\pi\) | ||||
−0.711827 | + | 0.702355i | \(0.752132\pi\) | |||||||
\(620\) | −2.60524 | −0.104629 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 2.93703 | 0.117764 | ||||||||
\(623\) | −14.9319 | −0.598233 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.8453 | 0.953813 | ||||||||
\(626\) | 8.01023 | 0.320153 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −8.39018 | −0.334805 | ||||||||
\(629\) | 0.570314 | 0.0227399 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −29.4582 | −1.17271 | −0.586355 | − | 0.810054i | \(-0.699438\pi\) | ||||
−0.586355 | + | 0.810054i | \(0.699438\pi\) | |||||||
\(632\) | −26.1839 | −1.04154 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −17.4073 | −0.691334 | ||||||||
\(635\) | −2.61850 | −0.103912 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.164476 | −0.00651678 | ||||||||
\(638\) | 4.32356 | 0.171171 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.10547 | −0.0832262 | ||||||||
\(641\) | −14.9498 | −0.590481 | −0.295241 | − | 0.955423i | \(-0.595400\pi\) | ||||
−0.295241 | + | 0.955423i | \(0.595400\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 25.7271 | 1.01458 | 0.507289 | − | 0.861776i | \(-0.330648\pi\) | ||||
0.507289 | + | 0.861776i | \(0.330648\pi\) | |||||||
\(644\) | 3.44317 | 0.135680 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.195760 | 0.00770206 | ||||||||
\(647\) | −25.3141 | −0.995201 | −0.497600 | − | 0.867406i | \(-0.665785\pi\) | ||||
−0.497600 | + | 0.867406i | \(0.665785\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.64279 | 0.0644852 | ||||||||
\(650\) | 2.18206 | 0.0855873 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −27.0981 | −1.06124 | ||||||||
\(653\) | −17.9366 | −0.701914 | −0.350957 | − | 0.936391i | \(-0.614144\pi\) | ||||
−0.350957 | + | 0.936391i | \(0.614144\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.740869 | −0.0289481 | ||||||||
\(656\) | −0.0846587 | −0.00330537 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 28.6180 | 1.11565 | ||||||||
\(659\) | −0.907905 | −0.0353670 | −0.0176835 | − | 0.999844i | \(-0.505629\pi\) | ||||
−0.0176835 | + | 0.999844i | \(0.505629\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.1348 | −0.822048 | −0.411024 | − | 0.911624i | \(-0.634829\pi\) | ||||
−0.411024 | + | 0.911624i | \(0.634829\pi\) | |||||||
\(662\) | −1.39788 | −0.0543303 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −18.6304 | −0.723000 | ||||||||
\(665\) | −0.0786669 | −0.00305057 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | 23.7125 | 0.917462 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −0.785528 | −0.0303476 | ||||||||
\(671\) | −43.7682 | −1.68965 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.47393 | −0.365193 | −0.182597 | − | 0.983188i | \(-0.558450\pi\) | ||||
−0.182597 | + | 0.983188i | \(0.558450\pi\) | |||||||
\(674\) | 21.7163 | 0.836480 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 16.2043 | 0.623242 | ||||||||
\(677\) | 44.9991 | 1.72945 | 0.864727 | − | 0.502242i | \(-0.167491\pi\) | ||||
0.864727 | + | 0.502242i | \(0.167491\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.58785 | 0.0609359 | ||||||||
\(680\) | 1.70466 | 0.0653707 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −31.8105 | −1.21809 | ||||||||
\(683\) | 15.2628 | 0.584016 | 0.292008 | − | 0.956416i | \(-0.405677\pi\) | ||||
0.292008 | + | 0.956416i | \(0.405677\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.17525 | 0.121320 | ||||||||
\(686\) | −15.4150 | −0.588546 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.769998 | 0.0293559 | ||||||||
\(689\) | 0.542167 | 0.0206549 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 35.3108 | 1.34329 | 0.671644 | − | 0.740874i | \(-0.265589\pi\) | ||||
0.671644 | + | 0.740874i | \(0.265589\pi\) | |||||||
\(692\) | −12.9633 | −0.492790 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 26.3041 | 0.998489 | ||||||||
\(695\) | 3.51080 | 0.133172 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.11794 | 0.0423452 | ||||||||
\(698\) | 6.01967 | 0.227848 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 16.9494 | 0.640628 | ||||||||
\(701\) | −20.2694 | −0.765565 | −0.382782 | − | 0.923839i | \(-0.625034\pi\) | ||||
−0.382782 | + | 0.923839i | \(0.625034\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.0271545 | 0.00102415 | ||||||||
\(704\) | −23.0587 | −0.869058 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −13.9742 | −0.525926 | ||||||||
\(707\) | −33.4704 | −1.25879 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14.0026 | −0.525879 | −0.262939 | − | 0.964812i | \(-0.584692\pi\) | ||||
−0.262939 | + | 0.964812i | \(0.584692\pi\) | |||||||
\(710\) | 3.35053 | 0.125743 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 15.4059 | 0.577362 | ||||||||
\(713\) | −7.35747 | −0.275539 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.733253 | 0.0274221 | ||||||||
\(716\) | −6.60087 | −0.246686 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −20.7123 | −0.772975 | ||||||||
\(719\) | −29.9013 | −1.11513 | −0.557566 | − | 0.830133i | \(-0.688265\pi\) | ||||
−0.557566 | + | 0.830133i | \(0.688265\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 36.9721 | 1.37691 | ||||||||
\(722\) | −16.1915 | −0.602585 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −14.4237 | −0.536053 | ||||||||
\(725\) | 4.92262 | 0.182822 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.5958 | 0.652593 | 0.326297 | − | 0.945267i | \(-0.394199\pi\) | ||||
0.326297 | + | 0.945267i | \(0.394199\pi\) | |||||||
\(728\) | 3.92425 | 0.145442 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.113755 | −0.00421026 | ||||||||
\(731\) | −10.1681 | −0.376080 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −26.8913 | −0.993254 | −0.496627 | − | 0.867964i | \(-0.665428\pi\) | ||||
−0.496627 | + | 0.867964i | \(0.665428\pi\) | |||||||
\(734\) | 17.9003 | 0.660714 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.72330 | −0.210964 | ||||||||
\(737\) | 16.7930 | 0.618577 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −25.8478 | −0.950828 | −0.475414 | − | 0.879762i | \(-0.657702\pi\) | ||||
−0.475414 | + | 0.879762i | \(0.657702\pi\) | |||||||
\(740\) | 0.0919660 | 0.00338074 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.40535 | −0.0883032 | ||||||||
\(743\) | −40.1155 | −1.47170 | −0.735848 | − | 0.677147i | \(-0.763216\pi\) | ||||
−0.735848 | + | 0.677147i | \(0.763216\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.97315 | −0.108928 | ||||||||
\(746\) | 7.56039 | 0.276805 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −14.1734 | −0.518232 | ||||||||
\(749\) | 13.4997 | 0.493270 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17.9390 | 0.654603 | 0.327302 | − | 0.944920i | \(-0.393861\pi\) | ||||
0.327302 | + | 0.944920i | \(0.393861\pi\) | |||||||
\(752\) | 2.06331 | 0.0752413 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.443271 | 0.0161430 | ||||||||
\(755\) | −2.21433 | −0.0805878 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −39.6003 | −1.43930 | −0.719648 | − | 0.694339i | \(-0.755697\pi\) | ||||
−0.719648 | + | 0.694339i | \(0.755697\pi\) | |||||||
\(758\) | −15.3580 | −0.557829 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.0811644 | 0.00294414 | ||||||||
\(761\) | −4.42374 | −0.160361 | −0.0801803 | − | 0.996780i | \(-0.525550\pi\) | ||||
−0.0801803 | + | 0.996780i | \(0.525550\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 22.0425 | 0.797992 | ||||||||
\(764\) | −19.1388 | −0.692416 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −19.7895 | −0.715025 | ||||||||
\(767\) | 0.168426 | 0.00608153 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22.4905 | −0.811029 | −0.405514 | − | 0.914089i | \(-0.632908\pi\) | ||||
−0.405514 | + | 0.914089i | \(0.632908\pi\) | |||||||
\(770\) | −3.25311 | −0.117234 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −14.5982 | −0.525400 | ||||||||
\(773\) | 24.2864 | 0.873521 | 0.436760 | − | 0.899578i | \(-0.356126\pi\) | ||||
0.436760 | + | 0.899578i | \(0.356126\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −36.2180 | −1.30099 | ||||||||
\(776\) | −1.63826 | −0.0588100 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 10.8692 | 0.389678 | ||||||||
\(779\) | 0.0532290 | 0.00190713 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −71.6273 | −2.56303 | ||||||||
\(782\) | 1.87236 | 0.0669554 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.0526107 | 0.00187895 | ||||||||
\(785\) | 1.83346 | 0.0654388 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −33.4845 | −1.19359 | −0.596797 | − | 0.802393i | \(-0.703560\pi\) | ||||
−0.596797 | + | 0.802393i | \(0.703560\pi\) | |||||||
\(788\) | −31.8679 | −1.13525 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2.22539 | 0.0791757 | ||||||||
\(791\) | −40.3264 | −1.43384 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.48732 | −0.159349 | ||||||||
\(794\) | 0.228153 | 0.00809684 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7.32303 | 0.259558 | ||||||||
\(797\) | −31.4213 | −1.11300 | −0.556500 | − | 0.830847i | \(-0.687856\pi\) | ||||
−0.556500 | + | 0.830847i | \(0.687856\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −27.2467 | −0.963919 | ||||||||
\(800\) | −28.1737 | −0.996089 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 21.3984 | 0.755603 | ||||||||
\(803\) | 2.43185 | 0.0858180 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.752416 | −0.0265192 | ||||||||
\(806\) | −3.26135 | −0.114876 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 34.5331 | 1.21487 | ||||||||
\(809\) | −33.6559 | −1.18328 | −0.591639 | − | 0.806203i | \(-0.701519\pi\) | ||||
−0.591639 | + | 0.806203i | \(0.701519\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.12467 | −0.0746072 | −0.0373036 | − | 0.999304i | \(-0.511877\pi\) | ||||
−0.0373036 | + | 0.999304i | \(0.511877\pi\) | |||||||
\(812\) | 3.44317 | 0.120832 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.12292 | 0.0393584 | ||||||||
\(815\) | 5.92159 | 0.207424 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.484135 | −0.0169377 | ||||||||
\(818\) | −21.0639 | −0.736481 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.180274 | 0.00629545 | ||||||||
\(821\) | 33.4063 | 1.16589 | 0.582944 | − | 0.812512i | \(-0.301901\pi\) | ||||
0.582944 | + | 0.812512i | \(0.301901\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21.5526 | 0.751276 | 0.375638 | − | 0.926766i | \(-0.377424\pi\) | ||||
0.375638 | + | 0.926766i | \(0.377424\pi\) | |||||||
\(824\) | −38.1459 | −1.32888 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.747232 | −0.0259995 | ||||||||
\(827\) | −37.6143 | −1.30798 | −0.653988 | − | 0.756505i | \(-0.726905\pi\) | ||||
−0.653988 | + | 0.756505i | \(0.726905\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 27.0749 | 0.940349 | 0.470174 | − | 0.882574i | \(-0.344191\pi\) | ||||
0.470174 | + | 0.882574i | \(0.344191\pi\) | |||||||
\(830\) | 1.58341 | 0.0549609 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.36408 | −0.0819598 | ||||||||
\(833\) | −0.694740 | −0.0240713 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.18174 | −0.179322 | ||||||||
\(836\) | −0.674843 | −0.0233399 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 12.0219 | 0.415291 | ||||||||
\(839\) | −36.0003 | −1.24287 | −0.621434 | − | 0.783467i | \(-0.713449\pi\) | ||||
−0.621434 | + | 0.783467i | \(0.713449\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 16.1268 | 0.555765 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −4.48733 | −0.154460 | ||||||||
\(845\) | −3.54103 | −0.121815 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 39.7912 | 1.36724 | ||||||||
\(848\) | −0.173422 | −0.00595534 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 9.21692 | 0.316138 | ||||||||
\(851\) | 0.259721 | 0.00890313 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.31131 | −0.284574 | −0.142287 | − | 0.989825i | \(-0.545446\pi\) | ||||
−0.142287 | + | 0.989825i | \(0.545446\pi\) | |||||||
\(854\) | 19.9082 | 0.681245 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −13.9283 | −0.476061 | ||||||||
\(857\) | −13.7510 | −0.469726 | −0.234863 | − | 0.972029i | \(-0.575464\pi\) | ||||
−0.234863 | + | 0.972029i | \(0.575464\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −28.3847 | −0.968474 | −0.484237 | − | 0.874937i | \(-0.660903\pi\) | ||||
−0.484237 | + | 0.874937i | \(0.660903\pi\) | |||||||
\(860\) | −1.63965 | −0.0559117 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 5.99606 | 0.204226 | ||||||||
\(863\) | −13.2385 | −0.450643 | −0.225322 | − | 0.974284i | \(-0.572343\pi\) | ||||
−0.225322 | + | 0.974284i | \(0.572343\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.83279 | 0.0963177 | ||||||||
\(866\) | −17.4448 | −0.592798 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −25.3330 | −0.859859 | ||||||||
\(869\) | −47.5742 | −1.61384 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.72169 | 0.0583373 | ||||||||
\(872\) | −22.7423 | −0.770152 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.0891492 | 0.00301552 | ||||||||
\(875\) | −7.46593 | −0.252395 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 51.8672 | 1.75143 | 0.875715 | − | 0.482829i | \(-0.160391\pi\) | ||||
0.875715 | + | 0.482829i | \(0.160391\pi\) | |||||||
\(878\) | −24.4321 | −0.824543 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.234545 | −0.00790649 | ||||||||
\(881\) | −53.8584 | −1.81454 | −0.907268 | − | 0.420553i | \(-0.861836\pi\) | ||||
−0.907268 | + | 0.420553i | \(0.861836\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.91168 | 0.266249 | 0.133125 | − | 0.991099i | \(-0.457499\pi\) | ||||
0.133125 | + | 0.991099i | \(0.457499\pi\) | |||||||
\(884\) | −1.45312 | −0.0488738 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 31.9189 | 1.07234 | ||||||||
\(887\) | −23.3214 | −0.783054 | −0.391527 | − | 0.920167i | \(-0.628053\pi\) | ||||
−0.391527 | + | 0.920167i | \(0.628053\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −25.4620 | −0.853967 | ||||||||
\(890\) | −1.30936 | −0.0438898 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 28.6063 | 0.957811 | ||||||||
\(893\) | −1.29730 | −0.0434126 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.44245 | 0.0482158 | ||||||||
\(896\) | −20.4733 | −0.683967 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −3.55174 | −0.118523 | ||||||||
\(899\) | −7.35747 | −0.245385 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.29009 | 0.0762941 | ||||||||
\(902\) | 2.20118 | 0.0732913 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 41.6067 | 1.38382 | ||||||||
\(905\) | 3.15193 | 0.104774 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −23.9008 | −0.793612 | −0.396806 | − | 0.917902i | \(-0.629881\pi\) | ||||
−0.396806 | + | 0.917902i | \(0.629881\pi\) | |||||||
\(908\) | −17.2039 | −0.570931 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.333524 | −0.0110562 | ||||||||
\(911\) | 29.0376 | 0.962058 | 0.481029 | − | 0.876705i | \(-0.340263\pi\) | ||||
0.481029 | + | 0.876705i | \(0.340263\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −33.8500 | −1.12027 | ||||||||
\(914\) | 13.3502 | 0.441587 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7.77846 | 0.257008 | ||||||||
\(917\) | −7.20411 | −0.237901 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 43.7999 | 1.44483 | 0.722413 | − | 0.691462i | \(-0.243033\pi\) | ||||
0.722413 | + | 0.691462i | \(0.243033\pi\) | |||||||
\(920\) | 0.776303 | 0.0255940 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 19.3028 | 0.635703 | ||||||||
\(923\) | −7.34356 | −0.241716 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.27851 | 0.0420372 | ||||||||
\(926\) | −3.45150 | −0.113423 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −5.72330 | −0.187877 | ||||||||
\(929\) | 26.4998 | 0.869431 | 0.434715 | − | 0.900568i | \(-0.356849\pi\) | ||||
0.434715 | + | 0.900568i | \(0.356849\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.0330789 | −0.00108412 | ||||||||
\(932\) | −22.1319 | −0.724954 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2.13995 | 0.0700213 | ||||||||
\(935\) | 3.09723 | 0.101290 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −20.4056 | −0.666621 | −0.333310 | − | 0.942817i | \(-0.608166\pi\) | ||||
−0.333310 | + | 0.942817i | \(0.608166\pi\) | |||||||
\(938\) | −7.63837 | −0.249402 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −4.39367 | −0.143306 | ||||||||
\(941\) | 50.4396 | 1.64428 | 0.822142 | − | 0.569282i | \(-0.192779\pi\) | ||||
0.822142 | + | 0.569282i | \(0.192779\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.509113 | 0.0165790 | ||||||||
\(944\) | −0.0538743 | −0.00175346 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −20.0205 | −0.650921 | ||||||||
\(947\) | −33.4712 | −1.08767 | −0.543833 | − | 0.839193i | \(-0.683028\pi\) | ||||
−0.543833 | + | 0.839193i | \(0.683028\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.249324 | 0.00809340 | ||||||||
\(950\) | 0.438848 | 0.0142381 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 16.5759 | 0.537227 | ||||||||
\(953\) | 17.1268 | 0.554790 | 0.277395 | − | 0.960756i | \(-0.410529\pi\) | ||||
0.277395 | + | 0.960756i | \(0.410529\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.18228 | 0.135335 | ||||||||
\(956\) | 2.10961 | 0.0682297 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −13.0474 | −0.421542 | ||||||||
\(959\) | 30.8757 | 0.997029 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23.1323 | 0.746204 | ||||||||
\(962\) | 0.115127 | 0.00371184 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −25.2230 | −0.812378 | ||||||||
\(965\) | 3.19006 | 0.102692 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 50.4031 | 1.62085 | 0.810427 | − | 0.585839i | \(-0.199235\pi\) | ||||
0.810427 | + | 0.585839i | \(0.199235\pi\) | |||||||
\(968\) | −41.0545 | −1.31954 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.139236 | 0.00447061 | ||||||||
\(971\) | −24.2480 | −0.778156 | −0.389078 | − | 0.921205i | \(-0.627206\pi\) | ||||
−0.389078 | + | 0.921205i | \(0.627206\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 34.1386 | 1.09443 | ||||||||
\(974\) | −10.6270 | −0.340512 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.43535 | 0.0459445 | ||||||||
\(977\) | 17.1751 | 0.549480 | 0.274740 | − | 0.961519i | \(-0.411408\pi\) | ||||
0.274740 | + | 0.961519i | \(0.411408\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 27.9914 | 0.894608 | ||||||||
\(980\) | −0.112030 | −0.00357868 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −5.90937 | −0.188576 | ||||||||
\(983\) | 34.0769 | 1.08689 | 0.543443 | − | 0.839446i | \(-0.317121\pi\) | ||||
0.543443 | + | 0.839446i | \(0.317121\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.96390 | 0.221888 | ||||||||
\(986\) | 1.87236 | 0.0596281 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.0691880 | −0.00220116 | ||||||||
\(989\) | −4.63055 | −0.147243 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −52.6162 | −1.67141 | −0.835705 | − | 0.549179i | \(-0.814940\pi\) | ||||
−0.835705 | + | 0.549179i | \(0.814940\pi\) | |||||||
\(992\) | 42.1090 | 1.33696 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 32.5801 | 1.03338 | ||||||||
\(995\) | −1.60026 | −0.0507316 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −15.7721 | −0.499506 | −0.249753 | − | 0.968310i | \(-0.580349\pi\) | ||||
−0.249753 | + | 0.968310i | \(0.580349\pi\) | |||||||
\(998\) | 23.4948 | 0.743715 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6003.2.a.s.1.13 | 20 | ||
3.2 | odd | 2 | 2001.2.a.o.1.8 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2001.2.a.o.1.8 | ✓ | 20 | 3.2 | odd | 2 | ||
6003.2.a.s.1.13 | 20 | 1.1 | even | 1 | trivial |