Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2672,2,Mod(1,2672)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2672, 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("2672.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2672 = 2^{4} \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2672.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: | \(21.3360274201\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.826865.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 5x^{3} + 6x^{2} + 6x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 668) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.873948\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2672.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.36227 | −0.786504 | −0.393252 | − | 0.919431i | \(-0.628650\pi\) | ||||
−0.393252 | + | 0.919431i | \(0.628650\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.00000 | 0.894427 | 0.447214 | − | 0.894427i | \(-0.352416\pi\) | ||||
0.447214 | + | 0.894427i | \(0.352416\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.42676 | 0.539266 | 0.269633 | − | 0.962963i | \(-0.413098\pi\) | ||||
0.269633 | + | 0.962963i | \(0.413098\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.14423 | −0.381411 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.19055 | −0.660476 | −0.330238 | − | 0.943898i | \(-0.607129\pi\) | ||||
−0.330238 | + | 0.943898i | \(0.607129\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.74790 | 0.484779 | 0.242390 | − | 0.970179i | \(-0.422069\pi\) | ||||
0.242390 | + | 0.970179i | \(0.422069\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.72453 | −0.703471 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.26510 | 0.791903 | 0.395951 | − | 0.918271i | \(-0.370415\pi\) | ||||
0.395951 | + | 0.918271i | \(0.370415\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.89213 | −1.35175 | −0.675874 | − | 0.737018i | \(-0.736233\pi\) | ||||
−0.675874 | + | 0.737018i | \(0.736233\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.94363 | −0.424135 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.12900 | −1.27798 | −0.638992 | − | 0.769213i | \(-0.720648\pi\) | ||||
−0.638992 | + | 0.769213i | \(0.720648\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.64555 | 1.08649 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.321133 | −0.0596329 | −0.0298164 | − | 0.999555i | \(-0.509492\pi\) | ||||
−0.0298164 | + | 0.999555i | \(0.509492\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.75308 | −0.314863 | −0.157431 | − | 0.987530i | \(-0.550321\pi\) | ||||
−0.157431 | + | 0.987530i | \(0.550321\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.98411 | 0.519467 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.85353 | 0.482334 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.47243 | −0.406465 | −0.203232 | − | 0.979131i | \(-0.565145\pi\) | ||||
−0.203232 | + | 0.979131i | \(0.565145\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.38110 | −0.381281 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.98963 | −0.935423 | −0.467712 | − | 0.883881i | \(-0.654921\pi\) | ||||
−0.467712 | + | 0.883881i | \(0.654921\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.49579 | 0.533104 | 0.266552 | − | 0.963821i | \(-0.414116\pi\) | ||||
0.266552 | + | 0.963821i | \(0.414116\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.28846 | −0.341144 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.39634 | −0.349541 | −0.174771 | − | 0.984609i | \(-0.555918\pi\) | ||||
−0.174771 | + | 0.984609i | \(0.555918\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.96434 | −0.709192 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.44793 | −0.622835 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.51720 | −0.208404 | −0.104202 | − | 0.994556i | \(-0.533229\pi\) | ||||
−0.104202 | + | 0.994556i | \(0.533229\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.38110 | −0.590747 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.02665 | 1.06316 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.65526 | −0.736252 | −0.368126 | − | 0.929776i | \(-0.620001\pi\) | ||||
−0.368126 | + | 0.929776i | \(0.620001\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.51463 | −0.578039 | −0.289019 | − | 0.957323i | \(-0.593329\pi\) | ||||
−0.289019 | + | 0.957323i | \(0.593329\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.63255 | −0.205682 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.49579 | 0.433600 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.61442 | 1.17459 | 0.587294 | − | 0.809374i | \(-0.300193\pi\) | ||||
0.587294 | + | 0.809374i | \(0.300193\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.34932 | 1.00514 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.66956 | 0.791532 | 0.395766 | − | 0.918351i | \(-0.370479\pi\) | ||||
0.395766 | + | 0.918351i | \(0.370479\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.86390 | 0.335194 | 0.167597 | − | 0.985856i | \(-0.446399\pi\) | ||||
0.167597 | + | 0.985856i | \(0.446399\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.36227 | 0.157301 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.12540 | −0.356172 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.4997 | −1.18131 | −0.590656 | − | 0.806924i | \(-0.701131\pi\) | ||||
−0.590656 | + | 0.806924i | \(0.701131\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.25804 | −0.473115 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.24369 | 0.795098 | 0.397549 | − | 0.917581i | \(-0.369861\pi\) | ||||
0.397549 | + | 0.917581i | \(0.369861\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.53020 | 0.708299 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.437468 | 0.0469015 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.256634 | −0.0272032 | −0.0136016 | − | 0.999907i | \(-0.504330\pi\) | ||||
−0.0136016 | + | 0.999907i | \(0.504330\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.49384 | 0.261425 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.38816 | 0.247641 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −11.7843 | −1.20904 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.83544 | 0.592499 | 0.296250 | − | 0.955111i | \(-0.404264\pi\) | ||||
0.296250 | + | 0.955111i | \(0.404264\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.50650 | 0.251913 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.58843 | −0.556069 | −0.278035 | − | 0.960571i | \(-0.589683\pi\) | ||||
−0.278035 | + | 0.960571i | \(0.589683\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.17359 | −0.608302 | −0.304151 | − | 0.952624i | \(-0.598373\pi\) | ||||
−0.304151 | + | 0.952624i | \(0.598373\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.88726 | −0.379358 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.9570 | 1.15592 | 0.577962 | − | 0.816064i | \(-0.303848\pi\) | ||||
0.577962 | + | 0.816064i | \(0.303848\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.1784 | −1.45382 | −0.726911 | − | 0.686731i | \(-0.759045\pi\) | ||||
−0.726911 | + | 0.686731i | \(0.759045\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.36810 | 0.319686 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.710405 | −0.0668293 | −0.0334146 | − | 0.999442i | \(-0.510638\pi\) | ||||
−0.0334146 | + | 0.999442i | \(0.510638\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −12.2580 | −1.14306 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.00000 | −0.184900 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.65853 | 0.427046 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.20149 | −0.563772 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.15947 | 0.735714 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.0000 | −1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.5165 | −1.02192 | −0.510962 | − | 0.859603i | \(-0.670711\pi\) | ||||
−0.510962 | + | 0.859603i | \(0.670711\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.76220 | −0.419288 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.02599 | −0.701234 | −0.350617 | − | 0.936519i | \(-0.614028\pi\) | ||||
−0.350617 | + | 0.936519i | \(0.614028\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.40668 | −0.728951 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 11.2911 | 0.971782 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −15.6656 | −1.33840 | −0.669201 | − | 0.743081i | \(-0.733364\pi\) | ||||
−0.669201 | + | 0.743081i | \(0.733364\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.22163 | 0.188436 | 0.0942182 | − | 0.995552i | \(-0.469965\pi\) | ||||
0.0942182 | + | 0.995552i | \(0.469965\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.26445 | 0.274916 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.82886 | −0.320185 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.642266 | −0.0533373 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.76276 | 0.557783 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.02599 | 0.493668 | 0.246834 | − | 0.969058i | \(-0.420610\pi\) | ||||
0.246834 | + | 0.969058i | \(0.420610\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.9684 | 0.892596 | 0.446298 | − | 0.894884i | \(-0.352742\pi\) | ||||
0.446298 | + | 0.894884i | \(0.352742\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.73603 | −0.302040 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.50616 | −0.281622 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.0474 | 1.59996 | 0.799980 | − | 0.600027i | \(-0.204843\pi\) | ||||
0.799980 | + | 0.600027i | \(0.204843\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.06683 | 0.163910 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.74463 | −0.689174 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.21770 | −0.408682 | −0.204341 | − | 0.978900i | \(-0.565505\pi\) | ||||
−0.204341 | + | 0.978900i | \(0.565505\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.96822 | 0.464625 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.00000 | 0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.94486 | −0.764989 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.74196 | 0.515571 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −21.5165 | −1.63587 | −0.817935 | − | 0.575311i | \(-0.804881\pi\) | ||||
−0.817935 | + | 0.575311i | \(0.804881\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.42676 | −0.107853 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.70397 | 0.579066 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.1501 | −0.758656 | −0.379328 | − | 0.925262i | \(-0.623845\pi\) | ||||
−0.379328 | + | 0.925262i | \(0.623845\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.64003 | −0.270561 | −0.135281 | − | 0.990807i | \(-0.543194\pi\) | ||||
−0.135281 | + | 0.990807i | \(0.543194\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.15012 | 0.454630 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.94486 | −0.363553 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.15236 | −0.523033 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 8.05486 | 0.585905 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 17.4861 | 1.26525 | 0.632626 | − | 0.774457i | \(-0.281977\pi\) | ||||
0.632626 | + | 0.774457i | \(0.281977\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.75052 | 0.341950 | 0.170975 | − | 0.985275i | \(-0.445308\pi\) | ||||
0.170975 | + | 0.985275i | \(0.445308\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.76220 | −0.341028 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.67780 | −0.190785 | −0.0953927 | − | 0.995440i | \(-0.530411\pi\) | ||||
−0.0953927 | + | 0.995440i | \(0.530411\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −25.6656 | −1.81939 | −0.909693 | − | 0.415281i | \(-0.863683\pi\) | ||||
−0.909693 | + | 0.415281i | \(0.863683\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −13.0974 | −0.923819 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.458181 | −0.0321580 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.9793 | −0.836668 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.01300 | 0.487437 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 12.9070 | 0.892796 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.73234 | −0.670002 | −0.335001 | − | 0.942218i | \(-0.608737\pi\) | ||||
−0.335001 | + | 0.942218i | \(0.608737\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −9.08572 | −0.622543 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.99159 | 0.476822 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.50123 | −0.169795 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.90139 | −0.263631 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.70706 | 0.383898 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −21.5995 | −1.44641 | −0.723205 | − | 0.690633i | \(-0.757332\pi\) | ||||
−0.723205 | + | 0.690633i | \(0.757332\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.14423 | 0.0762822 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 14.0401 | 0.931875 | 0.465938 | − | 0.884818i | \(-0.345717\pi\) | ||||
0.465938 | + | 0.884818i | \(0.345717\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.77020 | 0.381305 | 0.190653 | − | 0.981658i | \(-0.438940\pi\) | ||||
0.190653 | + | 0.981658i | \(0.438940\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.25762 | 0.280131 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −19.4705 | −1.27556 | −0.637778 | − | 0.770221i | \(-0.720146\pi\) | ||||
−0.637778 | + | 0.770221i | \(0.720146\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.79267 | −0.312639 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 14.3034 | 0.929107 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.7014 | 0.950954 | 0.475477 | − | 0.879728i | \(-0.342275\pi\) | ||||
0.475477 | + | 0.879728i | \(0.342275\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.6813 | −1.39661 | −0.698306 | − | 0.715799i | \(-0.746063\pi\) | ||||
−0.698306 | + | 0.715799i | \(0.746063\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −11.1361 | −0.714379 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −9.92869 | −0.634321 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10.2988 | −0.655299 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −9.86783 | −0.625348 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.71130 | 0.423613 | 0.211807 | − | 0.977312i | \(-0.432065\pi\) | ||||
0.211807 | + | 0.977312i | \(0.432065\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 13.4259 | 0.844077 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −8.89586 | −0.557081 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −26.1000 | −1.62807 | −0.814037 | − | 0.580813i | \(-0.802735\pi\) | ||||
−0.814037 | + | 0.580813i | \(0.802735\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.52757 | −0.219193 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.367451 | 0.0227446 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −16.1595 | −0.996439 | −0.498219 | − | 0.867051i | \(-0.666013\pi\) | ||||
−0.498219 | + | 0.867051i | \(0.666013\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.03440 | −0.186402 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.349604 | 0.0213954 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.9418 | 0.667131 | 0.333566 | − | 0.942727i | \(-0.391748\pi\) | ||||
0.333566 | + | 0.942727i | \(0.391748\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.49579 | −0.576828 | −0.288414 | − | 0.957506i | \(-0.593128\pi\) | ||||
−0.288414 | + | 0.957506i | \(0.593128\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.39727 | −0.205612 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.19055 | 0.132095 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.86063 | 0.111795 | 0.0558973 | − | 0.998437i | \(-0.482198\pi\) | ||||
0.0558973 | + | 0.998437i | \(0.482198\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.00593 | 0.120092 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.01042 | 0.239242 | 0.119621 | − | 0.992820i | \(-0.461832\pi\) | ||||
0.119621 | + | 0.992820i | \(0.461832\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.71234 | 0.458451 | 0.229225 | − | 0.973373i | \(-0.426381\pi\) | ||||
0.229225 | + | 0.973373i | \(0.426381\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 16.0533 | 0.950915 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.54579 | −0.504442 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.33913 | −0.372890 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.94942 | −0.466003 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.05585 | 0.529048 | 0.264524 | − | 0.964379i | \(-0.414785\pi\) | ||||
0.264524 | + | 0.964379i | \(0.414785\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.3105 | −0.658524 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −12.3668 | −0.717597 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10.7129 | −0.619540 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.98767 | 0.287485 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.61293 | 0.437351 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9.02926 | −0.517014 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.1632 | −0.694192 | −0.347096 | − | 0.937830i | \(-0.612832\pi\) | ||||
−0.347096 | + | 0.937830i | \(0.612832\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.41008 | 0.478432 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −24.4952 | −1.38900 | −0.694499 | − | 0.719494i | \(-0.744374\pi\) | ||||
−0.694499 | + | 0.719494i | \(0.744374\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22.5593 | 1.27513 | 0.637563 | − | 0.770398i | \(-0.279943\pi\) | ||||
0.637563 | + | 0.770398i | \(0.279943\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.26510 | −0.183967 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 13.9546 | 0.783770 | 0.391885 | − | 0.920014i | \(-0.371823\pi\) | ||||
0.391885 | + | 0.920014i | \(0.371823\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.703457 | 0.0393861 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −16.2886 | −0.909139 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −19.2384 | −1.07045 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.74790 | −0.0969559 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 20.6770 | 1.14344 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.41901 | −0.188496 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.5826 | 1.18629 | 0.593145 | − | 0.805096i | \(-0.297886\pi\) | ||||
0.593145 | + | 0.805096i | \(0.297886\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.82903 | 0.155030 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 19.2288 | 1.05058 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.7494 | 0.912399 | 0.456199 | − | 0.889878i | \(-0.349210\pi\) | ||||
0.456199 | + | 0.889878i | \(0.349210\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.967760 | 0.0525615 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.84021 | 0.207959 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.0703 | −0.921709 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 16.6986 | 0.899025 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.7273 | 0.683239 | 0.341620 | − | 0.939838i | \(-0.389025\pi\) | ||||
0.341620 | + | 0.939838i | \(0.389025\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.8665 | 1.17049 | 0.585244 | − | 0.810857i | \(-0.300999\pi\) | ||||
0.585244 | + | 0.810857i | \(0.300999\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.86783 | 0.526706 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 27.7352 | 1.47620 | 0.738099 | − | 0.674692i | \(-0.235724\pi\) | ||||
0.738099 | + | 0.674692i | \(0.235724\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 13.3391 | 0.707967 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.34615 | −0.335874 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.30402 | 0.438269 | 0.219135 | − | 0.975695i | \(-0.429677\pi\) | ||||
0.219135 | + | 0.975695i | \(0.429677\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.7172 | 0.827220 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.44808 | 0.443409 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.72780 | 0.299807 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.4528 | −0.650031 | −0.325015 | − | 0.945709i | \(-0.605369\pi\) | ||||
−0.325015 | + | 0.945709i | \(0.605369\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.85353 | 0.356780 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.16469 | −0.112385 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.6189 | 0.912272 | 0.456136 | − | 0.889910i | \(-0.349233\pi\) | ||||
0.456136 | + | 0.889910i | \(0.349233\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 16.3472 | 0.844165 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.561307 | −0.0289088 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.1749 | −0.625383 | −0.312691 | − | 0.949855i | \(-0.601231\pi\) | ||||
−0.312691 | + | 0.949855i | \(0.601231\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 15.6885 | 0.803748 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −16.9672 | −0.866981 | −0.433491 | − | 0.901158i | \(-0.642718\pi\) | ||||
−0.433491 | + | 0.901158i | \(0.642718\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.25080 | −0.318570 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.00000 | −0.203331 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 14.9358 | 0.757275 | 0.378637 | − | 0.925545i | \(-0.376393\pi\) | ||||
0.378637 | + | 0.925545i | \(0.376393\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −20.0118 | −1.01204 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 10.9335 | 0.551524 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −20.9995 | −1.05660 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 27.3638 | 1.37335 | 0.686674 | − | 0.726966i | \(-0.259070\pi\) | ||||
0.686674 | + | 0.726966i | \(0.259070\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 11.4521 | 0.573324 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.3411 | 0.816035 | 0.408017 | − | 0.912974i | \(-0.366220\pi\) | ||||
0.408017 | + | 0.912974i | \(0.366220\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.06421 | −0.152639 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −8.51607 | −0.423167 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.41598 | 0.268460 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −19.2236 | −0.950544 | −0.475272 | − | 0.879839i | \(-0.657650\pi\) | ||||
−0.475272 | + | 0.879839i | \(0.657650\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 21.3407 | 1.05266 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8.06872 | −0.397036 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 14.4874 | 0.711158 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.02645 | −0.148206 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.15541 | −0.0564456 | −0.0282228 | − | 0.999602i | \(-0.508985\pi\) | ||||
−0.0282228 | + | 0.999602i | \(0.508985\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.80899 | 0.234376 | 0.117188 | − | 0.993110i | \(-0.462612\pi\) | ||||
0.117188 | + | 0.993110i | \(0.462612\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.74196 | 0.133319 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.26510 | −0.158381 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.44131 | −0.311717 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.21592 | 0.251827 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 34.3708 | 1.65558 | 0.827791 | − | 0.561036i | \(-0.189597\pi\) | ||||
0.827791 | + | 0.561036i | \(0.189597\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −20.0626 | −0.964145 | −0.482072 | − | 0.876131i | \(-0.660116\pi\) | ||||
−0.482072 | + | 0.876131i | \(0.660116\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.874936 | 0.0419500 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 36.1128 | 1.72751 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.90270 | −0.0908108 | −0.0454054 | − | 0.998969i | \(-0.514458\pi\) | ||||
−0.0454054 | + | 0.998969i | \(0.514458\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.68036 | 0.270493 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13.8782 | 0.659373 | 0.329687 | − | 0.944090i | \(-0.393057\pi\) | ||||
0.329687 | + | 0.944090i | \(0.393057\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.513269 | −0.0243313 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8.20900 | −0.388272 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.6316 | 0.690509 | 0.345254 | − | 0.938509i | \(-0.387793\pi\) | ||||
0.345254 | + | 0.938509i | \(0.387793\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13.1206 | 0.617824 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −14.9419 | −0.702030 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.98767 | 0.233826 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.1270 | −0.707613 | −0.353807 | − | 0.935319i | \(-0.615113\pi\) | ||||
−0.353807 | + | 0.935319i | \(0.615113\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 18.4333 | 0.860391 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.617968 | −0.0287816 | −0.0143908 | − | 0.999896i | \(-0.504581\pi\) | ||||
−0.0143908 | + | 0.999896i | \(0.504581\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.12321 | 0.284570 | 0.142285 | − | 0.989826i | \(-0.454555\pi\) | ||||
0.142285 | + | 0.989826i | \(0.454555\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.77633 | 0.221497 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 22.0319 | 1.01952 | 0.509758 | − | 0.860318i | \(-0.329735\pi\) | ||||
0.509758 | + | 0.860318i | \(0.329735\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.7175 | 0.633416 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −27.3099 | −1.25838 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.65771 | −0.352102 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.89213 | 0.270349 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.73603 | 0.0794874 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.88989 | 0.314807 | 0.157404 | − | 0.987534i | \(-0.449688\pi\) | ||||
0.157404 | + | 0.987534i | \(0.449688\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.32155 | −0.197046 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 11.9125 | 0.542038 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 11.6709 | 0.529948 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.9486 | 0.949272 | 0.474636 | − | 0.880182i | \(-0.342580\pi\) | ||||
0.474636 | + | 0.880182i | \(0.342580\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.10789 | 0.321430 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.3184 | −0.601051 | −0.300525 | − | 0.953774i | \(-0.597162\pi\) | ||||
−0.300525 | + | 0.953774i | \(0.597162\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.04853 | −0.0472234 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.01300 | 0.225317 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.51589 | 0.426846 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.2496 | −0.682665 | −0.341333 | − | 0.939943i | \(-0.610878\pi\) | ||||
−0.341333 | + | 0.939943i | \(0.610878\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.36227 | −0.0608615 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 26.7387 | 1.19222 | 0.596110 | − | 0.802903i | \(-0.296712\pi\) | ||||
0.596110 | + | 0.802903i | \(0.296712\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.1769 | −0.497364 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 13.5475 | 0.601667 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.156638 | 0.00694286 | 0.00347143 | − | 0.999994i | \(-0.498895\pi\) | ||||
0.00347143 | + | 0.999994i | \(0.498895\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.08611 | 0.180759 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −33.2643 | −1.46865 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −12.3472 | −0.544082 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.24929 | 0.230864 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 29.3112 | 1.28662 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −32.1200 | −1.40720 | −0.703602 | − | 0.710594i | \(-0.748426\pi\) | ||||
−0.703602 | + | 0.710594i | \(0.748426\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.73691 | −0.207131 | −0.103565 | − | 0.994623i | \(-0.533025\pi\) | ||||
−0.103565 | + | 0.994623i | \(0.533025\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.94363 | 0.0848270 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.72399 | −0.249341 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 14.5646 | 0.633244 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.47093 | 0.280815 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10.4693 | −0.453474 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 23.9139 | 1.03389 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 13.8272 | 0.596686 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10.8746 | 0.468404 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.3824 | 0.661342 | 0.330671 | − | 0.943746i | \(-0.392725\pi\) | ||||
0.330671 | + | 0.943746i | \(0.392725\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.95868 | 0.212797 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −30.3567 | −1.30034 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.2682 | −0.823848 | −0.411924 | − | 0.911218i | \(-0.635143\pi\) | ||||
−0.411924 | + | 0.911218i | \(0.635143\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.16578 | 0.220470 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.89216 | 0.0806086 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −14.9806 | −0.637041 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.73621 | 0.285936 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −10.0313 | −0.425039 | −0.212519 | − | 0.977157i | \(-0.568167\pi\) | ||||
−0.212519 | + | 0.977157i | \(0.568167\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.11029 | 0.258438 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.74342 | 0.411367 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8.61733 | 0.363177 | 0.181589 | − | 0.983375i | \(-0.441876\pi\) | ||||
0.181589 | + | 0.983375i | \(0.441876\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.42081 | −0.0597739 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −6.07521 | −0.255135 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −22.8782 | −0.959105 | −0.479552 | − | 0.877513i | \(-0.659201\pi\) | ||||
−0.479552 | + | 0.877513i | \(0.659201\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 36.9981 | 1.54832 | 0.774162 | − | 0.632987i | \(-0.218171\pi\) | ||||
0.774162 | + | 0.632987i | \(0.218171\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −23.8208 | −0.995126 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.12900 | 0.255597 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.42378 | 0.392317 | 0.196158 | − | 0.980572i | \(-0.437153\pi\) | ||||
0.196158 | + | 0.980572i | \(0.437153\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6.47147 | −0.268945 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.3350 | 0.428770 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.32351 | 0.137646 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.00000 | −0.165380 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.06497 | 0.250328 | 0.125164 | − | 0.992136i | \(-0.460054\pi\) | ||||
0.125164 | + | 0.992136i | \(0.460054\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.3294 | 0.425615 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.64788 | 0.150054 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 30.0669 | 1.23470 | 0.617351 | − | 0.786688i | \(-0.288206\pi\) | ||||
0.617351 | + | 0.786688i | \(0.288206\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.31705 | 0.381962 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 34.9634 | 1.43096 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.74168 | 0.357175 | 0.178588 | − | 0.983924i | \(-0.442847\pi\) | ||||
0.178588 | + | 0.983924i | \(0.442847\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.47200 | −0.223208 | −0.111604 | − | 0.993753i | \(-0.535599\pi\) | ||||
−0.111604 | + | 0.993753i | \(0.535599\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −11.0011 | −0.448001 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −12.4030 | −0.504253 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.28118 | −0.336123 | −0.168061 | − | 0.985777i | \(-0.553751\pi\) | ||||
−0.168061 | + | 0.985777i | \(0.553751\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.624164 | 0.0252924 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.18855 | −0.169450 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 46.5063 | 1.87837 | 0.939186 | − | 0.343408i | \(-0.111581\pi\) | ||||
0.939186 | + | 0.343408i | \(0.111581\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 16.3189 | 0.658043 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 34.1883 | 1.37637 | 0.688185 | − | 0.725535i | \(-0.258408\pi\) | ||||
0.688185 | + | 0.725535i | \(0.258408\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23.3216 | 0.937373 | 0.468686 | − | 0.883365i | \(-0.344727\pi\) | ||||
0.468686 | + | 0.883365i | \(0.344727\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −34.6015 | −1.38851 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.366157 | −0.0146698 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.0000 | −0.760000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −17.5828 | −0.702188 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8.07272 | −0.321881 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.0863 | 1.15791 | 0.578953 | − | 0.815361i | \(-0.303462\pi\) | ||||
0.578953 | + | 0.815361i | \(0.303462\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 13.2580 | 0.526960 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −23.0330 | −0.914037 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.67716 | −0.343802 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7.63153 | −0.301899 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 31.0603 | 1.22681 | 0.613404 | − | 0.789769i | \(-0.289800\pi\) | ||||
0.613404 | + | 0.789769i | \(0.289800\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14.9145 | −0.588169 | −0.294085 | − | 0.955779i | \(-0.595015\pi\) | ||||
−0.294085 | + | 0.955779i | \(0.595015\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −9.52440 | −0.375023 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −28.9951 | −1.13991 | −0.569957 | − | 0.821675i | \(-0.693040\pi\) | ||||
−0.569957 | + | 0.821675i | \(0.693040\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12.3881 | 0.486277 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.40735 | 0.133544 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.42152 | 0.290426 | 0.145213 | − | 0.989400i | \(-0.453613\pi\) | ||||
0.145213 | + | 0.989400i | \(0.453613\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −16.0520 | −0.627203 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.27696 | −0.127847 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.40447 | 0.0547102 | 0.0273551 | − | 0.999626i | \(-0.491292\pi\) | ||||
0.0273551 | + | 0.999626i | \(0.491292\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.1593 | 0.511837 | 0.255919 | − | 0.966698i | \(-0.417622\pi\) | ||||
0.255919 | + | 0.966698i | \(0.417622\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −7.77453 | −0.301938 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −16.8134 | −0.651994 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.96822 | 0.0762099 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 29.4243 | 1.13761 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.88952 | 0.381781 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24.1775 | −0.931974 | −0.465987 | − | 0.884791i | \(-0.654301\pi\) | ||||
−0.465987 | + | 0.884791i | \(0.654301\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.64555 | −0.217297 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 13.6811 | 0.525806 | 0.262903 | − | 0.964822i | \(-0.415320\pi\) | ||||
0.262903 | + | 0.964822i | \(0.415320\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.32580 | 0.319515 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −19.1264 | −0.732924 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 14.3047 | 0.547355 | 0.273678 | − | 0.961822i | \(-0.411760\pi\) | ||||
0.273678 | + | 0.961822i | \(0.411760\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −31.3312 | −1.19710 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.86054 | −0.299898 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.65191 | −0.101030 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −27.8109 | −1.05798 | −0.528989 | − | 0.848629i | \(-0.677429\pi\) | ||||
−0.528989 | + | 0.848629i | \(0.677429\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.57618 | 0.135848 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.44326 | 0.168543 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −19.5567 | −0.740764 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 26.5240 | 1.00323 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10.7440 | 0.405796 | 0.202898 | − | 0.979200i | \(-0.434964\pi\) | ||||
0.202898 | + | 0.979200i | \(0.434964\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14.5679 | 0.549437 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.52889 | 0.245892 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7.97337 | −0.299869 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −39.8043 | −1.49488 | −0.747440 | − | 0.664329i | \(-0.768717\pi\) | ||||
−0.747440 | + | 0.664329i | \(0.768717\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.0141 | 0.450565 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10.7446 | 0.402390 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.65771 | −0.286382 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −20.0272 | −0.747930 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −23.3327 | −0.870162 | −0.435081 | − | 0.900391i | \(-0.643280\pi\) | ||||
−0.435081 | + | 0.900391i | \(0.643280\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.80826 | −0.328037 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 29.5356 | 1.09844 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.321133 | 0.0119266 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.2593 | 0.788464 | 0.394232 | − | 0.919011i | \(-0.371011\pi\) | ||||
0.394232 | + | 0.919011i | \(0.371011\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.9444 | 1.03498 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 11.4141 | 0.422166 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −40.8733 | −1.50969 | −0.754846 | − | 0.655902i | \(-0.772288\pi\) | ||||
−0.754846 | + | 0.655902i | \(0.772288\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 13.5255 | 0.498896 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −21.0609 | −0.775787 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −38.5912 | −1.41960 | −0.709799 | − | 0.704404i | \(-0.751214\pi\) | ||||
−0.709799 | + | 0.704404i | \(0.751214\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 14.0297 | 0.515396 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −18.3330 | −0.672572 | −0.336286 | − | 0.941760i | \(-0.609171\pi\) | ||||
−0.336286 | + | 0.941760i | \(0.609171\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.0520 | 0.441551 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.28846 | −0.303259 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 17.0598 | 0.623350 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 41.3572 | 1.50915 | 0.754573 | − | 0.656216i | \(-0.227844\pi\) | ||||
0.754573 | + | 0.656216i | \(0.227844\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −9.14257 | −0.333174 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 21.9368 | 0.798362 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14.2655 | 0.518490 | 0.259245 | − | 0.965812i | \(-0.416526\pi\) | ||||
0.259245 | + | 0.965812i | \(0.416526\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −18.2896 | −0.663871 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −41.8123 | −1.51569 | −0.757847 | − | 0.652432i | \(-0.773749\pi\) | ||||
−0.757847 | + | 0.652432i | \(0.773749\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −21.6559 | −0.783997 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −7.47206 | −0.270153 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9.88481 | −0.356920 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.27230 | 0.118002 | 0.0590010 | − | 0.998258i | \(-0.481208\pi\) | ||||
0.0590010 | + | 0.998258i | \(0.481208\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 35.5552 | 1.28049 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 23.3460 | 0.839696 | 0.419848 | − | 0.907594i | \(-0.362083\pi\) | ||||
0.419848 | + | 0.907594i | \(0.362083\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.75308 | 0.0629726 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.80549 | 0.172396 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 35.2917 | 1.26446 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14.6100 | −0.522787 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.81297 | −0.0647903 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 40.0949 | 1.43105 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −44.5309 | −1.58736 | −0.793678 | − | 0.608338i | \(-0.791837\pi\) | ||||
−0.793678 | + | 0.608338i | \(0.791837\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 22.0136 | 0.783703 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.01358 | −0.0360388 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.89110 | −0.280221 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.13366 | 0.146606 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7.60786 | 0.269484 | 0.134742 | − | 0.990881i | \(-0.456979\pi\) | ||||
0.134742 | + | 0.990881i | \(0.456979\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.82427 | −0.276803 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.293649 | 0.0103756 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.27351 | −0.221387 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −17.4893 | −0.616416 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −14.9056 | −0.524702 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.40132 | 0.260217 | 0.130108 | − | 0.991500i | \(-0.458468\pi\) | ||||
0.130108 | + | 0.991500i | \(0.458468\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.69610 | 0.200017 | 0.100009 | − | 0.994987i | \(-0.468113\pi\) | ||||
0.100009 | + | 0.994987i | \(0.468113\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.9358 | 0.453678 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10.4354 | −0.365536 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −20.5977 | −0.720621 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.85353 | −0.0997103 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −45.1962 | −1.57736 | −0.788680 | − | 0.614804i | \(-0.789235\pi\) | ||||
−0.788680 | + | 0.614804i | \(0.789235\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13.9450 | −0.486093 | −0.243047 | − | 0.970015i | \(-0.578147\pi\) | ||||
−0.243047 | + | 0.970015i | \(0.578147\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.98411 | −0.103893 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.90541 | −0.101031 | −0.0505155 | − | 0.998723i | \(-0.516086\pi\) | ||||
−0.0505155 | + | 0.998723i | \(0.516086\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 31.2634 | 1.08582 | 0.542912 | − | 0.839790i | \(-0.317322\pi\) | ||||
0.542912 | + | 0.839790i | \(0.317322\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.53468 | −0.0879270 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −16.2091 | −0.561611 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.00000 | 0.0692129 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −9.89710 | −0.342094 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 44.4886 | 1.53592 | 0.767958 | − | 0.640500i | \(-0.221273\pi\) | ||||
0.767958 | + | 0.640500i | \(0.221273\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.8969 | −0.996444 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5.46326 | −0.188165 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −19.8897 | −0.684227 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.84806 | −0.304023 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −10.5062 | −0.360574 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 15.1535 | 0.519455 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −17.2717 | −0.591371 | −0.295686 | − | 0.955285i | \(-0.595548\pi\) | ||||
−0.295686 | + | 0.955285i | \(0.595548\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 13.4839 | 0.461141 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −35.0334 | −1.19672 | −0.598359 | − | 0.801228i | \(-0.704180\pi\) | ||||
−0.598359 | + | 0.801228i | \(0.704180\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −38.9649 | −1.32947 | −0.664733 | − | 0.747081i | \(-0.731454\pi\) | ||||
−0.664733 | + | 0.747081i | \(0.731454\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 11.6416 | 0.396746 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −32.0638 | −1.09146 | −0.545732 | − | 0.837960i | \(-0.683748\pi\) | ||||
−0.545732 | + | 0.837960i | \(0.683748\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −43.0330 | −1.46317 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8.63558 | 0.293280 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 23.0002 | 0.780228 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.8050 | 0.569416 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.67710 | −0.225986 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −17.1212 | −0.578801 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 53.9033 | 1.82018 | 0.910092 | − | 0.414406i | \(-0.136011\pi\) | ||||
0.910092 | + | 0.414406i | \(0.136011\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −12.3365 | −0.416099 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 49.8614 | 1.67987 | 0.839937 | − | 0.542684i | \(-0.182592\pi\) | ||||
0.839937 | + | 0.542684i | \(0.182592\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12.9835 | −0.436930 | −0.218465 | − | 0.975845i | \(-0.570105\pi\) | ||||
−0.218465 | + | 0.975845i | \(0.570105\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 15.4079 | 0.517932 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −11.8245 | −0.397027 | −0.198513 | − | 0.980098i | \(-0.563611\pi\) | ||||
−0.198513 | + | 0.980098i | \(0.563611\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −16.4313 | −0.551089 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9.32744 | 0.312481 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 14.1195 | 0.472492 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −20.3002 | −0.678562 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 14.5938 | 0.487271 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.562972 | 0.0187762 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.95381 | −0.165036 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.79454 | −0.226108 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −7.28005 | −0.241997 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.08780 | −0.0361198 | −0.0180599 | − | 0.999837i | \(-0.505749\pi\) | ||||
−0.0180599 | + | 0.999837i | \(0.505749\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.39446 | 0.212091 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.16245 | 0.303566 | 0.151783 | − | 0.988414i | \(-0.451499\pi\) | ||||
0.151783 | + | 0.988414i | \(0.451499\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −15.8677 | −0.525143 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 12.3002 | 0.406634 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −11.4512 | −0.378152 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 23.2997 | 0.768587 | 0.384293 | − | 0.923211i | \(-0.374445\pi\) | ||||
0.384293 | + | 0.923211i | \(0.374445\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 16.5695 | 0.545985 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 11.6577 | 0.383718 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.47243 | 0.0812929 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7.06403 | 0.232013 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 48.9106 | 1.60471 | 0.802353 | − | 0.596850i | \(-0.203581\pi\) | ||||
0.802353 | + | 0.596850i | \(0.203581\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 29.2506 | 0.958648 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 33.3690 | 1.09245 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −14.3047 | −0.467815 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 29.3682 | 0.959418 | 0.479709 | − | 0.877428i | \(-0.340742\pi\) | ||||
0.479709 | + | 0.877428i | \(0.340742\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −30.7317 | −1.00289 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −33.9716 | −1.10744 | −0.553721 | − | 0.832702i | \(-0.686793\pi\) | ||||
−0.553721 | + | 0.832702i | \(0.686793\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 36.7104 | 1.19546 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 16.1097 | 0.524049 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −36.7945 | −1.19566 | −0.597830 | − | 0.801623i | \(-0.703970\pi\) | ||||
−0.597830 | + | 0.801623i | \(0.703970\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.00580 | 0.162495 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −19.0099 | −0.616439 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.19613 | −0.168319 | −0.0841596 | − | 0.996452i | \(-0.526821\pi\) | ||||
−0.0841596 | + | 0.996452i | \(0.526821\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 34.9723 | 1.13168 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.958296 | −0.0309773 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −22.3511 | −0.721755 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.9267 | −0.900861 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −13.6815 | −0.440882 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 9.50105 | 0.305849 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −49.3421 | −1.58673 | −0.793367 | − | 0.608743i | \(-0.791674\pi\) | ||||
−0.793367 | + | 0.608743i | \(0.791674\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 26.2078 | 0.841916 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 43.3773 | 1.39204 | 0.696021 | − | 0.718021i | \(-0.254952\pi\) | ||||
0.696021 | + | 0.718021i | \(0.254952\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.16975 | 0.101617 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.38110 | 0.0762562 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 55.2452 | 1.76745 | 0.883725 | − | 0.468006i | \(-0.155028\pi\) | ||||
0.883725 | + | 0.468006i | \(0.155028\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.562170 | 0.0179670 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 17.3676 | 0.554504 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 12.0299 | 0.383694 | 0.191847 | − | 0.981425i | \(-0.438552\pi\) | ||||
0.191847 | + | 0.981425i | \(0.438552\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.35560 | −0.170644 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4.65759 | 0.148253 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −21.4257 | −0.681298 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −44.9737 | −1.42864 | −0.714318 | − | 0.699822i | \(-0.753263\pi\) | ||||
−0.714318 | + | 0.699822i | \(0.753263\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −29.4013 | −0.933022 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −51.3312 | −1.62731 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 44.0823 | 1.39610 | 0.698050 | − | 0.716049i | \(-0.254051\pi\) | ||||
0.698050 | + | 0.716049i | \(0.254051\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −13.9582 | −0.441618 |
(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 | 2672.2.a.j.1.3 | 5 | ||
4.3 | odd | 2 | 668.2.a.b.1.3 | ✓ | 5 | ||
12.11 | even | 2 | 6012.2.a.d.1.1 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
668.2.a.b.1.3 | ✓ | 5 | 4.3 | odd | 2 | ||
2672.2.a.j.1.3 | 5 | 1.1 | even | 1 | trivial | ||
6012.2.a.d.1.1 | 5 | 12.11 | even | 2 |