Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5586,2,Mod(1,5586)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5586, 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("5586.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5586 = 2 \cdot 3 \cdot 7^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5586.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: | \(44.6044345691\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.29268.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 9x^{2} + 5x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 798) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.85121\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5586.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.46130 | −1.54794 | −0.773971 | − | 0.633221i | \(-0.781732\pi\) | ||||
−0.773971 | + | 0.633221i | \(0.781732\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 3.46130 | 1.09456 | ||||||||
\(11\) | 0.278197 | 0.0838795 | 0.0419397 | − | 0.999120i | \(-0.486646\pi\) | ||||
0.0419397 | + | 0.999120i | \(0.486646\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 6.92261 | 1.91999 | 0.959993 | − | 0.280025i | \(-0.0903427\pi\) | ||||
0.959993 | + | 0.280025i | \(0.0903427\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.46130 | 0.893705 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.79751 | 1.40610 | 0.703052 | − | 0.711139i | \(-0.251820\pi\) | ||||
0.703052 | + | 0.711139i | \(0.251820\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | −3.46130 | −0.773971 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.278197 | −0.0593118 | ||||||||
\(23\) | 3.09233 | 0.644796 | 0.322398 | − | 0.946604i | \(-0.395511\pi\) | ||||
0.322398 | + | 0.946604i | \(0.395511\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 6.98062 | 1.39612 | ||||||||
\(26\) | −6.92261 | −1.35763 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.55364 | −1.58837 | −0.794185 | − | 0.607676i | \(-0.792102\pi\) | ||||
−0.794185 | + | 0.607676i | \(0.792102\pi\) | |||||||
\(30\) | −3.46130 | −0.631945 | ||||||||
\(31\) | 7.34959 | 1.32003 | 0.660013 | − | 0.751254i | \(-0.270551\pi\) | ||||
0.660013 | + | 0.751254i | \(0.270551\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −0.278197 | −0.0484278 | ||||||||
\(34\) | −5.79751 | −0.994265 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −5.24112 | −0.861635 | −0.430817 | − | 0.902439i | \(-0.641775\pi\) | ||||
−0.430817 | + | 0.902439i | \(0.641775\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | −6.92261 | −1.10850 | ||||||||
\(40\) | 3.46130 | 0.547280 | ||||||||
\(41\) | 8.88553 | 1.38769 | 0.693843 | − | 0.720126i | \(-0.255916\pi\) | ||||
0.693843 | + | 0.720126i | \(0.255916\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.3705 | 1.58149 | 0.790745 | − | 0.612145i | \(-0.209693\pi\) | ||||
0.790745 | + | 0.612145i | \(0.209693\pi\) | |||||||
\(44\) | 0.278197 | 0.0419397 | ||||||||
\(45\) | −3.46130 | −0.515981 | ||||||||
\(46\) | −3.09233 | −0.455939 | ||||||||
\(47\) | −1.79320 | −0.261565 | −0.130782 | − | 0.991411i | \(-0.541749\pi\) | ||||
−0.130782 | + | 0.991411i | \(0.541749\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −6.98062 | −0.987209 | ||||||||
\(51\) | −5.79751 | −0.811814 | ||||||||
\(52\) | 6.92261 | 0.959993 | ||||||||
\(53\) | 8.38823 | 1.15221 | 0.576106 | − | 0.817375i | \(-0.304572\pi\) | ||||
0.576106 | + | 0.817375i | \(0.304572\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −0.962923 | −0.129841 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.00000 | −0.132453 | ||||||||
\(58\) | 8.55364 | 1.12315 | ||||||||
\(59\) | −7.79476 | −1.01479 | −0.507395 | − | 0.861713i | \(-0.669392\pi\) | ||||
−0.507395 | + | 0.861713i | \(0.669392\pi\) | |||||||
\(60\) | 3.46130 | 0.446852 | ||||||||
\(61\) | 9.12941 | 1.16890 | 0.584450 | − | 0.811429i | \(-0.301310\pi\) | ||||
0.584450 | + | 0.811429i | \(0.301310\pi\) | |||||||
\(62\) | −7.34959 | −0.933399 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −23.9612 | −2.97203 | ||||||||
\(66\) | 0.278197 | 0.0342437 | ||||||||
\(67\) | −13.7378 | −1.67834 | −0.839171 | − | 0.543868i | \(-0.816959\pi\) | ||||
−0.839171 | + | 0.543868i | \(0.816959\pi\) | |||||||
\(68\) | 5.79751 | 0.703052 | ||||||||
\(69\) | −3.09233 | −0.372273 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.684727 | 0.0812621 | 0.0406311 | − | 0.999174i | \(-0.487063\pi\) | ||||
0.0406311 | + | 0.999174i | \(0.487063\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −1.92536 | −0.225347 | −0.112673 | − | 0.993632i | \(-0.535941\pi\) | ||||
−0.112673 | + | 0.993632i | \(0.535941\pi\) | |||||||
\(74\) | 5.24112 | 0.609268 | ||||||||
\(75\) | −6.98062 | −0.806053 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 6.92261 | 0.783831 | ||||||||
\(79\) | 1.40761 | 0.158368 | 0.0791840 | − | 0.996860i | \(-0.474769\pi\) | ||||
0.0791840 | + | 0.996860i | \(0.474769\pi\) | |||||||
\(80\) | −3.46130 | −0.386985 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −8.88553 | −0.981243 | ||||||||
\(83\) | −0.146030 | −0.0160289 | −0.00801443 | − | 0.999968i | \(-0.502551\pi\) | ||||
−0.00801443 | + | 0.999968i | \(0.502551\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −20.0670 | −2.17657 | ||||||||
\(86\) | −10.3705 | −1.11828 | ||||||||
\(87\) | 8.55364 | 0.917046 | ||||||||
\(88\) | −0.278197 | −0.0296559 | ||||||||
\(89\) | −13.7007 | −1.45228 | −0.726138 | − | 0.687549i | \(-0.758687\pi\) | ||||
−0.726138 | + | 0.687549i | \(0.758687\pi\) | |||||||
\(90\) | 3.46130 | 0.364853 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 3.09233 | 0.322398 | ||||||||
\(93\) | −7.34959 | −0.762117 | ||||||||
\(94\) | 1.79320 | 0.184954 | ||||||||
\(95\) | −3.46130 | −0.355122 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 4.09233 | 0.415513 | 0.207757 | − | 0.978181i | \(-0.433384\pi\) | ||||
0.207757 | + | 0.978181i | \(0.433384\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.278197 | 0.0279598 | ||||||||
\(100\) | 6.98062 | 0.698062 | ||||||||
\(101\) | −2.45699 | −0.244479 | −0.122240 | − | 0.992501i | \(-0.539008\pi\) | ||||
−0.122240 | + | 0.992501i | \(0.539008\pi\) | |||||||
\(102\) | 5.79751 | 0.574039 | ||||||||
\(103\) | 17.3468 | 1.70923 | 0.854617 | − | 0.519259i | \(-0.173792\pi\) | ||||
0.854617 | + | 0.519259i | \(0.173792\pi\) | |||||||
\(104\) | −6.92261 | −0.678817 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.38823 | −0.814737 | ||||||||
\(107\) | −11.4779 | −1.10961 | −0.554806 | − | 0.831979i | \(-0.687208\pi\) | ||||
−0.554806 | + | 0.831979i | \(0.687208\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −18.6814 | −1.78935 | −0.894675 | − | 0.446718i | \(-0.852593\pi\) | ||||
−0.894675 | + | 0.446718i | \(0.852593\pi\) | |||||||
\(110\) | 0.962923 | 0.0918112 | ||||||||
\(111\) | 5.24112 | 0.497465 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.29913 | 0.310356 | 0.155178 | − | 0.987886i | \(-0.450405\pi\) | ||||
0.155178 | + | 0.987886i | \(0.450405\pi\) | |||||||
\(114\) | 1.00000 | 0.0936586 | ||||||||
\(115\) | −10.7035 | −0.998106 | ||||||||
\(116\) | −8.55364 | −0.794185 | ||||||||
\(117\) | 6.92261 | 0.639995 | ||||||||
\(118\) | 7.79476 | 0.717565 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −3.46130 | −0.315972 | ||||||||
\(121\) | −10.9226 | −0.992964 | ||||||||
\(122\) | −9.12941 | −0.826538 | ||||||||
\(123\) | −8.88553 | −0.801181 | ||||||||
\(124\) | 7.34959 | 0.660013 | ||||||||
\(125\) | −6.85553 | −0.613177 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.45699 | −0.306758 | −0.153379 | − | 0.988167i | \(-0.549016\pi\) | ||||
−0.153379 | + | 0.988167i | \(0.549016\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −10.3705 | −0.913074 | ||||||||
\(130\) | 23.9612 | 2.10154 | ||||||||
\(131\) | 18.4956 | 1.61597 | 0.807985 | − | 0.589203i | \(-0.200558\pi\) | ||||
0.807985 | + | 0.589203i | \(0.200558\pi\) | |||||||
\(132\) | −0.278197 | −0.0242139 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 13.7378 | 1.18677 | ||||||||
\(135\) | 3.46130 | 0.297902 | ||||||||
\(136\) | −5.79751 | −0.497133 | ||||||||
\(137\) | −12.1680 | −1.03959 | −0.519793 | − | 0.854292i | \(-0.673991\pi\) | ||||
−0.519793 | + | 0.854292i | \(0.673991\pi\) | |||||||
\(138\) | 3.09233 | 0.263237 | ||||||||
\(139\) | −2.91829 | −0.247526 | −0.123763 | − | 0.992312i | \(-0.539496\pi\) | ||||
−0.123763 | + | 0.992312i | \(0.539496\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.79320 | 0.151015 | ||||||||
\(142\) | −0.684727 | −0.0574610 | ||||||||
\(143\) | 1.92585 | 0.161047 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 29.6067 | 2.45870 | ||||||||
\(146\) | 1.92536 | 0.159344 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.24112 | −0.430817 | ||||||||
\(149\) | −4.16493 | −0.341204 | −0.170602 | − | 0.985340i | \(-0.554571\pi\) | ||||
−0.170602 | + | 0.985340i | \(0.554571\pi\) | |||||||
\(150\) | 6.98062 | 0.569965 | ||||||||
\(151\) | 19.2754 | 1.56861 | 0.784306 | − | 0.620374i | \(-0.213019\pi\) | ||||
0.784306 | + | 0.620374i | \(0.213019\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | 5.79751 | 0.468701 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −25.4392 | −2.04332 | ||||||||
\(156\) | −6.92261 | −0.554252 | ||||||||
\(157\) | −21.4569 | −1.71244 | −0.856222 | − | 0.516608i | \(-0.827194\pi\) | ||||
−0.856222 | + | 0.516608i | \(0.827194\pi\) | |||||||
\(158\) | −1.40761 | −0.111983 | ||||||||
\(159\) | −8.38823 | −0.665230 | ||||||||
\(160\) | 3.46130 | 0.273640 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 15.9446 | 1.24888 | 0.624439 | − | 0.781073i | \(-0.285327\pi\) | ||||
0.624439 | + | 0.781073i | \(0.285327\pi\) | |||||||
\(164\) | 8.88553 | 0.693843 | ||||||||
\(165\) | 0.962923 | 0.0749635 | ||||||||
\(166\) | 0.146030 | 0.0113341 | ||||||||
\(167\) | 17.6073 | 1.36250 | 0.681248 | − | 0.732053i | \(-0.261437\pi\) | ||||
0.681248 | + | 0.732053i | \(0.261437\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 34.9225 | 2.68634 | ||||||||
\(170\) | 20.0670 | 1.53907 | ||||||||
\(171\) | 1.00000 | 0.0764719 | ||||||||
\(172\) | 10.3705 | 0.790745 | ||||||||
\(173\) | 10.0106 | 0.761094 | 0.380547 | − | 0.924762i | \(-0.375736\pi\) | ||||
0.380547 | + | 0.924762i | \(0.375736\pi\) | |||||||
\(174\) | −8.55364 | −0.648449 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.278197 | 0.0209699 | ||||||||
\(177\) | 7.79476 | 0.585890 | ||||||||
\(178\) | 13.7007 | 1.02691 | ||||||||
\(179\) | 6.25882 | 0.467806 | 0.233903 | − | 0.972260i | \(-0.424850\pi\) | ||||
0.233903 | + | 0.972260i | \(0.424850\pi\) | |||||||
\(180\) | −3.46130 | −0.257990 | ||||||||
\(181\) | −4.25019 | −0.315914 | −0.157957 | − | 0.987446i | \(-0.550491\pi\) | ||||
−0.157957 | + | 0.987446i | \(0.550491\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.12941 | −0.674865 | ||||||||
\(184\) | −3.09233 | −0.227970 | ||||||||
\(185\) | 18.1411 | 1.33376 | ||||||||
\(186\) | 7.34959 | 0.538898 | ||||||||
\(187\) | 1.61285 | 0.117943 | ||||||||
\(188\) | −1.79320 | −0.130782 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.46130 | 0.251109 | ||||||||
\(191\) | −10.9479 | −0.792159 | −0.396080 | − | 0.918216i | \(-0.629630\pi\) | ||||
−0.396080 | + | 0.918216i | \(0.629630\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 21.2899 | 1.53248 | 0.766240 | − | 0.642554i | \(-0.222125\pi\) | ||||
0.766240 | + | 0.642554i | \(0.222125\pi\) | |||||||
\(194\) | −4.09233 | −0.293812 | ||||||||
\(195\) | 23.9612 | 1.71590 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.63103 | −0.472441 | −0.236221 | − | 0.971699i | \(-0.575909\pi\) | ||||
−0.236221 | + | 0.971699i | \(0.575909\pi\) | |||||||
\(198\) | −0.278197 | −0.0197706 | ||||||||
\(199\) | −7.87047 | −0.557923 | −0.278961 | − | 0.960302i | \(-0.589990\pi\) | ||||
−0.278961 | + | 0.960302i | \(0.589990\pi\) | |||||||
\(200\) | −6.98062 | −0.493604 | ||||||||
\(201\) | 13.7378 | 0.968991 | ||||||||
\(202\) | 2.45699 | 0.172873 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −5.79751 | −0.405907 | ||||||||
\(205\) | −30.7555 | −2.14806 | ||||||||
\(206\) | −17.3468 | −1.20861 | ||||||||
\(207\) | 3.09233 | 0.214932 | ||||||||
\(208\) | 6.92261 | 0.479996 | ||||||||
\(209\) | 0.278197 | 0.0192433 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.9123 | 1.02660 | 0.513302 | − | 0.858208i | \(-0.328422\pi\) | ||||
0.513302 | + | 0.858208i | \(0.328422\pi\) | |||||||
\(212\) | 8.38823 | 0.576106 | ||||||||
\(213\) | −0.684727 | −0.0469167 | ||||||||
\(214\) | 11.4779 | 0.784615 | ||||||||
\(215\) | −35.8955 | −2.44806 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 18.6814 | 1.26526 | ||||||||
\(219\) | 1.92536 | 0.130104 | ||||||||
\(220\) | −0.962923 | −0.0649203 | ||||||||
\(221\) | 40.1339 | 2.69970 | ||||||||
\(222\) | −5.24112 | −0.351761 | ||||||||
\(223\) | 3.92861 | 0.263079 | 0.131539 | − | 0.991311i | \(-0.458008\pi\) | ||||
0.131539 | + | 0.991311i | \(0.458008\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.98062 | 0.465375 | ||||||||
\(226\) | −3.29913 | −0.219455 | ||||||||
\(227\) | −7.03971 | −0.467242 | −0.233621 | − | 0.972328i | \(-0.575057\pi\) | ||||
−0.233621 | + | 0.972328i | \(0.575057\pi\) | |||||||
\(228\) | −1.00000 | −0.0662266 | ||||||||
\(229\) | 5.88397 | 0.388824 | 0.194412 | − | 0.980920i | \(-0.437720\pi\) | ||||
0.194412 | + | 0.980920i | \(0.437720\pi\) | |||||||
\(230\) | 10.7035 | 0.705768 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8.55364 | 0.561574 | ||||||||
\(233\) | 2.80658 | 0.183865 | 0.0919326 | − | 0.995765i | \(-0.470696\pi\) | ||||
0.0919326 | + | 0.995765i | \(0.470696\pi\) | |||||||
\(234\) | −6.92261 | −0.452545 | ||||||||
\(235\) | 6.20680 | 0.404887 | ||||||||
\(236\) | −7.79476 | −0.507395 | ||||||||
\(237\) | −1.40761 | −0.0914338 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.4016 | −0.802193 | −0.401097 | − | 0.916036i | \(-0.631371\pi\) | ||||
−0.401097 | + | 0.916036i | \(0.631371\pi\) | |||||||
\(240\) | 3.46130 | 0.223426 | ||||||||
\(241\) | −15.1965 | −0.978892 | −0.489446 | − | 0.872034i | \(-0.662801\pi\) | ||||
−0.489446 | + | 0.872034i | \(0.662801\pi\) | |||||||
\(242\) | 10.9226 | 0.702132 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 9.12941 | 0.584450 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 8.88553 | 0.566521 | ||||||||
\(247\) | 6.92261 | 0.440475 | ||||||||
\(248\) | −7.34959 | −0.466700 | ||||||||
\(249\) | 0.146030 | 0.00925427 | ||||||||
\(250\) | 6.85553 | 0.433582 | ||||||||
\(251\) | 5.91198 | 0.373161 | 0.186581 | − | 0.982440i | \(-0.440259\pi\) | ||||
0.186581 | + | 0.982440i | \(0.440259\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.860277 | 0.0540851 | ||||||||
\(254\) | 3.45699 | 0.216911 | ||||||||
\(255\) | 20.0670 | 1.25664 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 1.40485 | 0.0876320 | 0.0438160 | − | 0.999040i | \(-0.486048\pi\) | ||||
0.0438160 | + | 0.999040i | \(0.486048\pi\) | |||||||
\(258\) | 10.3705 | 0.645641 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −23.9612 | −1.48601 | ||||||||
\(261\) | −8.55364 | −0.529457 | ||||||||
\(262\) | −18.4956 | −1.14266 | ||||||||
\(263\) | −10.7781 | −0.664608 | −0.332304 | − | 0.943172i | \(-0.607826\pi\) | ||||
−0.332304 | + | 0.943172i | \(0.607826\pi\) | |||||||
\(264\) | 0.278197 | 0.0171218 | ||||||||
\(265\) | −29.0342 | −1.78356 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 13.7007 | 0.838472 | ||||||||
\(268\) | −13.7378 | −0.839171 | ||||||||
\(269\) | 22.4462 | 1.36857 | 0.684286 | − | 0.729214i | \(-0.260114\pi\) | ||||
0.684286 | + | 0.729214i | \(0.260114\pi\) | |||||||
\(270\) | −3.46130 | −0.210648 | ||||||||
\(271\) | −2.27651 | −0.138288 | −0.0691442 | − | 0.997607i | \(-0.522027\pi\) | ||||
−0.0691442 | + | 0.997607i | \(0.522027\pi\) | |||||||
\(272\) | 5.79751 | 0.351526 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 12.1680 | 0.735098 | ||||||||
\(275\) | 1.94199 | 0.117106 | ||||||||
\(276\) | −3.09233 | −0.186137 | ||||||||
\(277\) | 27.4521 | 1.64943 | 0.824717 | − | 0.565545i | \(-0.191334\pi\) | ||||
0.824717 | + | 0.565545i | \(0.191334\pi\) | |||||||
\(278\) | 2.91829 | 0.175027 | ||||||||
\(279\) | 7.34959 | 0.440009 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.14279 | 0.485758 | 0.242879 | − | 0.970057i | \(-0.421908\pi\) | ||||
0.242879 | + | 0.970057i | \(0.421908\pi\) | |||||||
\(282\) | −1.79320 | −0.106783 | ||||||||
\(283\) | −8.18586 | −0.486599 | −0.243300 | − | 0.969951i | \(-0.578230\pi\) | ||||
−0.243300 | + | 0.969951i | \(0.578230\pi\) | |||||||
\(284\) | 0.684727 | 0.0406311 | ||||||||
\(285\) | 3.46130 | 0.205030 | ||||||||
\(286\) | −1.92585 | −0.113878 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 16.6112 | 0.977127 | ||||||||
\(290\) | −29.6067 | −1.73857 | ||||||||
\(291\) | −4.09233 | −0.239897 | ||||||||
\(292\) | −1.92536 | −0.112673 | ||||||||
\(293\) | −19.3421 | −1.12998 | −0.564988 | − | 0.825099i | \(-0.691119\pi\) | ||||
−0.564988 | + | 0.825099i | \(0.691119\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 26.9800 | 1.57084 | ||||||||
\(296\) | 5.24112 | 0.304634 | ||||||||
\(297\) | −0.278197 | −0.0161426 | ||||||||
\(298\) | 4.16493 | 0.241268 | ||||||||
\(299\) | 21.4070 | 1.23800 | ||||||||
\(300\) | −6.98062 | −0.403026 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −19.2754 | −1.10918 | ||||||||
\(303\) | 2.45699 | 0.141150 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | −31.5997 | −1.80939 | ||||||||
\(306\) | −5.79751 | −0.331422 | ||||||||
\(307\) | −11.7007 | −0.667797 | −0.333898 | − | 0.942609i | \(-0.608364\pi\) | ||||
−0.333898 | + | 0.942609i | \(0.608364\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −17.3468 | −0.986827 | ||||||||
\(310\) | 25.4392 | 1.44485 | ||||||||
\(311\) | 13.8555 | 0.785675 | 0.392837 | − | 0.919608i | \(-0.371494\pi\) | ||||
0.392837 | + | 0.919608i | \(0.371494\pi\) | |||||||
\(312\) | 6.92261 | 0.391915 | ||||||||
\(313\) | −1.97199 | −0.111463 | −0.0557317 | − | 0.998446i | \(-0.517749\pi\) | ||||
−0.0557317 | + | 0.998446i | \(0.517749\pi\) | |||||||
\(314\) | 21.4569 | 1.21088 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.40761 | 0.0791840 | ||||||||
\(317\) | 19.9005 | 1.11772 | 0.558861 | − | 0.829261i | \(-0.311239\pi\) | ||||
0.558861 | + | 0.829261i | \(0.311239\pi\) | |||||||
\(318\) | 8.38823 | 0.470388 | ||||||||
\(319\) | −2.37959 | −0.133232 | ||||||||
\(320\) | −3.46130 | −0.193493 | ||||||||
\(321\) | 11.4779 | 0.640635 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.79751 | 0.322582 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 48.3241 | 2.68054 | ||||||||
\(326\) | −15.9446 | −0.883091 | ||||||||
\(327\) | 18.6814 | 1.03308 | ||||||||
\(328\) | −8.88553 | −0.490621 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −0.962923 | −0.0530072 | ||||||||
\(331\) | −4.66762 | −0.256556 | −0.128278 | − | 0.991738i | \(-0.540945\pi\) | ||||
−0.128278 | + | 0.991738i | \(0.540945\pi\) | |||||||
\(332\) | −0.146030 | −0.00801443 | ||||||||
\(333\) | −5.24112 | −0.287212 | ||||||||
\(334\) | −17.6073 | −0.963430 | ||||||||
\(335\) | 47.5508 | 2.59798 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.4639 | −0.624480 | −0.312240 | − | 0.950003i | \(-0.601079\pi\) | ||||
−0.312240 | + | 0.950003i | \(0.601079\pi\) | |||||||
\(338\) | −34.9225 | −1.89953 | ||||||||
\(339\) | −3.29913 | −0.179184 | ||||||||
\(340\) | −20.0670 | −1.08828 | ||||||||
\(341\) | 2.04463 | 0.110723 | ||||||||
\(342\) | −1.00000 | −0.0540738 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −10.3705 | −0.559141 | ||||||||
\(345\) | 10.7035 | 0.576257 | ||||||||
\(346\) | −10.0106 | −0.538174 | ||||||||
\(347\) | 7.84258 | 0.421012 | 0.210506 | − | 0.977593i | \(-0.432489\pi\) | ||||
0.210506 | + | 0.977593i | \(0.432489\pi\) | |||||||
\(348\) | 8.55364 | 0.458523 | ||||||||
\(349\) | 21.2991 | 1.14012 | 0.570058 | − | 0.821604i | \(-0.306921\pi\) | ||||
0.570058 | + | 0.821604i | \(0.306921\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.92261 | −0.369501 | ||||||||
\(352\) | −0.278197 | −0.0148279 | ||||||||
\(353\) | 8.71701 | 0.463959 | 0.231980 | − | 0.972721i | \(-0.425480\pi\) | ||||
0.231980 | + | 0.972721i | \(0.425480\pi\) | |||||||
\(354\) | −7.79476 | −0.414287 | ||||||||
\(355\) | −2.37005 | −0.125789 | ||||||||
\(356\) | −13.7007 | −0.726138 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6.25882 | −0.330789 | ||||||||
\(359\) | 1.17128 | 0.0618180 | 0.0309090 | − | 0.999522i | \(-0.490160\pi\) | ||||
0.0309090 | + | 0.999522i | \(0.490160\pi\) | |||||||
\(360\) | 3.46130 | 0.182427 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 4.25019 | 0.223385 | ||||||||
\(363\) | 10.9226 | 0.573288 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.66427 | 0.348824 | ||||||||
\(366\) | 9.12941 | 0.477202 | ||||||||
\(367\) | 5.01295 | 0.261674 | 0.130837 | − | 0.991404i | \(-0.458234\pi\) | ||||
0.130837 | + | 0.991404i | \(0.458234\pi\) | |||||||
\(368\) | 3.09233 | 0.161199 | ||||||||
\(369\) | 8.88553 | 0.462562 | ||||||||
\(370\) | −18.1411 | −0.943111 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −7.34959 | −0.381059 | ||||||||
\(373\) | 1.86584 | 0.0966096 | 0.0483048 | − | 0.998833i | \(-0.484618\pi\) | ||||
0.0483048 | + | 0.998833i | \(0.484618\pi\) | |||||||
\(374\) | −1.61285 | −0.0833985 | ||||||||
\(375\) | 6.85553 | 0.354018 | ||||||||
\(376\) | 1.79320 | 0.0924771 | ||||||||
\(377\) | −59.2135 | −3.04965 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.8065 | −0.606457 | −0.303228 | − | 0.952918i | \(-0.598065\pi\) | ||||
−0.303228 | + | 0.952918i | \(0.598065\pi\) | |||||||
\(380\) | −3.46130 | −0.177561 | ||||||||
\(381\) | 3.45699 | 0.177107 | ||||||||
\(382\) | 10.9479 | 0.560141 | ||||||||
\(383\) | 5.52639 | 0.282385 | 0.141193 | − | 0.989982i | \(-0.454906\pi\) | ||||
0.141193 | + | 0.989982i | \(0.454906\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −21.2899 | −1.08363 | ||||||||
\(387\) | 10.3705 | 0.527164 | ||||||||
\(388\) | 4.09233 | 0.207757 | ||||||||
\(389\) | 1.26421 | 0.0640979 | 0.0320490 | − | 0.999486i | \(-0.489797\pi\) | ||||
0.0320490 | + | 0.999486i | \(0.489797\pi\) | |||||||
\(390\) | −23.9612 | −1.21332 | ||||||||
\(391\) | 17.9278 | 0.906650 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −18.4956 | −0.932981 | ||||||||
\(394\) | 6.63103 | 0.334066 | ||||||||
\(395\) | −4.87215 | −0.245144 | ||||||||
\(396\) | 0.278197 | 0.0139799 | ||||||||
\(397\) | −1.40485 | −0.0705073 | −0.0352536 | − | 0.999378i | \(-0.511224\pi\) | ||||
−0.0352536 | + | 0.999378i | \(0.511224\pi\) | |||||||
\(398\) | 7.87047 | 0.394511 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 6.98062 | 0.349031 | ||||||||
\(401\) | −4.77119 | −0.238262 | −0.119131 | − | 0.992879i | \(-0.538011\pi\) | ||||
−0.119131 | + | 0.992879i | \(0.538011\pi\) | |||||||
\(402\) | −13.7378 | −0.685180 | ||||||||
\(403\) | 50.8783 | 2.53443 | ||||||||
\(404\) | −2.45699 | −0.122240 | ||||||||
\(405\) | −3.46130 | −0.171994 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.45806 | −0.0722735 | ||||||||
\(408\) | 5.79751 | 0.287020 | ||||||||
\(409\) | −18.0890 | −0.894442 | −0.447221 | − | 0.894424i | \(-0.647586\pi\) | ||||
−0.447221 | + | 0.894424i | \(0.647586\pi\) | |||||||
\(410\) | 30.7555 | 1.51891 | ||||||||
\(411\) | 12.1680 | 0.600205 | ||||||||
\(412\) | 17.3468 | 0.854617 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −3.09233 | −0.151980 | ||||||||
\(415\) | 0.505454 | 0.0248118 | ||||||||
\(416\) | −6.92261 | −0.339409 | ||||||||
\(417\) | 2.91829 | 0.142909 | ||||||||
\(418\) | −0.278197 | −0.0136071 | ||||||||
\(419\) | 2.70518 | 0.132157 | 0.0660784 | − | 0.997814i | \(-0.478951\pi\) | ||||
0.0660784 | + | 0.997814i | \(0.478951\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.14064 | 0.299276 | 0.149638 | − | 0.988741i | \(-0.452189\pi\) | ||||
0.149638 | + | 0.988741i | \(0.452189\pi\) | |||||||
\(422\) | −14.9123 | −0.725919 | ||||||||
\(423\) | −1.79320 | −0.0871883 | ||||||||
\(424\) | −8.38823 | −0.407368 | ||||||||
\(425\) | 40.4702 | 1.96310 | ||||||||
\(426\) | 0.684727 | 0.0331751 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −11.4779 | −0.554806 | ||||||||
\(429\) | −1.92585 | −0.0929808 | ||||||||
\(430\) | 35.8955 | 1.73104 | ||||||||
\(431\) | 21.2765 | 1.02485 | 0.512427 | − | 0.858731i | \(-0.328747\pi\) | ||||
0.512427 | + | 0.858731i | \(0.328747\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −9.42099 | −0.452744 | −0.226372 | − | 0.974041i | \(-0.572686\pi\) | ||||
−0.226372 | + | 0.974041i | \(0.572686\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −29.6067 | −1.41953 | ||||||||
\(436\) | −18.6814 | −0.894675 | ||||||||
\(437\) | 3.09233 | 0.147926 | ||||||||
\(438\) | −1.92536 | −0.0919975 | ||||||||
\(439\) | 12.5924 | 0.601002 | 0.300501 | − | 0.953781i | \(-0.402846\pi\) | ||||
0.300501 | + | 0.953781i | \(0.402846\pi\) | |||||||
\(440\) | 0.962923 | 0.0459056 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −40.1339 | −1.90898 | ||||||||
\(443\) | −23.2947 | −1.10676 | −0.553382 | − | 0.832927i | \(-0.686663\pi\) | ||||
−0.553382 | + | 0.832927i | \(0.686663\pi\) | |||||||
\(444\) | 5.24112 | 0.248733 | ||||||||
\(445\) | 47.4224 | 2.24804 | ||||||||
\(446\) | −3.92861 | −0.186025 | ||||||||
\(447\) | 4.16493 | 0.196994 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −0.486074 | −0.0229393 | −0.0114696 | − | 0.999934i | \(-0.503651\pi\) | ||||
−0.0114696 | + | 0.999934i | \(0.503651\pi\) | |||||||
\(450\) | −6.98062 | −0.329070 | ||||||||
\(451\) | 2.47193 | 0.116398 | ||||||||
\(452\) | 3.29913 | 0.155178 | ||||||||
\(453\) | −19.2754 | −0.905639 | ||||||||
\(454\) | 7.03971 | 0.330390 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.00000 | 0.0468293 | ||||||||
\(457\) | 14.4597 | 0.676398 | 0.338199 | − | 0.941075i | \(-0.390182\pi\) | ||||
0.338199 | + | 0.941075i | \(0.390182\pi\) | |||||||
\(458\) | −5.88397 | −0.274940 | ||||||||
\(459\) | −5.79751 | −0.270605 | ||||||||
\(460\) | −10.7035 | −0.499053 | ||||||||
\(461\) | 18.0188 | 0.839218 | 0.419609 | − | 0.907705i | \(-0.362167\pi\) | ||||
0.419609 | + | 0.907705i | \(0.362167\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 23.3408 | 1.08474 | 0.542370 | − | 0.840140i | \(-0.317527\pi\) | ||||
0.542370 | + | 0.840140i | \(0.317527\pi\) | |||||||
\(464\) | −8.55364 | −0.397093 | ||||||||
\(465\) | 25.4392 | 1.17971 | ||||||||
\(466\) | −2.80658 | −0.130012 | ||||||||
\(467\) | −8.14879 | −0.377081 | −0.188540 | − | 0.982065i | \(-0.560376\pi\) | ||||
−0.188540 | + | 0.982065i | \(0.560376\pi\) | |||||||
\(468\) | 6.92261 | 0.319998 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −6.20680 | −0.286298 | ||||||||
\(471\) | 21.4569 | 0.988680 | ||||||||
\(472\) | 7.79476 | 0.358783 | ||||||||
\(473\) | 2.88505 | 0.132655 | ||||||||
\(474\) | 1.40761 | 0.0646535 | ||||||||
\(475\) | 6.98062 | 0.320293 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.38823 | 0.384070 | ||||||||
\(478\) | 12.4016 | 0.567236 | ||||||||
\(479\) | 27.1627 | 1.24109 | 0.620547 | − | 0.784170i | \(-0.286911\pi\) | ||||
0.620547 | + | 0.784170i | \(0.286911\pi\) | |||||||
\(480\) | −3.46130 | −0.157986 | ||||||||
\(481\) | −36.2822 | −1.65433 | ||||||||
\(482\) | 15.1965 | 0.692181 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.9226 | −0.496482 | ||||||||
\(485\) | −14.1648 | −0.643191 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −11.9423 | −0.541159 | −0.270580 | − | 0.962698i | \(-0.587215\pi\) | ||||
−0.270580 | + | 0.962698i | \(0.587215\pi\) | |||||||
\(488\) | −9.12941 | −0.413269 | ||||||||
\(489\) | −15.9446 | −0.721041 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.00863 | −0.316295 | −0.158148 | − | 0.987415i | \(-0.550552\pi\) | ||||
−0.158148 | + | 0.987415i | \(0.550552\pi\) | |||||||
\(492\) | −8.88553 | −0.400591 | ||||||||
\(493\) | −49.5898 | −2.23341 | ||||||||
\(494\) | −6.92261 | −0.311463 | ||||||||
\(495\) | −0.962923 | −0.0432802 | ||||||||
\(496\) | 7.34959 | 0.330006 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −0.146030 | −0.00654376 | ||||||||
\(499\) | −9.12604 | −0.408538 | −0.204269 | − | 0.978915i | \(-0.565482\pi\) | ||||
−0.204269 | + | 0.978915i | \(0.565482\pi\) | |||||||
\(500\) | −6.85553 | −0.306589 | ||||||||
\(501\) | −17.6073 | −0.786638 | ||||||||
\(502\) | −5.91198 | −0.263865 | ||||||||
\(503\) | −24.1190 | −1.07541 | −0.537706 | − | 0.843133i | \(-0.680709\pi\) | ||||
−0.537706 | + | 0.843133i | \(0.680709\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.50438 | 0.378440 | ||||||||
\(506\) | −0.860277 | −0.0382440 | ||||||||
\(507\) | −34.9225 | −1.55096 | ||||||||
\(508\) | −3.45699 | −0.153379 | ||||||||
\(509\) | −37.5061 | −1.66243 | −0.831215 | − | 0.555951i | \(-0.812354\pi\) | ||||
−0.831215 | + | 0.555951i | \(0.812354\pi\) | |||||||
\(510\) | −20.0670 | −0.888580 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −1.00000 | −0.0441511 | ||||||||
\(514\) | −1.40485 | −0.0619651 | ||||||||
\(515\) | −60.0427 | −2.64580 | ||||||||
\(516\) | −10.3705 | −0.456537 | ||||||||
\(517\) | −0.498862 | −0.0219399 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10.0106 | −0.439418 | ||||||||
\(520\) | 23.9612 | 1.05077 | ||||||||
\(521\) | 42.2049 | 1.84903 | 0.924516 | − | 0.381143i | \(-0.124469\pi\) | ||||
0.924516 | + | 0.381143i | \(0.124469\pi\) | |||||||
\(522\) | 8.55364 | 0.374382 | ||||||||
\(523\) | 19.0938 | 0.834915 | 0.417458 | − | 0.908696i | \(-0.362921\pi\) | ||||
0.417458 | + | 0.908696i | \(0.362921\pi\) | |||||||
\(524\) | 18.4956 | 0.807985 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10.7781 | 0.469949 | ||||||||
\(527\) | 42.6094 | 1.85609 | ||||||||
\(528\) | −0.278197 | −0.0121070 | ||||||||
\(529\) | −13.4375 | −0.584238 | ||||||||
\(530\) | 29.0342 | 1.26116 | ||||||||
\(531\) | −7.79476 | −0.338264 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 61.5110 | 2.66434 | ||||||||
\(534\) | −13.7007 | −0.592889 | ||||||||
\(535\) | 39.7286 | 1.71762 | ||||||||
\(536\) | 13.7378 | 0.593383 | ||||||||
\(537\) | −6.25882 | −0.270088 | ||||||||
\(538\) | −22.4462 | −0.967726 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 3.46130 | 0.148951 | ||||||||
\(541\) | 0.786124 | 0.0337981 | 0.0168991 | − | 0.999857i | \(-0.494621\pi\) | ||||
0.0168991 | + | 0.999857i | \(0.494621\pi\) | |||||||
\(542\) | 2.27651 | 0.0977846 | ||||||||
\(543\) | 4.25019 | 0.182393 | ||||||||
\(544\) | −5.79751 | −0.248566 | ||||||||
\(545\) | 64.6619 | 2.76981 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.670738 | 0.0286787 | 0.0143394 | − | 0.999897i | \(-0.495435\pi\) | ||||
0.0143394 | + | 0.999897i | \(0.495435\pi\) | |||||||
\(548\) | −12.1680 | −0.519793 | ||||||||
\(549\) | 9.12941 | 0.389634 | ||||||||
\(550\) | −1.94199 | −0.0828066 | ||||||||
\(551\) | −8.55364 | −0.364397 | ||||||||
\(552\) | 3.09233 | 0.131618 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −27.4521 | −1.16633 | ||||||||
\(555\) | −18.1411 | −0.770047 | ||||||||
\(556\) | −2.91829 | −0.123763 | ||||||||
\(557\) | 6.15298 | 0.260710 | 0.130355 | − | 0.991467i | \(-0.458388\pi\) | ||||
0.130355 | + | 0.991467i | \(0.458388\pi\) | |||||||
\(558\) | −7.34959 | −0.311133 | ||||||||
\(559\) | 71.7911 | 3.03644 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.61285 | −0.0680946 | ||||||||
\(562\) | −8.14279 | −0.343483 | ||||||||
\(563\) | −23.6754 | −0.997798 | −0.498899 | − | 0.866660i | \(-0.666262\pi\) | ||||
−0.498899 | + | 0.866660i | \(0.666262\pi\) | |||||||
\(564\) | 1.79320 | 0.0755073 | ||||||||
\(565\) | −11.4193 | −0.480414 | ||||||||
\(566\) | 8.18586 | 0.344078 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −0.684727 | −0.0287305 | ||||||||
\(569\) | 36.6691 | 1.53725 | 0.768623 | − | 0.639702i | \(-0.220942\pi\) | ||||
0.768623 | + | 0.639702i | \(0.220942\pi\) | |||||||
\(570\) | −3.46130 | −0.144978 | ||||||||
\(571\) | −17.7280 | −0.741893 | −0.370947 | − | 0.928654i | \(-0.620967\pi\) | ||||
−0.370947 | + | 0.928654i | \(0.620967\pi\) | |||||||
\(572\) | 1.92585 | 0.0805237 | ||||||||
\(573\) | 10.9479 | 0.457353 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 21.5864 | 0.900215 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −1.23206 | −0.0512911 | −0.0256456 | − | 0.999671i | \(-0.508164\pi\) | ||||
−0.0256456 | + | 0.999671i | \(0.508164\pi\) | |||||||
\(578\) | −16.6112 | −0.690933 | ||||||||
\(579\) | −21.2899 | −0.884778 | ||||||||
\(580\) | 29.6067 | 1.22935 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 4.09233 | 0.169633 | ||||||||
\(583\) | 2.33358 | 0.0966469 | ||||||||
\(584\) | 1.92536 | 0.0796722 | ||||||||
\(585\) | −23.9612 | −0.990675 | ||||||||
\(586\) | 19.3421 | 0.799014 | ||||||||
\(587\) | −10.0714 | −0.415691 | −0.207845 | − | 0.978162i | \(-0.566645\pi\) | ||||
−0.207845 | + | 0.978162i | \(0.566645\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.34959 | 0.302835 | ||||||||
\(590\) | −26.9800 | −1.11075 | ||||||||
\(591\) | 6.63103 | 0.272764 | ||||||||
\(592\) | −5.24112 | −0.215409 | ||||||||
\(593\) | 28.2634 | 1.16064 | 0.580320 | − | 0.814388i | \(-0.302927\pi\) | ||||
0.580320 | + | 0.814388i | \(0.302927\pi\) | |||||||
\(594\) | 0.278197 | 0.0114146 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4.16493 | −0.170602 | ||||||||
\(597\) | 7.87047 | 0.322117 | ||||||||
\(598\) | −21.4070 | −0.875397 | ||||||||
\(599\) | 4.27975 | 0.174866 | 0.0874330 | − | 0.996170i | \(-0.472134\pi\) | ||||
0.0874330 | + | 0.996170i | \(0.472134\pi\) | |||||||
\(600\) | 6.98062 | 0.284983 | ||||||||
\(601\) | −47.6366 | −1.94314 | −0.971569 | − | 0.236757i | \(-0.923915\pi\) | ||||
−0.971569 | + | 0.236757i | \(0.923915\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −13.7378 | −0.559447 | ||||||||
\(604\) | 19.2754 | 0.784306 | ||||||||
\(605\) | 37.8065 | 1.53705 | ||||||||
\(606\) | −2.45699 | −0.0998083 | ||||||||
\(607\) | −20.6931 | −0.839905 | −0.419953 | − | 0.907546i | \(-0.637953\pi\) | ||||
−0.419953 | + | 0.907546i | \(0.637953\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 31.5997 | 1.27943 | ||||||||
\(611\) | −12.4136 | −0.502201 | ||||||||
\(612\) | 5.79751 | 0.234351 | ||||||||
\(613\) | 1.67398 | 0.0676114 | 0.0338057 | − | 0.999428i | \(-0.489237\pi\) | ||||
0.0338057 | + | 0.999428i | \(0.489237\pi\) | |||||||
\(614\) | 11.7007 | 0.472203 | ||||||||
\(615\) | 30.7555 | 1.24018 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.5252 | −0.544504 | −0.272252 | − | 0.962226i | \(-0.587768\pi\) | ||||
−0.272252 | + | 0.962226i | \(0.587768\pi\) | |||||||
\(618\) | 17.3468 | 0.697792 | ||||||||
\(619\) | 45.1559 | 1.81497 | 0.907485 | − | 0.420085i | \(-0.138000\pi\) | ||||
0.907485 | + | 0.420085i | \(0.138000\pi\) | |||||||
\(620\) | −25.4392 | −1.02166 | ||||||||
\(621\) | −3.09233 | −0.124091 | ||||||||
\(622\) | −13.8555 | −0.555556 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −6.92261 | −0.277126 | ||||||||
\(625\) | −11.1740 | −0.446962 | ||||||||
\(626\) | 1.97199 | 0.0788165 | ||||||||
\(627\) | −0.278197 | −0.0111101 | ||||||||
\(628\) | −21.4569 | −0.856222 | ||||||||
\(629\) | −30.3855 | −1.21155 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.01542 | −0.120042 | −0.0600210 | − | 0.998197i | \(-0.519117\pi\) | ||||
−0.0600210 | + | 0.998197i | \(0.519117\pi\) | |||||||
\(632\) | −1.40761 | −0.0559915 | ||||||||
\(633\) | −14.9123 | −0.592710 | ||||||||
\(634\) | −19.9005 | −0.790349 | ||||||||
\(635\) | 11.9657 | 0.474844 | ||||||||
\(636\) | −8.38823 | −0.332615 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 2.37959 | 0.0942090 | ||||||||
\(639\) | 0.684727 | 0.0270874 | ||||||||
\(640\) | 3.46130 | 0.136820 | ||||||||
\(641\) | 15.9962 | 0.631811 | 0.315905 | − | 0.948791i | \(-0.397692\pi\) | ||||
0.315905 | + | 0.948791i | \(0.397692\pi\) | |||||||
\(642\) | −11.4779 | −0.452998 | ||||||||
\(643\) | −20.9315 | −0.825460 | −0.412730 | − | 0.910854i | \(-0.635425\pi\) | ||||
−0.412730 | + | 0.910854i | \(0.635425\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 35.8955 | 1.41339 | ||||||||
\(646\) | −5.79751 | −0.228100 | ||||||||
\(647\) | 43.4198 | 1.70701 | 0.853504 | − | 0.521086i | \(-0.174473\pi\) | ||||
0.853504 | + | 0.521086i | \(0.174473\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −2.16848 | −0.0851201 | ||||||||
\(650\) | −48.3241 | −1.89543 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 15.9446 | 0.624439 | ||||||||
\(653\) | −6.06220 | −0.237232 | −0.118616 | − | 0.992940i | \(-0.537846\pi\) | ||||
−0.118616 | + | 0.992940i | \(0.537846\pi\) | |||||||
\(654\) | −18.6814 | −0.730499 | ||||||||
\(655\) | −64.0190 | −2.50143 | ||||||||
\(656\) | 8.88553 | 0.346922 | ||||||||
\(657\) | −1.92536 | −0.0751156 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −0.570382 | −0.0222189 | −0.0111095 | − | 0.999938i | \(-0.503536\pi\) | ||||
−0.0111095 | + | 0.999938i | \(0.503536\pi\) | |||||||
\(660\) | 0.962923 | 0.0374817 | ||||||||
\(661\) | −17.6396 | −0.686101 | −0.343051 | − | 0.939317i | \(-0.611460\pi\) | ||||
−0.343051 | + | 0.939317i | \(0.611460\pi\) | |||||||
\(662\) | 4.66762 | 0.181412 | ||||||||
\(663\) | −40.1339 | −1.55867 | ||||||||
\(664\) | 0.146030 | 0.00566706 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 5.24112 | 0.203089 | ||||||||
\(667\) | −26.4507 | −1.02417 | ||||||||
\(668\) | 17.6073 | 0.681248 | ||||||||
\(669\) | −3.92861 | −0.151889 | ||||||||
\(670\) | −47.5508 | −1.83705 | ||||||||
\(671\) | 2.53977 | 0.0980468 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −39.1296 | −1.50833 | −0.754167 | − | 0.656682i | \(-0.771959\pi\) | ||||
−0.754167 | + | 0.656682i | \(0.771959\pi\) | |||||||
\(674\) | 11.4639 | 0.441574 | ||||||||
\(675\) | −6.98062 | −0.268684 | ||||||||
\(676\) | 34.9225 | 1.34317 | ||||||||
\(677\) | 35.4149 | 1.36110 | 0.680552 | − | 0.732700i | \(-0.261740\pi\) | ||||
0.680552 | + | 0.732700i | \(0.261740\pi\) | |||||||
\(678\) | 3.29913 | 0.126702 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 20.0670 | 0.769533 | ||||||||
\(681\) | 7.03971 | 0.269762 | ||||||||
\(682\) | −2.04463 | −0.0782930 | ||||||||
\(683\) | −36.2898 | −1.38859 | −0.694295 | − | 0.719691i | \(-0.744284\pi\) | ||||
−0.694295 | + | 0.719691i | \(0.744284\pi\) | |||||||
\(684\) | 1.00000 | 0.0382360 | ||||||||
\(685\) | 42.1173 | 1.60922 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.88397 | −0.224488 | ||||||||
\(688\) | 10.3705 | 0.395373 | ||||||||
\(689\) | 58.0684 | 2.21223 | ||||||||
\(690\) | −10.7035 | −0.407475 | ||||||||
\(691\) | 33.7147 | 1.28257 | 0.641284 | − | 0.767303i | \(-0.278402\pi\) | ||||
0.641284 | + | 0.767303i | \(0.278402\pi\) | |||||||
\(692\) | 10.0106 | 0.380547 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7.84258 | −0.297700 | ||||||||
\(695\) | 10.1011 | 0.383156 | ||||||||
\(696\) | −8.55364 | −0.324225 | ||||||||
\(697\) | 51.5140 | 1.95123 | ||||||||
\(698\) | −21.2991 | −0.806184 | ||||||||
\(699\) | −2.80658 | −0.106155 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.6976 | 0.479583 | 0.239791 | − | 0.970824i | \(-0.422921\pi\) | ||||
0.239791 | + | 0.970824i | \(0.422921\pi\) | |||||||
\(702\) | 6.92261 | 0.261277 | ||||||||
\(703\) | −5.24112 | −0.197673 | ||||||||
\(704\) | 0.278197 | 0.0104849 | ||||||||
\(705\) | −6.20680 | −0.233762 | ||||||||
\(706\) | −8.71701 | −0.328069 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 7.79476 | 0.292945 | ||||||||
\(709\) | −21.2791 | −0.799155 | −0.399578 | − | 0.916699i | \(-0.630843\pi\) | ||||
−0.399578 | + | 0.916699i | \(0.630843\pi\) | |||||||
\(710\) | 2.37005 | 0.0889463 | ||||||||
\(711\) | 1.40761 | 0.0527893 | ||||||||
\(712\) | 13.7007 | 0.513457 | ||||||||
\(713\) | 22.7274 | 0.851147 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.66594 | −0.249292 | ||||||||
\(716\) | 6.25882 | 0.233903 | ||||||||
\(717\) | 12.4016 | 0.463146 | ||||||||
\(718\) | −1.17128 | −0.0437119 | ||||||||
\(719\) | 48.2232 | 1.79842 | 0.899210 | − | 0.437516i | \(-0.144142\pi\) | ||||
0.899210 | + | 0.437516i | \(0.144142\pi\) | |||||||
\(720\) | −3.46130 | −0.128995 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | 15.1965 | 0.565163 | ||||||||
\(724\) | −4.25019 | −0.157957 | ||||||||
\(725\) | −59.7097 | −2.21756 | ||||||||
\(726\) | −10.9226 | −0.405376 | ||||||||
\(727\) | 49.2945 | 1.82823 | 0.914116 | − | 0.405452i | \(-0.132886\pi\) | ||||
0.914116 | + | 0.405452i | \(0.132886\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −6.66427 | −0.246656 | ||||||||
\(731\) | 60.1233 | 2.22374 | ||||||||
\(732\) | −9.12941 | −0.337433 | ||||||||
\(733\) | −0.924289 | −0.0341394 | −0.0170697 | − | 0.999854i | \(-0.505434\pi\) | ||||
−0.0170697 | + | 0.999854i | \(0.505434\pi\) | |||||||
\(734\) | −5.01295 | −0.185031 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.09233 | −0.113985 | ||||||||
\(737\) | −3.82182 | −0.140778 | ||||||||
\(738\) | −8.88553 | −0.327081 | ||||||||
\(739\) | 2.35176 | 0.0865108 | 0.0432554 | − | 0.999064i | \(-0.486227\pi\) | ||||
0.0432554 | + | 0.999064i | \(0.486227\pi\) | |||||||
\(740\) | 18.1411 | 0.666880 | ||||||||
\(741\) | −6.92261 | −0.254308 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −50.4616 | −1.85126 | −0.925628 | − | 0.378433i | \(-0.876463\pi\) | ||||
−0.925628 | + | 0.378433i | \(0.876463\pi\) | |||||||
\(744\) | 7.34959 | 0.269449 | ||||||||
\(745\) | 14.4161 | 0.528164 | ||||||||
\(746\) | −1.86584 | −0.0683133 | ||||||||
\(747\) | −0.146030 | −0.00534296 | ||||||||
\(748\) | 1.61285 | 0.0589716 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −6.85553 | −0.250328 | ||||||||
\(751\) | −6.22282 | −0.227074 | −0.113537 | − | 0.993534i | \(-0.536218\pi\) | ||||
−0.113537 | + | 0.993534i | \(0.536218\pi\) | |||||||
\(752\) | −1.79320 | −0.0653912 | ||||||||
\(753\) | −5.91198 | −0.215445 | ||||||||
\(754\) | 59.2135 | 2.15643 | ||||||||
\(755\) | −66.7181 | −2.42812 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.9762 | 0.726047 | 0.363023 | − | 0.931780i | \(-0.381745\pi\) | ||||
0.363023 | + | 0.931780i | \(0.381745\pi\) | |||||||
\(758\) | 11.8065 | 0.428830 | ||||||||
\(759\) | −0.860277 | −0.0312261 | ||||||||
\(760\) | 3.46130 | 0.125555 | ||||||||
\(761\) | 15.3054 | 0.554822 | 0.277411 | − | 0.960751i | \(-0.410524\pi\) | ||||
0.277411 | + | 0.960751i | \(0.410524\pi\) | |||||||
\(762\) | −3.45699 | −0.125233 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −10.9479 | −0.396080 | ||||||||
\(765\) | −20.0670 | −0.725522 | ||||||||
\(766\) | −5.52639 | −0.199677 | ||||||||
\(767\) | −53.9600 | −1.94838 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −18.0461 | −0.650761 | −0.325380 | − | 0.945583i | \(-0.605492\pi\) | ||||
−0.325380 | + | 0.945583i | \(0.605492\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.40485 | −0.0505943 | ||||||||
\(772\) | 21.2899 | 0.766240 | ||||||||
\(773\) | −40.2781 | −1.44870 | −0.724351 | − | 0.689432i | \(-0.757860\pi\) | ||||
−0.724351 | + | 0.689432i | \(0.757860\pi\) | |||||||
\(774\) | −10.3705 | −0.372761 | ||||||||
\(775\) | 51.3047 | 1.84292 | ||||||||
\(776\) | −4.09233 | −0.146906 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.26421 | −0.0453241 | ||||||||
\(779\) | 8.88553 | 0.318357 | ||||||||
\(780\) | 23.9612 | 0.857950 | ||||||||
\(781\) | 0.190489 | 0.00681622 | ||||||||
\(782\) | −17.9278 | −0.641098 | ||||||||
\(783\) | 8.55364 | 0.305682 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 74.2687 | 2.65076 | ||||||||
\(786\) | 18.4956 | 0.659717 | ||||||||
\(787\) | −22.2856 | −0.794395 | −0.397198 | − | 0.917733i | \(-0.630017\pi\) | ||||
−0.397198 | + | 0.917733i | \(0.630017\pi\) | |||||||
\(788\) | −6.63103 | −0.236221 | ||||||||
\(789\) | 10.7781 | 0.383712 | ||||||||
\(790\) | 4.87215 | 0.173343 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −0.278197 | −0.00988529 | ||||||||
\(793\) | 63.1993 | 2.24427 | ||||||||
\(794\) | 1.40485 | 0.0498562 | ||||||||
\(795\) | 29.0342 | 1.02974 | ||||||||
\(796\) | −7.87047 | −0.278961 | ||||||||
\(797\) | −11.6159 | −0.411457 | −0.205728 | − | 0.978609i | \(-0.565956\pi\) | ||||
−0.205728 | + | 0.978609i | \(0.565956\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.3961 | −0.367787 | ||||||||
\(800\) | −6.98062 | −0.246802 | ||||||||
\(801\) | −13.7007 | −0.484092 | ||||||||
\(802\) | 4.77119 | 0.168476 | ||||||||
\(803\) | −0.535630 | −0.0189020 | ||||||||
\(804\) | 13.7378 | 0.484495 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −50.8783 | −1.79211 | ||||||||
\(807\) | −22.4462 | −0.790145 | ||||||||
\(808\) | 2.45699 | 0.0864365 | ||||||||
\(809\) | −21.9957 | −0.773327 | −0.386664 | − | 0.922221i | \(-0.626373\pi\) | ||||
−0.386664 | + | 0.922221i | \(0.626373\pi\) | |||||||
\(810\) | 3.46130 | 0.121618 | ||||||||
\(811\) | 24.2399 | 0.851177 | 0.425588 | − | 0.904917i | \(-0.360067\pi\) | ||||
0.425588 | + | 0.904917i | \(0.360067\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.27651 | 0.0798408 | ||||||||
\(814\) | 1.45806 | 0.0511051 | ||||||||
\(815\) | −55.1892 | −1.93319 | ||||||||
\(816\) | −5.79751 | −0.202954 | ||||||||
\(817\) | 10.3705 | 0.362819 | ||||||||
\(818\) | 18.0890 | 0.632466 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −30.7555 | −1.07403 | ||||||||
\(821\) | −13.4332 | −0.468821 | −0.234410 | − | 0.972138i | \(-0.575316\pi\) | ||||
−0.234410 | + | 0.972138i | \(0.575316\pi\) | |||||||
\(822\) | −12.1680 | −0.424409 | ||||||||
\(823\) | 9.53653 | 0.332423 | 0.166211 | − | 0.986090i | \(-0.446847\pi\) | ||||
0.166211 | + | 0.986090i | \(0.446847\pi\) | |||||||
\(824\) | −17.3468 | −0.604306 | ||||||||
\(825\) | −1.94199 | −0.0676113 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 46.7140 | 1.62440 | 0.812202 | − | 0.583376i | \(-0.198268\pi\) | ||||
0.812202 | + | 0.583376i | \(0.198268\pi\) | |||||||
\(828\) | 3.09233 | 0.107466 | ||||||||
\(829\) | 17.3276 | 0.601812 | 0.300906 | − | 0.953654i | \(-0.402711\pi\) | ||||
0.300906 | + | 0.953654i | \(0.402711\pi\) | |||||||
\(830\) | −0.505454 | −0.0175446 | ||||||||
\(831\) | −27.4521 | −0.952302 | ||||||||
\(832\) | 6.92261 | 0.239998 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −2.91829 | −0.101052 | ||||||||
\(835\) | −60.9443 | −2.10907 | ||||||||
\(836\) | 0.278197 | 0.00962164 | ||||||||
\(837\) | −7.34959 | −0.254039 | ||||||||
\(838\) | −2.70518 | −0.0934490 | ||||||||
\(839\) | −26.5740 | −0.917435 | −0.458718 | − | 0.888582i | \(-0.651691\pi\) | ||||
−0.458718 | + | 0.888582i | \(0.651691\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 44.1647 | 1.52292 | ||||||||
\(842\) | −6.14064 | −0.211620 | ||||||||
\(843\) | −8.14279 | −0.280453 | ||||||||
\(844\) | 14.9123 | 0.513302 | ||||||||
\(845\) | −120.877 | −4.15831 | ||||||||
\(846\) | 1.79320 | 0.0616514 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 8.38823 | 0.288053 | ||||||||
\(849\) | 8.18586 | 0.280938 | ||||||||
\(850\) | −40.4702 | −1.38812 | ||||||||
\(851\) | −16.2073 | −0.555579 | ||||||||
\(852\) | −0.684727 | −0.0234583 | ||||||||
\(853\) | −4.35464 | −0.149100 | −0.0745500 | − | 0.997217i | \(-0.523752\pi\) | ||||
−0.0745500 | + | 0.997217i | \(0.523752\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.46130 | −0.118374 | ||||||||
\(856\) | 11.4779 | 0.392307 | ||||||||
\(857\) | −44.7011 | −1.52696 | −0.763480 | − | 0.645832i | \(-0.776511\pi\) | ||||
−0.763480 | + | 0.645832i | \(0.776511\pi\) | |||||||
\(858\) | 1.92585 | 0.0657473 | ||||||||
\(859\) | 5.42050 | 0.184945 | 0.0924726 | − | 0.995715i | \(-0.470523\pi\) | ||||
0.0924726 | + | 0.995715i | \(0.470523\pi\) | |||||||
\(860\) | −35.8955 | −1.22403 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −21.2765 | −0.724681 | ||||||||
\(863\) | −41.7588 | −1.42148 | −0.710742 | − | 0.703453i | \(-0.751641\pi\) | ||||
−0.710742 | + | 0.703453i | \(0.751641\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −34.6498 | −1.17813 | ||||||||
\(866\) | 9.42099 | 0.320138 | ||||||||
\(867\) | −16.6112 | −0.564145 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.391591 | 0.0132838 | ||||||||
\(870\) | 29.6067 | 1.00376 | ||||||||
\(871\) | −95.1015 | −3.22239 | ||||||||
\(872\) | 18.6814 | 0.632631 | ||||||||
\(873\) | 4.09233 | 0.138504 | ||||||||
\(874\) | −3.09233 | −0.104600 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.92536 | 0.0650520 | ||||||||
\(877\) | 35.9401 | 1.21361 | 0.606805 | − | 0.794851i | \(-0.292451\pi\) | ||||
0.606805 | + | 0.794851i | \(0.292451\pi\) | |||||||
\(878\) | −12.5924 | −0.424973 | ||||||||
\(879\) | 19.3421 | 0.652392 | ||||||||
\(880\) | −0.962923 | −0.0324601 | ||||||||
\(881\) | 49.3541 | 1.66278 | 0.831391 | − | 0.555688i | \(-0.187545\pi\) | ||||
0.831391 | + | 0.555688i | \(0.187545\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.0927 | 0.406951 | 0.203476 | − | 0.979080i | \(-0.434776\pi\) | ||||
0.203476 | + | 0.979080i | \(0.434776\pi\) | |||||||
\(884\) | 40.1339 | 1.34985 | ||||||||
\(885\) | −26.9800 | −0.906923 | ||||||||
\(886\) | 23.2947 | 0.782601 | ||||||||
\(887\) | 27.5621 | 0.925445 | 0.462722 | − | 0.886503i | \(-0.346873\pi\) | ||||
0.462722 | + | 0.886503i | \(0.346873\pi\) | |||||||
\(888\) | −5.24112 | −0.175880 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −47.4224 | −1.58960 | ||||||||
\(891\) | 0.278197 | 0.00931994 | ||||||||
\(892\) | 3.92861 | 0.131539 | ||||||||
\(893\) | −1.79320 | −0.0600071 | ||||||||
\(894\) | −4.16493 | −0.139296 | ||||||||
\(895\) | −21.6637 | −0.724136 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −21.4070 | −0.714759 | ||||||||
\(898\) | 0.486074 | 0.0162205 | ||||||||
\(899\) | −62.8657 | −2.09669 | ||||||||
\(900\) | 6.98062 | 0.232687 | ||||||||
\(901\) | 48.6309 | 1.62013 | ||||||||
\(902\) | −2.47193 | −0.0823061 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.29913 | −0.109728 | ||||||||
\(905\) | 14.7112 | 0.489016 | ||||||||
\(906\) | 19.2754 | 0.640384 | ||||||||
\(907\) | 40.3679 | 1.34039 | 0.670197 | − | 0.742183i | \(-0.266210\pi\) | ||||
0.670197 | + | 0.742183i | \(0.266210\pi\) | |||||||
\(908\) | −7.03971 | −0.233621 | ||||||||
\(909\) | −2.45699 | −0.0814931 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.02988 | −0.199779 | −0.0998894 | − | 0.994999i | \(-0.531849\pi\) | ||||
−0.0998894 | + | 0.994999i | \(0.531849\pi\) | |||||||
\(912\) | −1.00000 | −0.0331133 | ||||||||
\(913\) | −0.0406251 | −0.00134449 | ||||||||
\(914\) | −14.4597 | −0.478286 | ||||||||
\(915\) | 31.5997 | 1.04465 | ||||||||
\(916\) | 5.88397 | 0.194412 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 5.79751 | 0.191346 | ||||||||
\(919\) | 51.5149 | 1.69932 | 0.849659 | − | 0.527332i | \(-0.176807\pi\) | ||||
0.849659 | + | 0.527332i | \(0.176807\pi\) | |||||||
\(920\) | 10.7035 | 0.352884 | ||||||||
\(921\) | 11.7007 | 0.385553 | ||||||||
\(922\) | −18.0188 | −0.593417 | ||||||||
\(923\) | 4.74009 | 0.156022 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −36.5863 | −1.20295 | ||||||||
\(926\) | −23.3408 | −0.767027 | ||||||||
\(927\) | 17.3468 | 0.569745 | ||||||||
\(928\) | 8.55364 | 0.280787 | ||||||||
\(929\) | −8.68537 | −0.284958 | −0.142479 | − | 0.989798i | \(-0.545507\pi\) | ||||
−0.142479 | + | 0.989798i | \(0.545507\pi\) | |||||||
\(930\) | −25.4392 | −0.834183 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 2.80658 | 0.0919326 | ||||||||
\(933\) | −13.8555 | −0.453610 | ||||||||
\(934\) | 8.14879 | 0.266636 | ||||||||
\(935\) | −5.58256 | −0.182569 | ||||||||
\(936\) | −6.92261 | −0.226272 | ||||||||
\(937\) | −59.2801 | −1.93660 | −0.968298 | − | 0.249799i | \(-0.919635\pi\) | ||||
−0.968298 | + | 0.249799i | \(0.919635\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.97199 | 0.0643534 | ||||||||
\(940\) | 6.20680 | 0.202444 | ||||||||
\(941\) | −14.2282 | −0.463825 | −0.231913 | − | 0.972737i | \(-0.574498\pi\) | ||||
−0.231913 | + | 0.972737i | \(0.574498\pi\) | |||||||
\(942\) | −21.4569 | −0.699102 | ||||||||
\(943\) | 27.4770 | 0.894775 | ||||||||
\(944\) | −7.79476 | −0.253698 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.88505 | −0.0938010 | ||||||||
\(947\) | 15.6081 | 0.507194 | 0.253597 | − | 0.967310i | \(-0.418386\pi\) | ||||
0.253597 | + | 0.967310i | \(0.418386\pi\) | |||||||
\(948\) | −1.40761 | −0.0457169 | ||||||||
\(949\) | −13.3285 | −0.432663 | ||||||||
\(950\) | −6.98062 | −0.226481 | ||||||||
\(951\) | −19.9005 | −0.645317 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.11279 | 0.295192 | 0.147596 | − | 0.989048i | \(-0.452846\pi\) | ||||
0.147596 | + | 0.989048i | \(0.452846\pi\) | |||||||
\(954\) | −8.38823 | −0.271579 | ||||||||
\(955\) | 37.8939 | 1.22622 | ||||||||
\(956\) | −12.4016 | −0.401097 | ||||||||
\(957\) | 2.37959 | 0.0769213 | ||||||||
\(958\) | −27.1627 | −0.877585 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 3.46130 | 0.111713 | ||||||||
\(961\) | 23.0165 | 0.742468 | ||||||||
\(962\) | 36.2822 | 1.16979 | ||||||||
\(963\) | −11.4779 | −0.369871 | ||||||||
\(964\) | −15.1965 | −0.489446 | ||||||||
\(965\) | −73.6908 | −2.37219 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.04494 | −0.130077 | −0.0650383 | − | 0.997883i | \(-0.520717\pi\) | ||||
−0.0650383 | + | 0.997883i | \(0.520717\pi\) | |||||||
\(968\) | 10.9226 | 0.351066 | ||||||||
\(969\) | −5.79751 | −0.186243 | ||||||||
\(970\) | 14.1648 | 0.454804 | ||||||||
\(971\) | 18.0859 | 0.580403 | 0.290201 | − | 0.956966i | \(-0.406278\pi\) | ||||
0.290201 | + | 0.956966i | \(0.406278\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 11.9423 | 0.382657 | ||||||||
\(975\) | −48.3241 | −1.54761 | ||||||||
\(976\) | 9.12941 | 0.292225 | ||||||||
\(977\) | −43.1513 | −1.38053 | −0.690266 | − | 0.723556i | \(-0.742507\pi\) | ||||
−0.690266 | + | 0.723556i | \(0.742507\pi\) | |||||||
\(978\) | 15.9446 | 0.509853 | ||||||||
\(979\) | −3.81150 | −0.121816 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −18.6814 | −0.596450 | ||||||||
\(982\) | 7.00863 | 0.223654 | ||||||||
\(983\) | −31.5917 | −1.00762 | −0.503809 | − | 0.863815i | \(-0.668068\pi\) | ||||
−0.503809 | + | 0.863815i | \(0.668068\pi\) | |||||||
\(984\) | 8.88553 | 0.283260 | ||||||||
\(985\) | 22.9520 | 0.731312 | ||||||||
\(986\) | 49.5898 | 1.57926 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6.92261 | 0.220237 | ||||||||
\(989\) | 32.0691 | 1.01974 | ||||||||
\(990\) | 0.962923 | 0.0306037 | ||||||||
\(991\) | 36.7951 | 1.16883 | 0.584417 | − | 0.811453i | \(-0.301323\pi\) | ||||
0.584417 | + | 0.811453i | \(0.301323\pi\) | |||||||
\(992\) | −7.34959 | −0.233350 | ||||||||
\(993\) | 4.66762 | 0.148123 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 27.2421 | 0.863632 | ||||||||
\(996\) | 0.146030 | 0.00462714 | ||||||||
\(997\) | −42.3123 | −1.34005 | −0.670023 | − | 0.742341i | \(-0.733716\pi\) | ||||
−0.670023 | + | 0.742341i | \(0.733716\pi\) | |||||||
\(998\) | 9.12604 | 0.288880 | ||||||||
\(999\) | 5.24112 | 0.165822 |
(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 | 5586.2.a.bw.1.1 | 4 | ||
7.2 | even | 3 | 798.2.j.l.571.4 | yes | 8 | ||
7.4 | even | 3 | 798.2.j.l.457.4 | ✓ | 8 | ||
7.6 | odd | 2 | 5586.2.a.bz.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
798.2.j.l.457.4 | ✓ | 8 | 7.4 | even | 3 | ||
798.2.j.l.571.4 | yes | 8 | 7.2 | even | 3 | ||
5586.2.a.bw.1.1 | 4 | 1.1 | even | 1 | trivial | ||
5586.2.a.bz.1.4 | 4 | 7.6 | odd | 2 |