Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8027,2,Mod(1,8027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8027, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8027 = 23 \cdot 349 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8027.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.0959177025\) |
Analytic rank: | \(1\) |
Dimension: | \(143\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 8027.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.59213 | −1.83292 | −0.916458 | − | 0.400131i | \(-0.868965\pi\) | ||||
−0.916458 | + | 0.400131i | \(0.868965\pi\) | |||||||
\(3\) | 0.439138 | 0.253536 | 0.126768 | − | 0.991932i | \(-0.459540\pi\) | ||||
0.126768 | + | 0.991932i | \(0.459540\pi\) | |||||||
\(4\) | 4.71916 | 2.35958 | ||||||||
\(5\) | 1.76571 | 0.789652 | 0.394826 | − | 0.918756i | \(-0.370805\pi\) | ||||
0.394826 | + | 0.918756i | \(0.370805\pi\) | |||||||
\(6\) | −1.13830 | −0.464711 | ||||||||
\(7\) | 3.87571 | 1.46488 | 0.732440 | − | 0.680832i | \(-0.238382\pi\) | ||||
0.732440 | + | 0.680832i | \(0.238382\pi\) | |||||||
\(8\) | −7.04843 | −2.49200 | ||||||||
\(9\) | −2.80716 | −0.935719 | ||||||||
\(10\) | −4.57697 | −1.44736 | ||||||||
\(11\) | −0.425064 | −0.128162 | −0.0640809 | − | 0.997945i | \(-0.520412\pi\) | ||||
−0.0640809 | + | 0.997945i | \(0.520412\pi\) | |||||||
\(12\) | 2.07236 | 0.598239 | ||||||||
\(13\) | 2.93224 | 0.813257 | 0.406629 | − | 0.913594i | \(-0.366704\pi\) | ||||
0.406629 | + | 0.913594i | \(0.366704\pi\) | |||||||
\(14\) | −10.0464 | −2.68500 | ||||||||
\(15\) | 0.775392 | 0.200205 | ||||||||
\(16\) | 8.83216 | 2.20804 | ||||||||
\(17\) | 3.85408 | 0.934753 | 0.467376 | − | 0.884058i | \(-0.345199\pi\) | ||||
0.467376 | + | 0.884058i | \(0.345199\pi\) | |||||||
\(18\) | 7.27653 | 1.71509 | ||||||||
\(19\) | −5.95740 | −1.36672 | −0.683360 | − | 0.730081i | \(-0.739482\pi\) | ||||
−0.683360 | + | 0.730081i | \(0.739482\pi\) | |||||||
\(20\) | 8.33269 | 1.86325 | ||||||||
\(21\) | 1.70197 | 0.371400 | ||||||||
\(22\) | 1.10182 | 0.234910 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | −3.09523 | −0.631811 | ||||||||
\(25\) | −1.88225 | −0.376450 | ||||||||
\(26\) | −7.60076 | −1.49063 | ||||||||
\(27\) | −2.55014 | −0.490775 | ||||||||
\(28\) | 18.2901 | 3.45650 | ||||||||
\(29\) | 1.41876 | 0.263457 | 0.131728 | − | 0.991286i | \(-0.457947\pi\) | ||||
0.131728 | + | 0.991286i | \(0.457947\pi\) | |||||||
\(30\) | −2.00992 | −0.366959 | ||||||||
\(31\) | −3.04581 | −0.547043 | −0.273522 | − | 0.961866i | \(-0.588189\pi\) | ||||
−0.273522 | + | 0.961866i | \(0.588189\pi\) | |||||||
\(32\) | −8.79728 | −1.55515 | ||||||||
\(33\) | −0.186662 | −0.0324936 | ||||||||
\(34\) | −9.99030 | −1.71332 | ||||||||
\(35\) | 6.84339 | 1.15674 | ||||||||
\(36\) | −13.2474 | −2.20791 | ||||||||
\(37\) | −6.61404 | −1.08734 | −0.543671 | − | 0.839299i | \(-0.682966\pi\) | ||||
−0.543671 | + | 0.839299i | \(0.682966\pi\) | |||||||
\(38\) | 15.4424 | 2.50508 | ||||||||
\(39\) | 1.28766 | 0.206190 | ||||||||
\(40\) | −12.4455 | −1.96781 | ||||||||
\(41\) | −6.83451 | −1.06737 | −0.533686 | − | 0.845683i | \(-0.679194\pi\) | ||||
−0.533686 | + | 0.845683i | \(0.679194\pi\) | |||||||
\(42\) | −4.41173 | −0.680745 | ||||||||
\(43\) | −8.75390 | −1.33496 | −0.667478 | − | 0.744629i | \(-0.732626\pi\) | ||||
−0.667478 | + | 0.744629i | \(0.732626\pi\) | |||||||
\(44\) | −2.00595 | −0.302408 | ||||||||
\(45\) | −4.95664 | −0.738892 | ||||||||
\(46\) | −2.59213 | −0.382189 | ||||||||
\(47\) | 9.05510 | 1.32082 | 0.660411 | − | 0.750904i | \(-0.270382\pi\) | ||||
0.660411 | + | 0.750904i | \(0.270382\pi\) | |||||||
\(48\) | 3.87853 | 0.559818 | ||||||||
\(49\) | 8.02110 | 1.14587 | ||||||||
\(50\) | 4.87905 | 0.690002 | ||||||||
\(51\) | 1.69247 | 0.236994 | ||||||||
\(52\) | 13.8377 | 1.91895 | ||||||||
\(53\) | −11.2826 | −1.54978 | −0.774891 | − | 0.632095i | \(-0.782195\pi\) | ||||
−0.774891 | + | 0.632095i | \(0.782195\pi\) | |||||||
\(54\) | 6.61031 | 0.899549 | ||||||||
\(55\) | −0.750542 | −0.101203 | ||||||||
\(56\) | −27.3176 | −3.65047 | ||||||||
\(57\) | −2.61612 | −0.346513 | ||||||||
\(58\) | −3.67761 | −0.482894 | ||||||||
\(59\) | 0.400990 | 0.0522044 | 0.0261022 | − | 0.999659i | \(-0.491690\pi\) | ||||
0.0261022 | + | 0.999659i | \(0.491690\pi\) | |||||||
\(60\) | 3.65920 | 0.472400 | ||||||||
\(61\) | −8.12831 | −1.04072 | −0.520362 | − | 0.853946i | \(-0.674203\pi\) | ||||
−0.520362 | + | 0.853946i | \(0.674203\pi\) | |||||||
\(62\) | 7.89514 | 1.00268 | ||||||||
\(63\) | −10.8797 | −1.37072 | ||||||||
\(64\) | 5.13941 | 0.642426 | ||||||||
\(65\) | 5.17750 | 0.642190 | ||||||||
\(66\) | 0.483852 | 0.0595581 | ||||||||
\(67\) | −3.52526 | −0.430679 | −0.215340 | − | 0.976539i | \(-0.569086\pi\) | ||||
−0.215340 | + | 0.976539i | \(0.569086\pi\) | |||||||
\(68\) | 18.1880 | 2.20562 | ||||||||
\(69\) | 0.439138 | 0.0528660 | ||||||||
\(70\) | −17.7390 | −2.12021 | ||||||||
\(71\) | −12.9178 | −1.53306 | −0.766532 | − | 0.642206i | \(-0.778019\pi\) | ||||
−0.766532 | + | 0.642206i | \(0.778019\pi\) | |||||||
\(72\) | 19.7861 | 2.33181 | ||||||||
\(73\) | 14.0257 | 1.64159 | 0.820795 | − | 0.571223i | \(-0.193531\pi\) | ||||
0.820795 | + | 0.571223i | \(0.193531\pi\) | |||||||
\(74\) | 17.1445 | 1.99301 | ||||||||
\(75\) | −0.826568 | −0.0954438 | ||||||||
\(76\) | −28.1139 | −3.22489 | ||||||||
\(77\) | −1.64742 | −0.187741 | ||||||||
\(78\) | −3.33778 | −0.377929 | ||||||||
\(79\) | −13.4192 | −1.50978 | −0.754889 | − | 0.655852i | \(-0.772309\pi\) | ||||
−0.754889 | + | 0.655852i | \(0.772309\pi\) | |||||||
\(80\) | 15.5951 | 1.74358 | ||||||||
\(81\) | 7.30161 | 0.811290 | ||||||||
\(82\) | 17.7160 | 1.95640 | ||||||||
\(83\) | 13.2891 | 1.45867 | 0.729337 | − | 0.684155i | \(-0.239829\pi\) | ||||
0.729337 | + | 0.684155i | \(0.239829\pi\) | |||||||
\(84\) | 8.03186 | 0.876348 | ||||||||
\(85\) | 6.80521 | 0.738129 | ||||||||
\(86\) | 22.6913 | 2.44686 | ||||||||
\(87\) | 0.623030 | 0.0667958 | ||||||||
\(88\) | 2.99604 | 0.319379 | ||||||||
\(89\) | −10.5444 | −1.11770 | −0.558851 | − | 0.829268i | \(-0.688758\pi\) | ||||
−0.558851 | + | 0.829268i | \(0.688758\pi\) | |||||||
\(90\) | 12.8483 | 1.35433 | ||||||||
\(91\) | 11.3645 | 1.19132 | ||||||||
\(92\) | 4.71916 | 0.492007 | ||||||||
\(93\) | −1.33753 | −0.138695 | ||||||||
\(94\) | −23.4720 | −2.42096 | ||||||||
\(95\) | −10.5191 | −1.07923 | ||||||||
\(96\) | −3.86321 | −0.394288 | ||||||||
\(97\) | 11.7938 | 1.19748 | 0.598738 | − | 0.800945i | \(-0.295669\pi\) | ||||
0.598738 | + | 0.800945i | \(0.295669\pi\) | |||||||
\(98\) | −20.7918 | −2.10029 | ||||||||
\(99\) | 1.19322 | 0.119923 | ||||||||
\(100\) | −8.88265 | −0.888265 | ||||||||
\(101\) | −5.96673 | −0.593712 | −0.296856 | − | 0.954922i | \(-0.595938\pi\) | ||||
−0.296856 | + | 0.954922i | \(0.595938\pi\) | |||||||
\(102\) | −4.38712 | −0.434389 | ||||||||
\(103\) | 4.87692 | 0.480537 | 0.240269 | − | 0.970706i | \(-0.422765\pi\) | ||||
0.240269 | + | 0.970706i | \(0.422765\pi\) | |||||||
\(104\) | −20.6677 | −2.02663 | ||||||||
\(105\) | 3.00519 | 0.293277 | ||||||||
\(106\) | 29.2460 | 2.84062 | ||||||||
\(107\) | −14.5181 | −1.40352 | −0.701761 | − | 0.712412i | \(-0.747603\pi\) | ||||
−0.701761 | + | 0.712412i | \(0.747603\pi\) | |||||||
\(108\) | −12.0345 | −1.15802 | ||||||||
\(109\) | −13.5994 | −1.30259 | −0.651295 | − | 0.758825i | \(-0.725774\pi\) | ||||
−0.651295 | + | 0.758825i | \(0.725774\pi\) | |||||||
\(110\) | 1.94551 | 0.185497 | ||||||||
\(111\) | −2.90447 | −0.275680 | ||||||||
\(112\) | 34.2308 | 3.23451 | ||||||||
\(113\) | 7.18318 | 0.675737 | 0.337868 | − | 0.941193i | \(-0.390294\pi\) | ||||
0.337868 | + | 0.941193i | \(0.390294\pi\) | |||||||
\(114\) | 6.78133 | 0.635129 | ||||||||
\(115\) | 1.76571 | 0.164654 | ||||||||
\(116\) | 6.69534 | 0.621647 | ||||||||
\(117\) | −8.23126 | −0.760981 | ||||||||
\(118\) | −1.03942 | −0.0956863 | ||||||||
\(119\) | 14.9373 | 1.36930 | ||||||||
\(120\) | −5.46529 | −0.498911 | ||||||||
\(121\) | −10.8193 | −0.983575 | ||||||||
\(122\) | 21.0697 | 1.90756 | ||||||||
\(123\) | −3.00129 | −0.270617 | ||||||||
\(124\) | −14.3737 | −1.29079 | ||||||||
\(125\) | −12.1521 | −1.08692 | ||||||||
\(126\) | 28.2017 | 2.51241 | ||||||||
\(127\) | −12.4260 | −1.10263 | −0.551317 | − | 0.834296i | \(-0.685874\pi\) | ||||
−0.551317 | + | 0.834296i | \(0.685874\pi\) | |||||||
\(128\) | 4.27251 | 0.377641 | ||||||||
\(129\) | −3.84417 | −0.338460 | ||||||||
\(130\) | −13.4208 | −1.17708 | ||||||||
\(131\) | 11.1298 | 0.972414 | 0.486207 | − | 0.873844i | \(-0.338380\pi\) | ||||
0.486207 | + | 0.873844i | \(0.338380\pi\) | |||||||
\(132\) | −0.880887 | −0.0766714 | ||||||||
\(133\) | −23.0891 | −2.00208 | ||||||||
\(134\) | 9.13795 | 0.789399 | ||||||||
\(135\) | −4.50282 | −0.387541 | ||||||||
\(136\) | −27.1652 | −2.32940 | ||||||||
\(137\) | 13.5842 | 1.16057 | 0.580286 | − | 0.814412i | \(-0.302941\pi\) | ||||
0.580286 | + | 0.814412i | \(0.302941\pi\) | |||||||
\(138\) | −1.13830 | −0.0968989 | ||||||||
\(139\) | −4.56980 | −0.387605 | −0.193803 | − | 0.981041i | \(-0.562082\pi\) | ||||
−0.193803 | + | 0.981041i | \(0.562082\pi\) | |||||||
\(140\) | 32.2951 | 2.72943 | ||||||||
\(141\) | 3.97643 | 0.334876 | ||||||||
\(142\) | 33.4847 | 2.80998 | ||||||||
\(143\) | −1.24639 | −0.104228 | ||||||||
\(144\) | −24.7933 | −2.06610 | ||||||||
\(145\) | 2.50512 | 0.208039 | ||||||||
\(146\) | −36.3566 | −3.00890 | ||||||||
\(147\) | 3.52237 | 0.290520 | ||||||||
\(148\) | −31.2127 | −2.56567 | ||||||||
\(149\) | 4.26014 | 0.349004 | 0.174502 | − | 0.984657i | \(-0.444168\pi\) | ||||
0.174502 | + | 0.984657i | \(0.444168\pi\) | |||||||
\(150\) | 2.14257 | 0.174940 | ||||||||
\(151\) | −11.6171 | −0.945386 | −0.472693 | − | 0.881227i | \(-0.656718\pi\) | ||||
−0.472693 | + | 0.881227i | \(0.656718\pi\) | |||||||
\(152\) | 41.9903 | 3.40586 | ||||||||
\(153\) | −10.8190 | −0.874666 | ||||||||
\(154\) | 4.27035 | 0.344114 | ||||||||
\(155\) | −5.37803 | −0.431974 | ||||||||
\(156\) | 6.07666 | 0.486522 | ||||||||
\(157\) | 0.863024 | 0.0688768 | 0.0344384 | − | 0.999407i | \(-0.489036\pi\) | ||||
0.0344384 | + | 0.999407i | \(0.489036\pi\) | |||||||
\(158\) | 34.7844 | 2.76730 | ||||||||
\(159\) | −4.95460 | −0.392926 | ||||||||
\(160\) | −15.5335 | −1.22803 | ||||||||
\(161\) | 3.87571 | 0.305448 | ||||||||
\(162\) | −18.9268 | −1.48703 | ||||||||
\(163\) | 14.8330 | 1.16181 | 0.580905 | − | 0.813971i | \(-0.302699\pi\) | ||||
0.580905 | + | 0.813971i | \(0.302699\pi\) | |||||||
\(164\) | −32.2532 | −2.51855 | ||||||||
\(165\) | −0.329591 | −0.0256587 | ||||||||
\(166\) | −34.4472 | −2.67362 | ||||||||
\(167\) | 1.94262 | 0.150325 | 0.0751624 | − | 0.997171i | \(-0.476052\pi\) | ||||
0.0751624 | + | 0.997171i | \(0.476052\pi\) | |||||||
\(168\) | −11.9962 | −0.925527 | ||||||||
\(169\) | −4.40197 | −0.338613 | ||||||||
\(170\) | −17.6400 | −1.35293 | ||||||||
\(171\) | 16.7234 | 1.27887 | ||||||||
\(172\) | −41.3110 | −3.14994 | ||||||||
\(173\) | −16.4012 | −1.24696 | −0.623482 | − | 0.781838i | \(-0.714282\pi\) | ||||
−0.623482 | + | 0.781838i | \(0.714282\pi\) | |||||||
\(174\) | −1.61498 | −0.122431 | ||||||||
\(175\) | −7.29506 | −0.551454 | ||||||||
\(176\) | −3.75423 | −0.282986 | ||||||||
\(177\) | 0.176090 | 0.0132357 | ||||||||
\(178\) | 27.3325 | 2.04865 | ||||||||
\(179\) | −8.86556 | −0.662643 | −0.331321 | − | 0.943518i | \(-0.607494\pi\) | ||||
−0.331321 | + | 0.943518i | \(0.607494\pi\) | |||||||
\(180\) | −23.3912 | −1.74348 | ||||||||
\(181\) | −9.59756 | −0.713381 | −0.356691 | − | 0.934223i | \(-0.616095\pi\) | ||||
−0.356691 | + | 0.934223i | \(0.616095\pi\) | |||||||
\(182\) | −29.4583 | −2.18360 | ||||||||
\(183\) | −3.56945 | −0.263861 | ||||||||
\(184\) | −7.04843 | −0.519617 | ||||||||
\(185\) | −11.6785 | −0.858621 | ||||||||
\(186\) | 3.46706 | 0.254217 | ||||||||
\(187\) | −1.63823 | −0.119800 | ||||||||
\(188\) | 42.7325 | 3.11659 | ||||||||
\(189\) | −9.88360 | −0.718926 | ||||||||
\(190\) | 27.2668 | 1.97814 | ||||||||
\(191\) | −9.66206 | −0.699122 | −0.349561 | − | 0.936914i | \(-0.613669\pi\) | ||||
−0.349561 | + | 0.936914i | \(0.613669\pi\) | |||||||
\(192\) | 2.25691 | 0.162878 | ||||||||
\(193\) | 7.16520 | 0.515763 | 0.257881 | − | 0.966177i | \(-0.416976\pi\) | ||||
0.257881 | + | 0.966177i | \(0.416976\pi\) | |||||||
\(194\) | −30.5710 | −2.19487 | ||||||||
\(195\) | 2.27364 | 0.162818 | ||||||||
\(196\) | 37.8529 | 2.70378 | ||||||||
\(197\) | −24.4627 | −1.74289 | −0.871447 | − | 0.490491i | \(-0.836818\pi\) | ||||
−0.871447 | + | 0.490491i | \(0.836818\pi\) | |||||||
\(198\) | −3.09299 | −0.219809 | ||||||||
\(199\) | −7.77121 | −0.550887 | −0.275443 | − | 0.961317i | \(-0.588825\pi\) | ||||
−0.275443 | + | 0.961317i | \(0.588825\pi\) | |||||||
\(200\) | 13.2669 | 0.938113 | ||||||||
\(201\) | −1.54807 | −0.109193 | ||||||||
\(202\) | 15.4666 | 1.08822 | ||||||||
\(203\) | 5.49869 | 0.385932 | ||||||||
\(204\) | 7.98705 | 0.559206 | ||||||||
\(205\) | −12.0678 | −0.842852 | ||||||||
\(206\) | −12.6416 | −0.880784 | ||||||||
\(207\) | −2.80716 | −0.195111 | ||||||||
\(208\) | 25.8980 | 1.79570 | ||||||||
\(209\) | 2.53228 | 0.175161 | ||||||||
\(210\) | −7.78986 | −0.537551 | ||||||||
\(211\) | −2.69766 | −0.185714 | −0.0928572 | − | 0.995679i | \(-0.529600\pi\) | ||||
−0.0928572 | + | 0.995679i | \(0.529600\pi\) | |||||||
\(212\) | −53.2443 | −3.65683 | ||||||||
\(213\) | −5.67270 | −0.388687 | ||||||||
\(214\) | 37.6330 | 2.57254 | ||||||||
\(215\) | −15.4569 | −1.05415 | ||||||||
\(216\) | 17.9745 | 1.22301 | ||||||||
\(217\) | −11.8047 | −0.801352 | ||||||||
\(218\) | 35.2516 | 2.38754 | ||||||||
\(219\) | 6.15923 | 0.416202 | ||||||||
\(220\) | −3.54193 | −0.238797 | ||||||||
\(221\) | 11.3011 | 0.760194 | ||||||||
\(222\) | 7.52879 | 0.505299 | ||||||||
\(223\) | −29.8109 | −1.99629 | −0.998143 | − | 0.0609141i | \(-0.980598\pi\) | ||||
−0.998143 | + | 0.0609141i | \(0.980598\pi\) | |||||||
\(224\) | −34.0957 | −2.27811 | ||||||||
\(225\) | 5.28378 | 0.352252 | ||||||||
\(226\) | −18.6198 | −1.23857 | ||||||||
\(227\) | 12.4237 | 0.824593 | 0.412296 | − | 0.911050i | \(-0.364727\pi\) | ||||
0.412296 | + | 0.911050i | \(0.364727\pi\) | |||||||
\(228\) | −12.3459 | −0.817626 | ||||||||
\(229\) | −3.69389 | −0.244099 | −0.122049 | − | 0.992524i | \(-0.538947\pi\) | ||||
−0.122049 | + | 0.992524i | \(0.538947\pi\) | |||||||
\(230\) | −4.57697 | −0.301796 | ||||||||
\(231\) | −0.723446 | −0.0475993 | ||||||||
\(232\) | −10.0000 | −0.656533 | ||||||||
\(233\) | 10.2924 | 0.674276 | 0.337138 | − | 0.941455i | \(-0.390541\pi\) | ||||
0.337138 | + | 0.941455i | \(0.390541\pi\) | |||||||
\(234\) | 21.3365 | 1.39481 | ||||||||
\(235\) | 15.9887 | 1.04299 | ||||||||
\(236\) | 1.89234 | 0.123181 | ||||||||
\(237\) | −5.89288 | −0.382784 | ||||||||
\(238\) | −38.7195 | −2.50981 | ||||||||
\(239\) | 2.98807 | 0.193282 | 0.0966410 | − | 0.995319i | \(-0.469190\pi\) | ||||
0.0966410 | + | 0.995319i | \(0.469190\pi\) | |||||||
\(240\) | 6.84838 | 0.442061 | ||||||||
\(241\) | −28.8211 | −1.85653 | −0.928266 | − | 0.371918i | \(-0.878700\pi\) | ||||
−0.928266 | + | 0.371918i | \(0.878700\pi\) | |||||||
\(242\) | 28.0451 | 1.80281 | ||||||||
\(243\) | 10.8568 | 0.696466 | ||||||||
\(244\) | −38.3588 | −2.45567 | ||||||||
\(245\) | 14.1630 | 0.904839 | ||||||||
\(246\) | 7.77975 | 0.496019 | ||||||||
\(247\) | −17.4685 | −1.11150 | ||||||||
\(248\) | 21.4682 | 1.36323 | ||||||||
\(249\) | 5.83576 | 0.369826 | ||||||||
\(250\) | 31.4999 | 1.99223 | ||||||||
\(251\) | 4.74170 | 0.299293 | 0.149647 | − | 0.988740i | \(-0.452186\pi\) | ||||
0.149647 | + | 0.988740i | \(0.452186\pi\) | |||||||
\(252\) | −51.3431 | −3.23431 | ||||||||
\(253\) | −0.425064 | −0.0267236 | ||||||||
\(254\) | 32.2100 | 2.02103 | ||||||||
\(255\) | 2.98843 | 0.187142 | ||||||||
\(256\) | −21.3537 | −1.33461 | ||||||||
\(257\) | 30.2429 | 1.88650 | 0.943249 | − | 0.332086i | \(-0.107752\pi\) | ||||
0.943249 | + | 0.332086i | \(0.107752\pi\) | |||||||
\(258\) | 9.96459 | 0.620369 | ||||||||
\(259\) | −25.6341 | −1.59282 | ||||||||
\(260\) | 24.4335 | 1.51530 | ||||||||
\(261\) | −3.98268 | −0.246522 | ||||||||
\(262\) | −28.8499 | −1.78235 | ||||||||
\(263\) | 18.3913 | 1.13406 | 0.567028 | − | 0.823699i | \(-0.308093\pi\) | ||||
0.567028 | + | 0.823699i | \(0.308093\pi\) | |||||||
\(264\) | 1.31567 | 0.0809740 | ||||||||
\(265\) | −19.9218 | −1.22379 | ||||||||
\(266\) | 59.8501 | 3.66964 | ||||||||
\(267\) | −4.63044 | −0.283378 | ||||||||
\(268\) | −16.6363 | −1.01622 | ||||||||
\(269\) | −5.53956 | −0.337753 | −0.168876 | − | 0.985637i | \(-0.554014\pi\) | ||||
−0.168876 | + | 0.985637i | \(0.554014\pi\) | |||||||
\(270\) | 11.6719 | 0.710331 | ||||||||
\(271\) | 3.25775 | 0.197894 | 0.0989472 | − | 0.995093i | \(-0.468453\pi\) | ||||
0.0989472 | + | 0.995093i | \(0.468453\pi\) | |||||||
\(272\) | 34.0399 | 2.06397 | ||||||||
\(273\) | 4.99058 | 0.302044 | ||||||||
\(274\) | −35.2120 | −2.12723 | ||||||||
\(275\) | 0.800078 | 0.0482465 | ||||||||
\(276\) | 2.07236 | 0.124741 | ||||||||
\(277\) | −24.7134 | −1.48489 | −0.742443 | − | 0.669909i | \(-0.766333\pi\) | ||||
−0.742443 | + | 0.669909i | \(0.766333\pi\) | |||||||
\(278\) | 11.8455 | 0.710447 | ||||||||
\(279\) | 8.55007 | 0.511879 | ||||||||
\(280\) | −48.2352 | −2.88260 | ||||||||
\(281\) | 28.2987 | 1.68816 | 0.844078 | − | 0.536220i | \(-0.180148\pi\) | ||||
0.844078 | + | 0.536220i | \(0.180148\pi\) | |||||||
\(282\) | −10.3075 | −0.613800 | ||||||||
\(283\) | 2.21284 | 0.131539 | 0.0657697 | − | 0.997835i | \(-0.479050\pi\) | ||||
0.0657697 | + | 0.997835i | \(0.479050\pi\) | |||||||
\(284\) | −60.9613 | −3.61739 | ||||||||
\(285\) | −4.61932 | −0.273625 | ||||||||
\(286\) | 3.23081 | 0.191042 | ||||||||
\(287\) | −26.4886 | −1.56357 | ||||||||
\(288\) | 24.6953 | 1.45519 | ||||||||
\(289\) | −2.14604 | −0.126237 | ||||||||
\(290\) | −6.49361 | −0.381318 | ||||||||
\(291\) | 5.17908 | 0.303603 | ||||||||
\(292\) | 66.1898 | 3.87346 | ||||||||
\(293\) | −8.00948 | −0.467919 | −0.233959 | − | 0.972246i | \(-0.575168\pi\) | ||||
−0.233959 | + | 0.972246i | \(0.575168\pi\) | |||||||
\(294\) | −9.13045 | −0.532499 | ||||||||
\(295\) | 0.708033 | 0.0412233 | ||||||||
\(296\) | 46.6186 | 2.70965 | ||||||||
\(297\) | 1.08397 | 0.0628986 | ||||||||
\(298\) | −11.0428 | −0.639695 | ||||||||
\(299\) | 2.93224 | 0.169576 | ||||||||
\(300\) | −3.90071 | −0.225207 | ||||||||
\(301\) | −33.9275 | −1.95555 | ||||||||
\(302\) | 30.1131 | 1.73281 | ||||||||
\(303\) | −2.62022 | −0.150528 | ||||||||
\(304\) | −52.6166 | −3.01777 | ||||||||
\(305\) | −14.3523 | −0.821809 | ||||||||
\(306\) | 28.0444 | 1.60319 | ||||||||
\(307\) | −8.21705 | −0.468972 | −0.234486 | − | 0.972120i | \(-0.575341\pi\) | ||||
−0.234486 | + | 0.972120i | \(0.575341\pi\) | |||||||
\(308\) | −7.77446 | −0.442991 | ||||||||
\(309\) | 2.14164 | 0.121834 | ||||||||
\(310\) | 13.9406 | 0.791771 | ||||||||
\(311\) | 28.0492 | 1.59053 | 0.795263 | − | 0.606265i | \(-0.207333\pi\) | ||||
0.795263 | + | 0.606265i | \(0.207333\pi\) | |||||||
\(312\) | −9.07596 | −0.513825 | ||||||||
\(313\) | 17.3555 | 0.980990 | 0.490495 | − | 0.871444i | \(-0.336816\pi\) | ||||
0.490495 | + | 0.871444i | \(0.336816\pi\) | |||||||
\(314\) | −2.23707 | −0.126245 | ||||||||
\(315\) | −19.2105 | −1.08239 | ||||||||
\(316\) | −63.3274 | −3.56244 | ||||||||
\(317\) | −14.4181 | −0.809802 | −0.404901 | − | 0.914361i | \(-0.632694\pi\) | ||||
−0.404901 | + | 0.914361i | \(0.632694\pi\) | |||||||
\(318\) | 12.8430 | 0.720200 | ||||||||
\(319\) | −0.603063 | −0.0337651 | ||||||||
\(320\) | 9.07473 | 0.507293 | ||||||||
\(321\) | −6.37546 | −0.355844 | ||||||||
\(322\) | −10.0464 | −0.559861 | ||||||||
\(323\) | −22.9603 | −1.27755 | ||||||||
\(324\) | 34.4575 | 1.91430 | ||||||||
\(325\) | −5.51922 | −0.306151 | ||||||||
\(326\) | −38.4491 | −2.12950 | ||||||||
\(327\) | −5.97202 | −0.330254 | ||||||||
\(328\) | 48.1726 | 2.65989 | ||||||||
\(329\) | 35.0949 | 1.93484 | ||||||||
\(330\) | 0.854345 | 0.0470302 | ||||||||
\(331\) | 4.45217 | 0.244713 | 0.122357 | − | 0.992486i | \(-0.460955\pi\) | ||||
0.122357 | + | 0.992486i | \(0.460955\pi\) | |||||||
\(332\) | 62.7136 | 3.44186 | ||||||||
\(333\) | 18.5667 | 1.01745 | ||||||||
\(334\) | −5.03554 | −0.275533 | ||||||||
\(335\) | −6.22460 | −0.340086 | ||||||||
\(336\) | 15.0321 | 0.820066 | ||||||||
\(337\) | 8.86932 | 0.483142 | 0.241571 | − | 0.970383i | \(-0.422337\pi\) | ||||
0.241571 | + | 0.970383i | \(0.422337\pi\) | |||||||
\(338\) | 11.4105 | 0.620649 | ||||||||
\(339\) | 3.15441 | 0.171324 | ||||||||
\(340\) | 32.1149 | 1.74167 | ||||||||
\(341\) | 1.29466 | 0.0701100 | ||||||||
\(342\) | −43.3492 | −2.34405 | ||||||||
\(343\) | 3.95748 | 0.213684 | ||||||||
\(344\) | 61.7012 | 3.32671 | ||||||||
\(345\) | 0.775392 | 0.0417457 | ||||||||
\(346\) | 42.5142 | 2.28558 | ||||||||
\(347\) | 10.7000 | 0.574406 | 0.287203 | − | 0.957870i | \(-0.407275\pi\) | ||||
0.287203 | + | 0.957870i | \(0.407275\pi\) | |||||||
\(348\) | 2.94018 | 0.157610 | ||||||||
\(349\) | 1.00000 | 0.0535288 | ||||||||
\(350\) | 18.9098 | 1.01077 | ||||||||
\(351\) | −7.47763 | −0.399126 | ||||||||
\(352\) | 3.73941 | 0.199311 | ||||||||
\(353\) | −5.11838 | −0.272424 | −0.136212 | − | 0.990680i | \(-0.543493\pi\) | ||||
−0.136212 | + | 0.990680i | \(0.543493\pi\) | |||||||
\(354\) | −0.456448 | −0.0242599 | ||||||||
\(355\) | −22.8092 | −1.21059 | ||||||||
\(356\) | −49.7606 | −2.63731 | ||||||||
\(357\) | 6.55953 | 0.347167 | ||||||||
\(358\) | 22.9807 | 1.21457 | ||||||||
\(359\) | −3.49180 | −0.184290 | −0.0921450 | − | 0.995746i | \(-0.529372\pi\) | ||||
−0.0921450 | + | 0.995746i | \(0.529372\pi\) | |||||||
\(360\) | 34.9365 | 1.84132 | ||||||||
\(361\) | 16.4906 | 0.867924 | ||||||||
\(362\) | 24.8782 | 1.30757 | ||||||||
\(363\) | −4.75117 | −0.249372 | ||||||||
\(364\) | 53.6309 | 2.81102 | ||||||||
\(365\) | 24.7655 | 1.29628 | ||||||||
\(366\) | 9.25249 | 0.483635 | ||||||||
\(367\) | 7.67135 | 0.400441 | 0.200221 | − | 0.979751i | \(-0.435834\pi\) | ||||
0.200221 | + | 0.979751i | \(0.435834\pi\) | |||||||
\(368\) | 8.83216 | 0.460408 | ||||||||
\(369\) | 19.1856 | 0.998760 | ||||||||
\(370\) | 30.2723 | 1.57378 | ||||||||
\(371\) | −43.7280 | −2.27024 | ||||||||
\(372\) | −6.31201 | −0.327263 | ||||||||
\(373\) | 32.1620 | 1.66528 | 0.832642 | − | 0.553812i | \(-0.186828\pi\) | ||||
0.832642 | + | 0.553812i | \(0.186828\pi\) | |||||||
\(374\) | 4.24652 | 0.219582 | ||||||||
\(375\) | −5.33644 | −0.275573 | ||||||||
\(376\) | −63.8242 | −3.29148 | ||||||||
\(377\) | 4.16014 | 0.214258 | ||||||||
\(378\) | 25.6196 | 1.31773 | ||||||||
\(379\) | 30.7862 | 1.58138 | 0.790691 | − | 0.612215i | \(-0.209721\pi\) | ||||
0.790691 | + | 0.612215i | \(0.209721\pi\) | |||||||
\(380\) | −49.6411 | −2.54654 | ||||||||
\(381\) | −5.45675 | −0.279558 | ||||||||
\(382\) | 25.0453 | 1.28143 | ||||||||
\(383\) | 20.7997 | 1.06281 | 0.531407 | − | 0.847117i | \(-0.321664\pi\) | ||||
0.531407 | + | 0.847117i | \(0.321664\pi\) | |||||||
\(384\) | 1.87622 | 0.0957456 | ||||||||
\(385\) | −2.90888 | −0.148250 | ||||||||
\(386\) | −18.5732 | −0.945349 | ||||||||
\(387\) | 24.5736 | 1.24914 | ||||||||
\(388\) | 55.6567 | 2.82554 | ||||||||
\(389\) | 31.9910 | 1.62201 | 0.811005 | − | 0.585040i | \(-0.198921\pi\) | ||||
0.811005 | + | 0.585040i | \(0.198921\pi\) | |||||||
\(390\) | −5.89357 | −0.298432 | ||||||||
\(391\) | 3.85408 | 0.194909 | ||||||||
\(392\) | −56.5362 | −2.85551 | ||||||||
\(393\) | 4.88751 | 0.246542 | ||||||||
\(394\) | 63.4105 | 3.19458 | ||||||||
\(395\) | −23.6945 | −1.19220 | ||||||||
\(396\) | 5.63101 | 0.282969 | ||||||||
\(397\) | 20.2033 | 1.01397 | 0.506986 | − | 0.861954i | \(-0.330760\pi\) | ||||
0.506986 | + | 0.861954i | \(0.330760\pi\) | |||||||
\(398\) | 20.1440 | 1.00973 | ||||||||
\(399\) | −10.1393 | −0.507600 | ||||||||
\(400\) | −16.6243 | −0.831217 | ||||||||
\(401\) | 14.3564 | 0.716922 | 0.358461 | − | 0.933545i | \(-0.383302\pi\) | ||||
0.358461 | + | 0.933545i | \(0.383302\pi\) | |||||||
\(402\) | 4.01282 | 0.200141 | ||||||||
\(403\) | −8.93104 | −0.444887 | ||||||||
\(404\) | −28.1580 | −1.40091 | ||||||||
\(405\) | 12.8926 | 0.640637 | ||||||||
\(406\) | −14.2533 | −0.707381 | ||||||||
\(407\) | 2.81139 | 0.139356 | ||||||||
\(408\) | −11.9293 | −0.590587 | ||||||||
\(409\) | −12.3492 | −0.610631 | −0.305315 | − | 0.952251i | \(-0.598762\pi\) | ||||
−0.305315 | + | 0.952251i | \(0.598762\pi\) | |||||||
\(410\) | 31.2814 | 1.54488 | ||||||||
\(411\) | 5.96532 | 0.294247 | ||||||||
\(412\) | 23.0150 | 1.13387 | ||||||||
\(413\) | 1.55412 | 0.0764732 | ||||||||
\(414\) | 7.27653 | 0.357622 | ||||||||
\(415\) | 23.4648 | 1.15184 | ||||||||
\(416\) | −25.7957 | −1.26474 | ||||||||
\(417\) | −2.00677 | −0.0982719 | ||||||||
\(418\) | −6.56400 | −0.321056 | ||||||||
\(419\) | 16.2225 | 0.792519 | 0.396259 | − | 0.918139i | \(-0.370308\pi\) | ||||
0.396259 | + | 0.918139i | \(0.370308\pi\) | |||||||
\(420\) | 14.1820 | 0.692010 | ||||||||
\(421\) | −14.4575 | −0.704616 | −0.352308 | − | 0.935884i | \(-0.614603\pi\) | ||||
−0.352308 | + | 0.935884i | \(0.614603\pi\) | |||||||
\(422\) | 6.99269 | 0.340399 | ||||||||
\(423\) | −25.4191 | −1.23592 | ||||||||
\(424\) | 79.5245 | 3.86205 | ||||||||
\(425\) | −7.25436 | −0.351888 | ||||||||
\(426\) | 14.7044 | 0.712431 | ||||||||
\(427\) | −31.5029 | −1.52453 | ||||||||
\(428\) | −68.5135 | −3.31172 | ||||||||
\(429\) | −0.547337 | −0.0264257 | ||||||||
\(430\) | 40.0663 | 1.93217 | ||||||||
\(431\) | 20.3683 | 0.981104 | 0.490552 | − | 0.871412i | \(-0.336795\pi\) | ||||
0.490552 | + | 0.871412i | \(0.336795\pi\) | |||||||
\(432\) | −22.5232 | −1.08365 | ||||||||
\(433\) | 15.3641 | 0.738352 | 0.369176 | − | 0.929359i | \(-0.379640\pi\) | ||||
0.369176 | + | 0.929359i | \(0.379640\pi\) | |||||||
\(434\) | 30.5993 | 1.46881 | ||||||||
\(435\) | 1.10009 | 0.0527454 | ||||||||
\(436\) | −64.1779 | −3.07356 | ||||||||
\(437\) | −5.95740 | −0.284981 | ||||||||
\(438\) | −15.9656 | −0.762864 | ||||||||
\(439\) | −0.0606116 | −0.00289283 | −0.00144642 | − | 0.999999i | \(-0.500460\pi\) | ||||
−0.00144642 | + | 0.999999i | \(0.500460\pi\) | |||||||
\(440\) | 5.29014 | 0.252198 | ||||||||
\(441\) | −22.5165 | −1.07221 | ||||||||
\(442\) | −29.2940 | −1.39337 | ||||||||
\(443\) | −2.19885 | −0.104470 | −0.0522351 | − | 0.998635i | \(-0.516635\pi\) | ||||
−0.0522351 | + | 0.998635i | \(0.516635\pi\) | |||||||
\(444\) | −13.7067 | −0.650490 | ||||||||
\(445\) | −18.6184 | −0.882595 | ||||||||
\(446\) | 77.2739 | 3.65902 | ||||||||
\(447\) | 1.87079 | 0.0884852 | ||||||||
\(448\) | 19.9188 | 0.941077 | ||||||||
\(449\) | −23.4892 | −1.10852 | −0.554261 | − | 0.832343i | \(-0.686999\pi\) | ||||
−0.554261 | + | 0.832343i | \(0.686999\pi\) | |||||||
\(450\) | −13.6963 | −0.645648 | ||||||||
\(451\) | 2.90511 | 0.136796 | ||||||||
\(452\) | 33.8986 | 1.59446 | ||||||||
\(453\) | −5.10151 | −0.239690 | ||||||||
\(454\) | −32.2040 | −1.51141 | ||||||||
\(455\) | 20.0665 | 0.940731 | ||||||||
\(456\) | 18.4395 | 0.863509 | ||||||||
\(457\) | −5.61328 | −0.262578 | −0.131289 | − | 0.991344i | \(-0.541912\pi\) | ||||
−0.131289 | + | 0.991344i | \(0.541912\pi\) | |||||||
\(458\) | 9.57505 | 0.447413 | ||||||||
\(459\) | −9.82846 | −0.458753 | ||||||||
\(460\) | 8.33269 | 0.388514 | ||||||||
\(461\) | −3.60559 | −0.167929 | −0.0839646 | − | 0.996469i | \(-0.526758\pi\) | ||||
−0.0839646 | + | 0.996469i | \(0.526758\pi\) | |||||||
\(462\) | 1.87527 | 0.0872454 | ||||||||
\(463\) | 35.5565 | 1.65245 | 0.826226 | − | 0.563339i | \(-0.190484\pi\) | ||||
0.826226 | + | 0.563339i | \(0.190484\pi\) | |||||||
\(464\) | 12.5307 | 0.581723 | ||||||||
\(465\) | −2.36169 | −0.109521 | ||||||||
\(466\) | −26.6792 | −1.23589 | ||||||||
\(467\) | −19.0557 | −0.881795 | −0.440897 | − | 0.897558i | \(-0.645340\pi\) | ||||
−0.440897 | + | 0.897558i | \(0.645340\pi\) | |||||||
\(468\) | −38.8447 | −1.79559 | ||||||||
\(469\) | −13.6629 | −0.630893 | ||||||||
\(470\) | −41.4449 | −1.91171 | ||||||||
\(471\) | 0.378986 | 0.0174628 | ||||||||
\(472\) | −2.82635 | −0.130093 | ||||||||
\(473\) | 3.72097 | 0.171090 | ||||||||
\(474\) | 15.2751 | 0.701610 | ||||||||
\(475\) | 11.2133 | 0.514502 | ||||||||
\(476\) | 70.4915 | 3.23097 | ||||||||
\(477\) | 31.6720 | 1.45016 | ||||||||
\(478\) | −7.74547 | −0.354270 | ||||||||
\(479\) | 24.2724 | 1.10903 | 0.554517 | − | 0.832173i | \(-0.312903\pi\) | ||||
0.554517 | + | 0.832173i | \(0.312903\pi\) | |||||||
\(480\) | −6.82133 | −0.311350 | ||||||||
\(481\) | −19.3940 | −0.884288 | ||||||||
\(482\) | 74.7082 | 3.40287 | ||||||||
\(483\) | 1.70197 | 0.0774423 | ||||||||
\(484\) | −51.0581 | −2.32082 | ||||||||
\(485\) | 20.8244 | 0.945588 | ||||||||
\(486\) | −28.1424 | −1.27656 | ||||||||
\(487\) | 25.7034 | 1.16473 | 0.582367 | − | 0.812926i | \(-0.302127\pi\) | ||||
0.582367 | + | 0.812926i | \(0.302127\pi\) | |||||||
\(488\) | 57.2918 | 2.59348 | ||||||||
\(489\) | 6.51373 | 0.294561 | ||||||||
\(490\) | −36.7123 | −1.65849 | ||||||||
\(491\) | −35.2498 | −1.59080 | −0.795401 | − | 0.606084i | \(-0.792740\pi\) | ||||
−0.795401 | + | 0.606084i | \(0.792740\pi\) | |||||||
\(492\) | −14.1636 | −0.638544 | ||||||||
\(493\) | 5.46801 | 0.246267 | ||||||||
\(494\) | 45.2807 | 2.03728 | ||||||||
\(495\) | 2.10689 | 0.0946977 | ||||||||
\(496\) | −26.9011 | −1.20789 | ||||||||
\(497\) | −50.0657 | −2.24575 | ||||||||
\(498\) | −15.1271 | −0.677861 | ||||||||
\(499\) | 41.5927 | 1.86195 | 0.930973 | − | 0.365089i | \(-0.118961\pi\) | ||||
0.930973 | + | 0.365089i | \(0.118961\pi\) | |||||||
\(500\) | −57.3477 | −2.56467 | ||||||||
\(501\) | 0.853079 | 0.0381128 | ||||||||
\(502\) | −12.2911 | −0.548580 | ||||||||
\(503\) | −34.5766 | −1.54170 | −0.770848 | − | 0.637019i | \(-0.780167\pi\) | ||||
−0.770848 | + | 0.637019i | \(0.780167\pi\) | |||||||
\(504\) | 76.6849 | 3.41582 | ||||||||
\(505\) | −10.5355 | −0.468826 | ||||||||
\(506\) | 1.10182 | 0.0489820 | ||||||||
\(507\) | −1.93307 | −0.0858506 | ||||||||
\(508\) | −58.6405 | −2.60175 | ||||||||
\(509\) | 3.08217 | 0.136615 | 0.0683073 | − | 0.997664i | \(-0.478240\pi\) | ||||
0.0683073 | + | 0.997664i | \(0.478240\pi\) | |||||||
\(510\) | −7.74640 | −0.343016 | ||||||||
\(511\) | 54.3597 | 2.40473 | ||||||||
\(512\) | 46.8068 | 2.06859 | ||||||||
\(513\) | 15.1922 | 0.670752 | ||||||||
\(514\) | −78.3936 | −3.45779 | ||||||||
\(515\) | 8.61125 | 0.379457 | ||||||||
\(516\) | −18.1412 | −0.798623 | ||||||||
\(517\) | −3.84900 | −0.169279 | ||||||||
\(518\) | 66.4470 | 2.91951 | ||||||||
\(519\) | −7.20240 | −0.316150 | ||||||||
\(520\) | −36.4932 | −1.60033 | ||||||||
\(521\) | −24.1346 | −1.05736 | −0.528678 | − | 0.848822i | \(-0.677312\pi\) | ||||
−0.528678 | + | 0.848822i | \(0.677312\pi\) | |||||||
\(522\) | 10.3236 | 0.451853 | ||||||||
\(523\) | −14.6107 | −0.638881 | −0.319441 | − | 0.947606i | \(-0.603495\pi\) | ||||
−0.319441 | + | 0.947606i | \(0.603495\pi\) | |||||||
\(524\) | 52.5232 | 2.29449 | ||||||||
\(525\) | −3.20353 | −0.139814 | ||||||||
\(526\) | −47.6727 | −2.07863 | ||||||||
\(527\) | −11.7388 | −0.511350 | ||||||||
\(528\) | −1.64863 | −0.0717472 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 51.6400 | 2.24310 | ||||||||
\(531\) | −1.12564 | −0.0488487 | ||||||||
\(532\) | −108.961 | −4.72407 | ||||||||
\(533\) | −20.0404 | −0.868048 | ||||||||
\(534\) | 12.0027 | 0.519408 | ||||||||
\(535\) | −25.6349 | −1.10829 | ||||||||
\(536\) | 24.8476 | 1.07325 | ||||||||
\(537\) | −3.89320 | −0.168004 | ||||||||
\(538\) | 14.3593 | 0.619072 | ||||||||
\(539\) | −3.40948 | −0.146857 | ||||||||
\(540\) | −21.2495 | −0.914435 | ||||||||
\(541\) | −16.2683 | −0.699427 | −0.349713 | − | 0.936857i | \(-0.613721\pi\) | ||||
−0.349713 | + | 0.936857i | \(0.613721\pi\) | |||||||
\(542\) | −8.44453 | −0.362724 | ||||||||
\(543\) | −4.21465 | −0.180868 | ||||||||
\(544\) | −33.9054 | −1.45368 | ||||||||
\(545\) | −24.0127 | −1.02859 | ||||||||
\(546\) | −12.9363 | −0.553621 | ||||||||
\(547\) | −1.04269 | −0.0445823 | −0.0222911 | − | 0.999752i | \(-0.507096\pi\) | ||||
−0.0222911 | + | 0.999752i | \(0.507096\pi\) | |||||||
\(548\) | 64.1058 | 2.73847 | ||||||||
\(549\) | 22.8174 | 0.973825 | ||||||||
\(550\) | −2.07391 | −0.0884318 | ||||||||
\(551\) | −8.45210 | −0.360072 | ||||||||
\(552\) | −3.09523 | −0.131742 | ||||||||
\(553\) | −52.0089 | −2.21164 | ||||||||
\(554\) | 64.0605 | 2.72167 | ||||||||
\(555\) | −5.12847 | −0.217692 | ||||||||
\(556\) | −21.5656 | −0.914585 | ||||||||
\(557\) | −5.76893 | −0.244438 | −0.122219 | − | 0.992503i | \(-0.539001\pi\) | ||||
−0.122219 | + | 0.992503i | \(0.539001\pi\) | |||||||
\(558\) | −22.1629 | −0.938231 | ||||||||
\(559\) | −25.6685 | −1.08566 | ||||||||
\(560\) | 60.4419 | 2.55414 | ||||||||
\(561\) | −0.719410 | −0.0303735 | ||||||||
\(562\) | −73.3539 | −3.09425 | ||||||||
\(563\) | −13.5330 | −0.570350 | −0.285175 | − | 0.958475i | \(-0.592052\pi\) | ||||
−0.285175 | + | 0.958475i | \(0.592052\pi\) | |||||||
\(564\) | 18.7654 | 0.790167 | ||||||||
\(565\) | 12.6834 | 0.533597 | ||||||||
\(566\) | −5.73597 | −0.241101 | ||||||||
\(567\) | 28.2989 | 1.18844 | ||||||||
\(568\) | 91.0504 | 3.82039 | ||||||||
\(569\) | −10.4713 | −0.438978 | −0.219489 | − | 0.975615i | \(-0.570439\pi\) | ||||
−0.219489 | + | 0.975615i | \(0.570439\pi\) | |||||||
\(570\) | 11.9739 | 0.501531 | ||||||||
\(571\) | −33.5946 | −1.40589 | −0.702945 | − | 0.711244i | \(-0.748132\pi\) | ||||
−0.702945 | + | 0.711244i | \(0.748132\pi\) | |||||||
\(572\) | −5.88192 | −0.245935 | ||||||||
\(573\) | −4.24297 | −0.177253 | ||||||||
\(574\) | 68.6619 | 2.86589 | ||||||||
\(575\) | −1.88225 | −0.0784953 | ||||||||
\(576\) | −14.4271 | −0.601130 | ||||||||
\(577\) | −6.56580 | −0.273338 | −0.136669 | − | 0.990617i | \(-0.543640\pi\) | ||||
−0.136669 | + | 0.990617i | \(0.543640\pi\) | |||||||
\(578\) | 5.56281 | 0.231383 | ||||||||
\(579\) | 3.14651 | 0.130765 | ||||||||
\(580\) | 11.8221 | 0.490885 | ||||||||
\(581\) | 51.5048 | 2.13678 | ||||||||
\(582\) | −13.4249 | −0.556479 | ||||||||
\(583\) | 4.79582 | 0.198623 | ||||||||
\(584\) | −98.8595 | −4.09084 | ||||||||
\(585\) | −14.5341 | −0.600909 | ||||||||
\(586\) | 20.7617 | 0.857656 | ||||||||
\(587\) | −23.2594 | −0.960019 | −0.480009 | − | 0.877263i | \(-0.659367\pi\) | ||||
−0.480009 | + | 0.877263i | \(0.659367\pi\) | |||||||
\(588\) | 16.6226 | 0.685505 | ||||||||
\(589\) | 18.1451 | 0.747655 | ||||||||
\(590\) | −1.83532 | −0.0755588 | ||||||||
\(591\) | −10.7425 | −0.441887 | ||||||||
\(592\) | −58.4162 | −2.40089 | ||||||||
\(593\) | 12.9879 | 0.533348 | 0.266674 | − | 0.963787i | \(-0.414075\pi\) | ||||
0.266674 | + | 0.963787i | \(0.414075\pi\) | |||||||
\(594\) | −2.80981 | −0.115288 | ||||||||
\(595\) | 26.3750 | 1.08127 | ||||||||
\(596\) | 20.1043 | 0.823503 | ||||||||
\(597\) | −3.41263 | −0.139670 | ||||||||
\(598\) | −7.60076 | −0.310818 | ||||||||
\(599\) | 39.2694 | 1.60451 | 0.802253 | − | 0.596984i | \(-0.203634\pi\) | ||||
0.802253 | + | 0.596984i | \(0.203634\pi\) | |||||||
\(600\) | 5.82600 | 0.237846 | ||||||||
\(601\) | 17.1472 | 0.699447 | 0.349723 | − | 0.936853i | \(-0.386276\pi\) | ||||
0.349723 | + | 0.936853i | \(0.386276\pi\) | |||||||
\(602\) | 87.9447 | 3.58436 | ||||||||
\(603\) | 9.89597 | 0.402995 | ||||||||
\(604\) | −54.8230 | −2.23071 | ||||||||
\(605\) | −19.1038 | −0.776681 | ||||||||
\(606\) | 6.79195 | 0.275904 | ||||||||
\(607\) | −9.79706 | −0.397650 | −0.198825 | − | 0.980035i | \(-0.563713\pi\) | ||||
−0.198825 | + | 0.980035i | \(0.563713\pi\) | |||||||
\(608\) | 52.4089 | 2.12546 | ||||||||
\(609\) | 2.41468 | 0.0978478 | ||||||||
\(610\) | 37.2030 | 1.50631 | ||||||||
\(611\) | 26.5517 | 1.07417 | ||||||||
\(612\) | −51.0567 | −2.06385 | ||||||||
\(613\) | 22.9411 | 0.926584 | 0.463292 | − | 0.886206i | \(-0.346668\pi\) | ||||
0.463292 | + | 0.886206i | \(0.346668\pi\) | |||||||
\(614\) | 21.2997 | 0.859586 | ||||||||
\(615\) | −5.29943 | −0.213693 | ||||||||
\(616\) | 11.6118 | 0.467851 | ||||||||
\(617\) | −13.6060 | −0.547759 | −0.273879 | − | 0.961764i | \(-0.588307\pi\) | ||||
−0.273879 | + | 0.961764i | \(0.588307\pi\) | |||||||
\(618\) | −5.55141 | −0.223311 | ||||||||
\(619\) | 21.4074 | 0.860437 | 0.430218 | − | 0.902725i | \(-0.358437\pi\) | ||||
0.430218 | + | 0.902725i | \(0.358437\pi\) | |||||||
\(620\) | −25.3798 | −1.01928 | ||||||||
\(621\) | −2.55014 | −0.102334 | ||||||||
\(622\) | −72.7074 | −2.91530 | ||||||||
\(623\) | −40.8669 | −1.63730 | ||||||||
\(624\) | 11.3728 | 0.455276 | ||||||||
\(625\) | −12.0459 | −0.481835 | ||||||||
\(626\) | −44.9877 | −1.79807 | ||||||||
\(627\) | 1.11202 | 0.0444097 | ||||||||
\(628\) | 4.07275 | 0.162520 | ||||||||
\(629\) | −25.4911 | −1.01640 | ||||||||
\(630\) | 49.7961 | 1.98393 | ||||||||
\(631\) | −22.2948 | −0.887541 | −0.443770 | − | 0.896141i | \(-0.646359\pi\) | ||||
−0.443770 | + | 0.896141i | \(0.646359\pi\) | |||||||
\(632\) | 94.5843 | 3.76236 | ||||||||
\(633\) | −1.18464 | −0.0470854 | ||||||||
\(634\) | 37.3737 | 1.48430 | ||||||||
\(635\) | −21.9409 | −0.870696 | ||||||||
\(636\) | −23.3816 | −0.927140 | ||||||||
\(637\) | 23.5198 | 0.931888 | ||||||||
\(638\) | 1.56322 | 0.0618885 | ||||||||
\(639\) | 36.2624 | 1.43452 | ||||||||
\(640\) | 7.54404 | 0.298204 | ||||||||
\(641\) | 26.2392 | 1.03639 | 0.518193 | − | 0.855264i | \(-0.326605\pi\) | ||||
0.518193 | + | 0.855264i | \(0.326605\pi\) | |||||||
\(642\) | 16.5261 | 0.652232 | ||||||||
\(643\) | −28.9523 | −1.14177 | −0.570883 | − | 0.821031i | \(-0.693399\pi\) | ||||
−0.570883 | + | 0.821031i | \(0.693399\pi\) | |||||||
\(644\) | 18.2901 | 0.720730 | ||||||||
\(645\) | −6.78770 | −0.267265 | ||||||||
\(646\) | 59.5162 | 2.34163 | ||||||||
\(647\) | 26.0969 | 1.02598 | 0.512988 | − | 0.858396i | \(-0.328538\pi\) | ||||
0.512988 | + | 0.858396i | \(0.328538\pi\) | |||||||
\(648\) | −51.4649 | −2.02173 | ||||||||
\(649\) | −0.170446 | −0.00669061 | ||||||||
\(650\) | 14.3065 | 0.561149 | ||||||||
\(651\) | −5.18387 | −0.203172 | ||||||||
\(652\) | 69.9993 | 2.74138 | ||||||||
\(653\) | −6.91791 | −0.270719 | −0.135359 | − | 0.990797i | \(-0.543219\pi\) | ||||
−0.135359 | + | 0.990797i | \(0.543219\pi\) | |||||||
\(654\) | 15.4803 | 0.605327 | ||||||||
\(655\) | 19.6520 | 0.767868 | ||||||||
\(656\) | −60.3635 | −2.35680 | ||||||||
\(657\) | −39.3725 | −1.53607 | ||||||||
\(658\) | −90.9707 | −3.54641 | ||||||||
\(659\) | 40.1526 | 1.56412 | 0.782062 | − | 0.623201i | \(-0.214168\pi\) | ||||
0.782062 | + | 0.623201i | \(0.214168\pi\) | |||||||
\(660\) | −1.55539 | −0.0605437 | ||||||||
\(661\) | −26.3183 | −1.02366 | −0.511832 | − | 0.859086i | \(-0.671033\pi\) | ||||
−0.511832 | + | 0.859086i | \(0.671033\pi\) | |||||||
\(662\) | −11.5406 | −0.448539 | ||||||||
\(663\) | 4.96274 | 0.192737 | ||||||||
\(664\) | −93.6676 | −3.63501 | ||||||||
\(665\) | −40.7688 | −1.58095 | ||||||||
\(666\) | −48.1273 | −1.86489 | ||||||||
\(667\) | 1.41876 | 0.0549345 | ||||||||
\(668\) | 9.16755 | 0.354703 | ||||||||
\(669\) | −13.0911 | −0.506131 | ||||||||
\(670\) | 16.1350 | 0.623350 | ||||||||
\(671\) | 3.45505 | 0.133381 | ||||||||
\(672\) | −14.9727 | −0.577584 | ||||||||
\(673\) | 51.5778 | 1.98818 | 0.994089 | − | 0.108565i | \(-0.0346256\pi\) | ||||
0.994089 | + | 0.108565i | \(0.0346256\pi\) | |||||||
\(674\) | −22.9905 | −0.885559 | ||||||||
\(675\) | 4.80001 | 0.184752 | ||||||||
\(676\) | −20.7736 | −0.798984 | ||||||||
\(677\) | 33.1590 | 1.27441 | 0.637203 | − | 0.770696i | \(-0.280091\pi\) | ||||
0.637203 | + | 0.770696i | \(0.280091\pi\) | |||||||
\(678\) | −8.17664 | −0.314022 | ||||||||
\(679\) | 45.7092 | 1.75416 | ||||||||
\(680\) | −47.9661 | −1.83941 | ||||||||
\(681\) | 5.45573 | 0.209064 | ||||||||
\(682\) | −3.35594 | −0.128506 | ||||||||
\(683\) | −42.2251 | −1.61570 | −0.807849 | − | 0.589389i | \(-0.799368\pi\) | ||||
−0.807849 | + | 0.589389i | \(0.799368\pi\) | |||||||
\(684\) | 78.9202 | 3.01759 | ||||||||
\(685\) | 23.9857 | 0.916448 | ||||||||
\(686\) | −10.2583 | −0.391665 | ||||||||
\(687\) | −1.62212 | −0.0618879 | ||||||||
\(688\) | −77.3158 | −2.94764 | ||||||||
\(689\) | −33.0832 | −1.26037 | ||||||||
\(690\) | −2.00992 | −0.0765163 | ||||||||
\(691\) | −20.6794 | −0.786682 | −0.393341 | − | 0.919393i | \(-0.628681\pi\) | ||||
−0.393341 | + | 0.919393i | \(0.628681\pi\) | |||||||
\(692\) | −77.4001 | −2.94231 | ||||||||
\(693\) | 4.62458 | 0.175673 | ||||||||
\(694\) | −27.7358 | −1.05284 | ||||||||
\(695\) | −8.06896 | −0.306073 | ||||||||
\(696\) | −4.39138 | −0.166455 | ||||||||
\(697\) | −26.3408 | −0.997729 | ||||||||
\(698\) | −2.59213 | −0.0981137 | ||||||||
\(699\) | 4.51977 | 0.170953 | ||||||||
\(700\) | −34.4265 | −1.30120 | ||||||||
\(701\) | 0.845619 | 0.0319386 | 0.0159693 | − | 0.999872i | \(-0.494917\pi\) | ||||
0.0159693 | + | 0.999872i | \(0.494917\pi\) | |||||||
\(702\) | 19.3830 | 0.731565 | ||||||||
\(703\) | 39.4025 | 1.48609 | ||||||||
\(704\) | −2.18458 | −0.0823344 | ||||||||
\(705\) | 7.02125 | 0.264436 | ||||||||
\(706\) | 13.2675 | 0.499330 | ||||||||
\(707\) | −23.1253 | −0.869717 | ||||||||
\(708\) | 0.830996 | 0.0312307 | ||||||||
\(709\) | −41.1909 | −1.54696 | −0.773478 | − | 0.633823i | \(-0.781485\pi\) | ||||
−0.773478 | + | 0.633823i | \(0.781485\pi\) | |||||||
\(710\) | 59.1245 | 2.21890 | ||||||||
\(711\) | 37.6698 | 1.41273 | ||||||||
\(712\) | 74.3213 | 2.78531 | ||||||||
\(713\) | −3.04581 | −0.114066 | ||||||||
\(714\) | −17.0032 | −0.636328 | ||||||||
\(715\) | −2.20077 | −0.0823042 | ||||||||
\(716\) | −41.8380 | −1.56356 | ||||||||
\(717\) | 1.31217 | 0.0490040 | ||||||||
\(718\) | 9.05121 | 0.337788 | ||||||||
\(719\) | −48.7779 | −1.81911 | −0.909554 | − | 0.415586i | \(-0.863577\pi\) | ||||
−0.909554 | + | 0.415586i | \(0.863577\pi\) | |||||||
\(720\) | −43.7778 | −1.63150 | ||||||||
\(721\) | 18.9015 | 0.703929 | ||||||||
\(722\) | −42.7458 | −1.59083 | ||||||||
\(723\) | −12.6564 | −0.470698 | ||||||||
\(724\) | −45.2924 | −1.68328 | ||||||||
\(725\) | −2.67046 | −0.0991784 | ||||||||
\(726\) | 12.3157 | 0.457078 | ||||||||
\(727\) | −5.07301 | −0.188147 | −0.0940737 | − | 0.995565i | \(-0.529989\pi\) | ||||
−0.0940737 | + | 0.995565i | \(0.529989\pi\) | |||||||
\(728\) | −80.1019 | −2.96877 | ||||||||
\(729\) | −17.1372 | −0.634711 | ||||||||
\(730\) | −64.1954 | −2.37598 | ||||||||
\(731\) | −33.7383 | −1.24785 | ||||||||
\(732\) | −16.8448 | −0.622601 | ||||||||
\(733\) | 6.31122 | 0.233110 | 0.116555 | − | 0.993184i | \(-0.462815\pi\) | ||||
0.116555 | + | 0.993184i | \(0.462815\pi\) | |||||||
\(734\) | −19.8852 | −0.733975 | ||||||||
\(735\) | 6.21949 | 0.229410 | ||||||||
\(736\) | −8.79728 | −0.324272 | ||||||||
\(737\) | 1.49846 | 0.0551966 | ||||||||
\(738\) | −49.7316 | −1.83064 | ||||||||
\(739\) | −8.73340 | −0.321263 | −0.160632 | − | 0.987014i | \(-0.551353\pi\) | ||||
−0.160632 | + | 0.987014i | \(0.551353\pi\) | |||||||
\(740\) | −55.1128 | −2.02599 | ||||||||
\(741\) | −7.67108 | −0.281804 | ||||||||
\(742\) | 113.349 | 4.16116 | ||||||||
\(743\) | 26.5264 | 0.973160 | 0.486580 | − | 0.873636i | \(-0.338244\pi\) | ||||
0.486580 | + | 0.873636i | \(0.338244\pi\) | |||||||
\(744\) | 9.42748 | 0.345628 | ||||||||
\(745\) | 7.52218 | 0.275592 | ||||||||
\(746\) | −83.3681 | −3.05232 | ||||||||
\(747\) | −37.3047 | −1.36491 | ||||||||
\(748\) | −7.73109 | −0.282677 | ||||||||
\(749\) | −56.2681 | −2.05599 | ||||||||
\(750\) | 13.8328 | 0.505101 | ||||||||
\(751\) | 19.4260 | 0.708866 | 0.354433 | − | 0.935081i | \(-0.384674\pi\) | ||||
0.354433 | + | 0.935081i | \(0.384674\pi\) | |||||||
\(752\) | 79.9760 | 2.91643 | ||||||||
\(753\) | 2.08226 | 0.0758817 | ||||||||
\(754\) | −10.7836 | −0.392717 | ||||||||
\(755\) | −20.5125 | −0.746526 | ||||||||
\(756\) | −46.6423 | −1.69636 | ||||||||
\(757\) | −40.5224 | −1.47281 | −0.736405 | − | 0.676541i | \(-0.763478\pi\) | ||||
−0.736405 | + | 0.676541i | \(0.763478\pi\) | |||||||
\(758\) | −79.8020 | −2.89854 | ||||||||
\(759\) | −0.186662 | −0.00677539 | ||||||||
\(760\) | 74.1429 | 2.68944 | ||||||||
\(761\) | 31.9554 | 1.15838 | 0.579191 | − | 0.815192i | \(-0.303369\pi\) | ||||
0.579191 | + | 0.815192i | \(0.303369\pi\) | |||||||
\(762\) | 14.1446 | 0.512405 | ||||||||
\(763\) | −52.7074 | −1.90814 | ||||||||
\(764\) | −45.5968 | −1.64963 | ||||||||
\(765\) | −19.1033 | −0.690682 | ||||||||
\(766\) | −53.9156 | −1.94805 | ||||||||
\(767\) | 1.17580 | 0.0424556 | ||||||||
\(768\) | −9.37723 | −0.338372 | ||||||||
\(769\) | 33.4862 | 1.20754 | 0.603772 | − | 0.797157i | \(-0.293664\pi\) | ||||
0.603772 | + | 0.797157i | \(0.293664\pi\) | |||||||
\(770\) | 7.54021 | 0.271730 | ||||||||
\(771\) | 13.2808 | 0.478296 | ||||||||
\(772\) | 33.8137 | 1.21698 | ||||||||
\(773\) | −19.4384 | −0.699151 | −0.349576 | − | 0.936908i | \(-0.613674\pi\) | ||||
−0.349576 | + | 0.936908i | \(0.613674\pi\) | |||||||
\(774\) | −63.6980 | −2.28958 | ||||||||
\(775\) | 5.73298 | 0.205935 | ||||||||
\(776\) | −83.1275 | −2.98410 | ||||||||
\(777\) | −11.2569 | −0.403839 | ||||||||
\(778\) | −82.9250 | −2.97301 | ||||||||
\(779\) | 40.7159 | 1.45880 | ||||||||
\(780\) | 10.7296 | 0.384183 | ||||||||
\(781\) | 5.49091 | 0.196480 | ||||||||
\(782\) | −9.99030 | −0.357253 | ||||||||
\(783\) | −3.61803 | −0.129298 | ||||||||
\(784\) | 70.8436 | 2.53013 | ||||||||
\(785\) | 1.52385 | 0.0543887 | ||||||||
\(786\) | −12.6691 | −0.451891 | ||||||||
\(787\) | 49.5116 | 1.76490 | 0.882449 | − | 0.470409i | \(-0.155894\pi\) | ||||
0.882449 | + | 0.470409i | \(0.155894\pi\) | |||||||
\(788\) | −115.443 | −4.11250 | ||||||||
\(789\) | 8.07631 | 0.287524 | ||||||||
\(790\) | 61.4193 | 2.18520 | ||||||||
\(791\) | 27.8399 | 0.989873 | ||||||||
\(792\) | −8.41035 | −0.298849 | ||||||||
\(793\) | −23.8342 | −0.846376 | ||||||||
\(794\) | −52.3695 | −1.85853 | ||||||||
\(795\) | −8.74842 | −0.310274 | ||||||||
\(796\) | −36.6736 | −1.29986 | ||||||||
\(797\) | 40.7335 | 1.44285 | 0.721427 | − | 0.692490i | \(-0.243486\pi\) | ||||
0.721427 | + | 0.692490i | \(0.243486\pi\) | |||||||
\(798\) | 26.2824 | 0.930388 | ||||||||
\(799\) | 34.8991 | 1.23464 | ||||||||
\(800\) | 16.5587 | 0.585438 | ||||||||
\(801\) | 29.5998 | 1.04586 | ||||||||
\(802\) | −37.2136 | −1.31406 | ||||||||
\(803\) | −5.96185 | −0.210389 | ||||||||
\(804\) | −7.30561 | −0.257649 | ||||||||
\(805\) | 6.84339 | 0.241198 | ||||||||
\(806\) | 23.1505 | 0.815440 | ||||||||
\(807\) | −2.43263 | −0.0856325 | ||||||||
\(808\) | 42.0561 | 1.47953 | ||||||||
\(809\) | 50.9732 | 1.79212 | 0.896062 | − | 0.443930i | \(-0.146416\pi\) | ||||
0.896062 | + | 0.443930i | \(0.146416\pi\) | |||||||
\(810\) | −33.4193 | −1.17423 | ||||||||
\(811\) | 41.1685 | 1.44562 | 0.722811 | − | 0.691046i | \(-0.242850\pi\) | ||||
0.722811 | + | 0.691046i | \(0.242850\pi\) | |||||||
\(812\) | 25.9492 | 0.910638 | ||||||||
\(813\) | 1.43060 | 0.0501734 | ||||||||
\(814\) | −7.28751 | −0.255427 | ||||||||
\(815\) | 26.1908 | 0.917425 | ||||||||
\(816\) | 14.9482 | 0.523291 | ||||||||
\(817\) | 52.1504 | 1.82451 | ||||||||
\(818\) | 32.0109 | 1.11923 | ||||||||
\(819\) | −31.9020 | −1.11474 | ||||||||
\(820\) | −56.9499 | −1.98878 | ||||||||
\(821\) | 50.7185 | 1.77009 | 0.885044 | − | 0.465508i | \(-0.154128\pi\) | ||||
0.885044 | + | 0.465508i | \(0.154128\pi\) | |||||||
\(822\) | −15.4629 | −0.539331 | ||||||||
\(823\) | 41.2904 | 1.43929 | 0.719646 | − | 0.694341i | \(-0.244304\pi\) | ||||
0.719646 | + | 0.694341i | \(0.244304\pi\) | |||||||
\(824\) | −34.3746 | −1.19750 | ||||||||
\(825\) | 0.351344 | 0.0122322 | ||||||||
\(826\) | −4.02848 | −0.140169 | ||||||||
\(827\) | −24.4792 | −0.851226 | −0.425613 | − | 0.904905i | \(-0.639941\pi\) | ||||
−0.425613 | + | 0.904905i | \(0.639941\pi\) | |||||||
\(828\) | −13.2474 | −0.460380 | ||||||||
\(829\) | −44.9811 | −1.56226 | −0.781129 | − | 0.624370i | \(-0.785356\pi\) | ||||
−0.781129 | + | 0.624370i | \(0.785356\pi\) | |||||||
\(830\) | −60.8240 | −2.11123 | ||||||||
\(831\) | −10.8526 | −0.376472 | ||||||||
\(832\) | 15.0700 | 0.522458 | ||||||||
\(833\) | 30.9140 | 1.07111 | ||||||||
\(834\) | 5.20182 | 0.180124 | ||||||||
\(835\) | 3.43012 | 0.118704 | ||||||||
\(836\) | 11.9502 | 0.413307 | ||||||||
\(837\) | 7.76724 | 0.268475 | ||||||||
\(838\) | −42.0508 | −1.45262 | ||||||||
\(839\) | −23.3001 | −0.804408 | −0.402204 | − | 0.915550i | \(-0.631756\pi\) | ||||
−0.402204 | + | 0.915550i | \(0.631756\pi\) | |||||||
\(840\) | −21.1819 | −0.730844 | ||||||||
\(841\) | −26.9871 | −0.930591 | ||||||||
\(842\) | 37.4758 | 1.29150 | ||||||||
\(843\) | 12.4270 | 0.428009 | ||||||||
\(844\) | −12.7307 | −0.438208 | ||||||||
\(845\) | −7.77261 | −0.267386 | ||||||||
\(846\) | 65.8897 | 2.26533 | ||||||||
\(847\) | −41.9325 | −1.44082 | ||||||||
\(848\) | −99.6495 | −3.42198 | ||||||||
\(849\) | 0.971739 | 0.0333500 | ||||||||
\(850\) | 18.8043 | 0.644981 | ||||||||
\(851\) | −6.61404 | −0.226726 | ||||||||
\(852\) | −26.7704 | −0.917139 | ||||||||
\(853\) | −6.06556 | −0.207681 | −0.103840 | − | 0.994594i | \(-0.533113\pi\) | ||||
−0.103840 | + | 0.994594i | \(0.533113\pi\) | |||||||
\(854\) | 81.6598 | 2.79434 | ||||||||
\(855\) | 29.5287 | 1.00986 | ||||||||
\(856\) | 102.330 | 3.49757 | ||||||||
\(857\) | 10.7078 | 0.365772 | 0.182886 | − | 0.983134i | \(-0.441456\pi\) | ||||
0.182886 | + | 0.983134i | \(0.441456\pi\) | |||||||
\(858\) | 1.41877 | 0.0484361 | ||||||||
\(859\) | 23.2676 | 0.793879 | 0.396939 | − | 0.917845i | \(-0.370072\pi\) | ||||
0.396939 | + | 0.917845i | \(0.370072\pi\) | |||||||
\(860\) | −72.9435 | −2.48735 | ||||||||
\(861\) | −11.6321 | −0.396422 | ||||||||
\(862\) | −52.7973 | −1.79828 | ||||||||
\(863\) | −45.7737 | −1.55815 | −0.779077 | − | 0.626928i | \(-0.784312\pi\) | ||||
−0.779077 | + | 0.626928i | \(0.784312\pi\) | |||||||
\(864\) | 22.4343 | 0.763230 | ||||||||
\(865\) | −28.9599 | −0.984667 | ||||||||
\(866\) | −39.8259 | −1.35334 | ||||||||
\(867\) | −0.942405 | −0.0320058 | ||||||||
\(868\) | −55.7081 | −1.89086 | ||||||||
\(869\) | 5.70402 | 0.193496 | ||||||||
\(870\) | −2.85159 | −0.0966779 | ||||||||
\(871\) | −10.3369 | −0.350253 | ||||||||
\(872\) | 95.8547 | 3.24605 | ||||||||
\(873\) | −33.1070 | −1.12050 | ||||||||
\(874\) | 15.4424 | 0.522346 | ||||||||
\(875\) | −47.0979 | −1.59220 | ||||||||
\(876\) | 29.0664 | 0.982063 | ||||||||
\(877\) | 4.04367 | 0.136545 | 0.0682724 | − | 0.997667i | \(-0.478251\pi\) | ||||
0.0682724 | + | 0.997667i | \(0.478251\pi\) | |||||||
\(878\) | 0.157113 | 0.00530232 | ||||||||
\(879\) | −3.51727 | −0.118634 | ||||||||
\(880\) | −6.62891 | −0.223460 | ||||||||
\(881\) | −15.2458 | −0.513644 | −0.256822 | − | 0.966459i | \(-0.582675\pi\) | ||||
−0.256822 | + | 0.966459i | \(0.582675\pi\) | |||||||
\(882\) | 58.3658 | 1.96528 | ||||||||
\(883\) | 0.634061 | 0.0213378 | 0.0106689 | − | 0.999943i | \(-0.496604\pi\) | ||||
0.0106689 | + | 0.999943i | \(0.496604\pi\) | |||||||
\(884\) | 53.3317 | 1.79374 | ||||||||
\(885\) | 0.310924 | 0.0104516 | ||||||||
\(886\) | 5.69970 | 0.191485 | ||||||||
\(887\) | −16.8057 | −0.564281 | −0.282140 | − | 0.959373i | \(-0.591044\pi\) | ||||
−0.282140 | + | 0.959373i | \(0.591044\pi\) | |||||||
\(888\) | 20.4720 | 0.686995 | ||||||||
\(889\) | −48.1597 | −1.61522 | ||||||||
\(890\) | 48.2613 | 1.61772 | ||||||||
\(891\) | −3.10365 | −0.103976 | ||||||||
\(892\) | −140.682 | −4.71040 | ||||||||
\(893\) | −53.9448 | −1.80519 | ||||||||
\(894\) | −4.84933 | −0.162186 | ||||||||
\(895\) | −15.6540 | −0.523257 | ||||||||
\(896\) | 16.5590 | 0.553198 | ||||||||
\(897\) | 1.28766 | 0.0429936 | ||||||||
\(898\) | 60.8871 | 2.03183 | ||||||||
\(899\) | −4.32126 | −0.144122 | ||||||||
\(900\) | 24.9350 | 0.831167 | ||||||||
\(901\) | −43.4840 | −1.44866 | ||||||||
\(902\) | −7.53043 | −0.250736 | ||||||||
\(903\) | −14.8989 | −0.495803 | ||||||||
\(904\) | −50.6301 | −1.68393 | ||||||||
\(905\) | −16.9466 | −0.563322 | ||||||||
\(906\) | 13.2238 | 0.439331 | ||||||||
\(907\) | 8.16077 | 0.270974 | 0.135487 | − | 0.990779i | \(-0.456740\pi\) | ||||
0.135487 | + | 0.990779i | \(0.456740\pi\) | |||||||
\(908\) | 58.6296 | 1.94569 | ||||||||
\(909\) | 16.7496 | 0.555548 | ||||||||
\(910\) | −52.0150 | −1.72428 | ||||||||
\(911\) | −31.5711 | −1.04600 | −0.522998 | − | 0.852334i | \(-0.675187\pi\) | ||||
−0.522998 | + | 0.852334i | \(0.675187\pi\) | |||||||
\(912\) | −23.1060 | −0.765114 | ||||||||
\(913\) | −5.64874 | −0.186946 | ||||||||
\(914\) | 14.5504 | 0.481284 | ||||||||
\(915\) | −6.30262 | −0.208358 | ||||||||
\(916\) | −17.4320 | −0.575971 | ||||||||
\(917\) | 43.1358 | 1.42447 | ||||||||
\(918\) | 25.4767 | 0.840856 | ||||||||
\(919\) | −28.1188 | −0.927552 | −0.463776 | − | 0.885952i | \(-0.653506\pi\) | ||||
−0.463776 | + | 0.885952i | \(0.653506\pi\) | |||||||
\(920\) | −12.4455 | −0.410316 | ||||||||
\(921\) | −3.60842 | −0.118901 | ||||||||
\(922\) | 9.34618 | 0.307800 | ||||||||
\(923\) | −37.8782 | −1.24678 | ||||||||
\(924\) | −3.41406 | −0.112314 | ||||||||
\(925\) | 12.4493 | 0.409330 | ||||||||
\(926\) | −92.1673 | −3.02880 | ||||||||
\(927\) | −13.6903 | −0.449648 | ||||||||
\(928\) | −12.4812 | −0.409715 | ||||||||
\(929\) | −40.3128 | −1.32262 | −0.661311 | − | 0.750112i | \(-0.730000\pi\) | ||||
−0.661311 | + | 0.750112i | \(0.730000\pi\) | |||||||
\(930\) | 6.12183 | 0.200743 | ||||||||
\(931\) | −47.7849 | −1.56609 | ||||||||
\(932\) | 48.5714 | 1.59101 | ||||||||
\(933\) | 12.3175 | 0.403256 | ||||||||
\(934\) | 49.3950 | 1.61626 | ||||||||
\(935\) | −2.89265 | −0.0945999 | ||||||||
\(936\) | 58.0175 | 1.89636 | ||||||||
\(937\) | −16.0114 | −0.523069 | −0.261534 | − | 0.965194i | \(-0.584228\pi\) | ||||
−0.261534 | + | 0.965194i | \(0.584228\pi\) | |||||||
\(938\) | 35.4160 | 1.15637 | ||||||||
\(939\) | 7.62145 | 0.248717 | ||||||||
\(940\) | 75.4533 | 2.46102 | ||||||||
\(941\) | −28.7211 | −0.936280 | −0.468140 | − | 0.883654i | \(-0.655076\pi\) | ||||
−0.468140 | + | 0.883654i | \(0.655076\pi\) | |||||||
\(942\) | −0.982384 | −0.0320078 | ||||||||
\(943\) | −6.83451 | −0.222562 | ||||||||
\(944\) | 3.54160 | 0.115269 | ||||||||
\(945\) | −17.4516 | −0.567701 | ||||||||
\(946\) | −9.64525 | −0.313594 | ||||||||
\(947\) | 8.77034 | 0.284998 | 0.142499 | − | 0.989795i | \(-0.454486\pi\) | ||||
0.142499 | + | 0.989795i | \(0.454486\pi\) | |||||||
\(948\) | −27.8094 | −0.903208 | ||||||||
\(949\) | 41.1269 | 1.33503 | ||||||||
\(950\) | −29.0664 | −0.943040 | ||||||||
\(951\) | −6.33154 | −0.205314 | ||||||||
\(952\) | −105.284 | −3.41229 | ||||||||
\(953\) | −28.0624 | −0.909030 | −0.454515 | − | 0.890739i | \(-0.650187\pi\) | ||||
−0.454515 | + | 0.890739i | \(0.650187\pi\) | |||||||
\(954\) | −82.0980 | −2.65802 | ||||||||
\(955\) | −17.0604 | −0.552063 | ||||||||
\(956\) | 14.1012 | 0.456065 | ||||||||
\(957\) | −0.264828 | −0.00856067 | ||||||||
\(958\) | −62.9173 | −2.03276 | ||||||||
\(959\) | 52.6482 | 1.70010 | ||||||||
\(960\) | 3.98505 | 0.128617 | ||||||||
\(961\) | −21.7231 | −0.700744 | ||||||||
\(962\) | 50.2717 | 1.62083 | ||||||||
\(963\) | 40.7547 | 1.31330 | ||||||||
\(964\) | −136.011 | −4.38063 | ||||||||
\(965\) | 12.6517 | 0.407273 | ||||||||
\(966\) | −4.41173 | −0.141945 | ||||||||
\(967\) | 45.3349 | 1.45787 | 0.728937 | − | 0.684581i | \(-0.240015\pi\) | ||||
0.728937 | + | 0.684581i | \(0.240015\pi\) | |||||||
\(968\) | 76.2592 | 2.45106 | ||||||||
\(969\) | −10.0827 | −0.323904 | ||||||||
\(970\) | −53.9797 | −1.73318 | ||||||||
\(971\) | −18.4049 | −0.590643 | −0.295321 | − | 0.955398i | \(-0.595427\pi\) | ||||
−0.295321 | + | 0.955398i | \(0.595427\pi\) | |||||||
\(972\) | 51.2352 | 1.64337 | ||||||||
\(973\) | −17.7112 | −0.567795 | ||||||||
\(974\) | −66.6268 | −2.13486 | ||||||||
\(975\) | −2.42370 | −0.0776204 | ||||||||
\(976\) | −71.7905 | −2.29796 | ||||||||
\(977\) | 17.3752 | 0.555882 | 0.277941 | − | 0.960598i | \(-0.410348\pi\) | ||||
0.277941 | + | 0.960598i | \(0.410348\pi\) | |||||||
\(978\) | −16.8845 | −0.539905 | ||||||||
\(979\) | 4.48204 | 0.143247 | ||||||||
\(980\) | 66.8373 | 2.13504 | ||||||||
\(981\) | 38.1758 | 1.21886 | ||||||||
\(982\) | 91.3723 | 2.91581 | ||||||||
\(983\) | −18.3327 | −0.584722 | −0.292361 | − | 0.956308i | \(-0.594441\pi\) | ||||
−0.292361 | + | 0.956308i | \(0.594441\pi\) | |||||||
\(984\) | 21.1544 | 0.674378 | ||||||||
\(985\) | −43.1941 | −1.37628 | ||||||||
\(986\) | −14.1738 | −0.451386 | ||||||||
\(987\) | 15.4115 | 0.490553 | ||||||||
\(988\) | −82.4367 | −2.62266 | ||||||||
\(989\) | −8.75390 | −0.278358 | ||||||||
\(990\) | −5.46134 | −0.173573 | ||||||||
\(991\) | 15.5741 | 0.494726 | 0.247363 | − | 0.968923i | \(-0.420436\pi\) | ||||
0.247363 | + | 0.968923i | \(0.420436\pi\) | |||||||
\(992\) | 26.7948 | 0.850736 | ||||||||
\(993\) | 1.95512 | 0.0620437 | ||||||||
\(994\) | 129.777 | 4.11628 | ||||||||
\(995\) | −13.7217 | −0.435008 | ||||||||
\(996\) | 27.5399 | 0.872635 | ||||||||
\(997\) | −43.5864 | −1.38039 | −0.690197 | − | 0.723622i | \(-0.742476\pi\) | ||||
−0.690197 | + | 0.723622i | \(0.742476\pi\) | |||||||
\(998\) | −107.814 | −3.41279 | ||||||||
\(999\) | 16.8667 | 0.533640 |
(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 | 8027.2.a.c.1.8 | ✓ | 143 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8027.2.a.c.1.8 | ✓ | 143 | 1.1 | even | 1 | trivial |