Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8005,2,Mod(1,8005)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8005, 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("8005.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8005 = 5 \cdot 1601 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8005.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: | \(63.9202468180\) |
Analytic rank: | \(1\) |
Dimension: | \(126\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 8005.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.44890 | −1.73163 | −0.865817 | − | 0.500362i | \(-0.833200\pi\) | ||||
−0.865817 | + | 0.500362i | \(0.833200\pi\) | |||||||
\(3\) | 0.480075 | 0.277171 | 0.138586 | − | 0.990350i | \(-0.455744\pi\) | ||||
0.138586 | + | 0.990350i | \(0.455744\pi\) | |||||||
\(4\) | 3.99711 | 1.99855 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −1.17566 | −0.479959 | ||||||||
\(7\) | −2.53410 | −0.957801 | −0.478900 | − | 0.877869i | \(-0.658964\pi\) | ||||
−0.478900 | + | 0.877869i | \(0.658964\pi\) | |||||||
\(8\) | −4.89071 | −1.72913 | ||||||||
\(9\) | −2.76953 | −0.923176 | ||||||||
\(10\) | −2.44890 | −0.774410 | ||||||||
\(11\) | 3.07951 | 0.928507 | 0.464253 | − | 0.885702i | \(-0.346323\pi\) | ||||
0.464253 | + | 0.885702i | \(0.346323\pi\) | |||||||
\(12\) | 1.91891 | 0.553942 | ||||||||
\(13\) | −3.14784 | −0.873053 | −0.436527 | − | 0.899691i | \(-0.643792\pi\) | ||||
−0.436527 | + | 0.899691i | \(0.643792\pi\) | |||||||
\(14\) | 6.20576 | 1.65856 | ||||||||
\(15\) | 0.480075 | 0.123955 | ||||||||
\(16\) | 3.98264 | 0.995661 | ||||||||
\(17\) | −6.24864 | −1.51552 | −0.757759 | − | 0.652535i | \(-0.773706\pi\) | ||||
−0.757759 | + | 0.652535i | \(0.773706\pi\) | |||||||
\(18\) | 6.78229 | 1.59860 | ||||||||
\(19\) | 5.29043 | 1.21371 | 0.606854 | − | 0.794813i | \(-0.292431\pi\) | ||||
0.606854 | + | 0.794813i | \(0.292431\pi\) | |||||||
\(20\) | 3.99711 | 0.893780 | ||||||||
\(21\) | −1.21656 | −0.265475 | ||||||||
\(22\) | −7.54140 | −1.60783 | ||||||||
\(23\) | −1.94717 | −0.406012 | −0.203006 | − | 0.979177i | \(-0.565071\pi\) | ||||
−0.203006 | + | 0.979177i | \(0.565071\pi\) | |||||||
\(24\) | −2.34791 | −0.479265 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 7.70874 | 1.51181 | ||||||||
\(27\) | −2.76981 | −0.533050 | ||||||||
\(28\) | −10.1291 | −1.91422 | ||||||||
\(29\) | 3.47422 | 0.645147 | 0.322574 | − | 0.946544i | \(-0.395452\pi\) | ||||
0.322574 | + | 0.946544i | \(0.395452\pi\) | |||||||
\(30\) | −1.17566 | −0.214644 | ||||||||
\(31\) | −3.41518 | −0.613385 | −0.306692 | − | 0.951809i | \(-0.599222\pi\) | ||||
−0.306692 | + | 0.951809i | \(0.599222\pi\) | |||||||
\(32\) | 0.0283274 | 0.00500763 | ||||||||
\(33\) | 1.47840 | 0.257356 | ||||||||
\(34\) | 15.3023 | 2.62432 | ||||||||
\(35\) | −2.53410 | −0.428341 | ||||||||
\(36\) | −11.0701 | −1.84502 | ||||||||
\(37\) | 8.02159 | 1.31874 | 0.659371 | − | 0.751818i | \(-0.270823\pi\) | ||||
0.659371 | + | 0.751818i | \(0.270823\pi\) | |||||||
\(38\) | −12.9557 | −2.10170 | ||||||||
\(39\) | −1.51120 | −0.241985 | ||||||||
\(40\) | −4.89071 | −0.773289 | ||||||||
\(41\) | 7.31748 | 1.14280 | 0.571399 | − | 0.820672i | \(-0.306401\pi\) | ||||
0.571399 | + | 0.820672i | \(0.306401\pi\) | |||||||
\(42\) | 2.97923 | 0.459705 | ||||||||
\(43\) | −5.82547 | −0.888376 | −0.444188 | − | 0.895934i | \(-0.646508\pi\) | ||||
−0.444188 | + | 0.895934i | \(0.646508\pi\) | |||||||
\(44\) | 12.3091 | 1.85567 | ||||||||
\(45\) | −2.76953 | −0.412857 | ||||||||
\(46\) | 4.76842 | 0.703065 | ||||||||
\(47\) | 5.99700 | 0.874753 | 0.437376 | − | 0.899279i | \(-0.355908\pi\) | ||||
0.437376 | + | 0.899279i | \(0.355908\pi\) | |||||||
\(48\) | 1.91197 | 0.275969 | ||||||||
\(49\) | −0.578326 | −0.0826181 | ||||||||
\(50\) | −2.44890 | −0.346327 | ||||||||
\(51\) | −2.99982 | −0.420058 | ||||||||
\(52\) | −12.5822 | −1.74484 | ||||||||
\(53\) | −1.80401 | −0.247800 | −0.123900 | − | 0.992295i | \(-0.539540\pi\) | ||||
−0.123900 | + | 0.992295i | \(0.539540\pi\) | |||||||
\(54\) | 6.78298 | 0.923046 | ||||||||
\(55\) | 3.07951 | 0.415241 | ||||||||
\(56\) | 12.3936 | 1.65616 | ||||||||
\(57\) | 2.53980 | 0.336405 | ||||||||
\(58\) | −8.50803 | −1.11716 | ||||||||
\(59\) | 9.00745 | 1.17267 | 0.586335 | − | 0.810069i | \(-0.300570\pi\) | ||||
0.586335 | + | 0.810069i | \(0.300570\pi\) | |||||||
\(60\) | 1.91891 | 0.247730 | ||||||||
\(61\) | 15.1378 | 1.93819 | 0.969096 | − | 0.246684i | \(-0.0793411\pi\) | ||||
0.969096 | + | 0.246684i | \(0.0793411\pi\) | |||||||
\(62\) | 8.36343 | 1.06216 | ||||||||
\(63\) | 7.01827 | 0.884218 | ||||||||
\(64\) | −8.03466 | −1.00433 | ||||||||
\(65\) | −3.14784 | −0.390441 | ||||||||
\(66\) | −3.62044 | −0.445645 | ||||||||
\(67\) | −5.98455 | −0.731129 | −0.365564 | − | 0.930786i | \(-0.619124\pi\) | ||||
−0.365564 | + | 0.930786i | \(0.619124\pi\) | |||||||
\(68\) | −24.9765 | −3.02884 | ||||||||
\(69\) | −0.934786 | −0.112535 | ||||||||
\(70\) | 6.20576 | 0.741730 | ||||||||
\(71\) | −14.8288 | −1.75985 | −0.879927 | − | 0.475109i | \(-0.842409\pi\) | ||||
−0.879927 | + | 0.475109i | \(0.842409\pi\) | |||||||
\(72\) | 13.5450 | 1.59629 | ||||||||
\(73\) | −3.35326 | −0.392469 | −0.196235 | − | 0.980557i | \(-0.562871\pi\) | ||||
−0.196235 | + | 0.980557i | \(0.562871\pi\) | |||||||
\(74\) | −19.6441 | −2.28358 | ||||||||
\(75\) | 0.480075 | 0.0554343 | ||||||||
\(76\) | 21.1464 | 2.42566 | ||||||||
\(77\) | −7.80379 | −0.889324 | ||||||||
\(78\) | 3.70077 | 0.419030 | ||||||||
\(79\) | 14.7884 | 1.66382 | 0.831912 | − | 0.554908i | \(-0.187247\pi\) | ||||
0.831912 | + | 0.554908i | \(0.187247\pi\) | |||||||
\(80\) | 3.98264 | 0.445273 | ||||||||
\(81\) | 6.97887 | 0.775430 | ||||||||
\(82\) | −17.9198 | −1.97891 | ||||||||
\(83\) | −4.72106 | −0.518204 | −0.259102 | − | 0.965850i | \(-0.583427\pi\) | ||||
−0.259102 | + | 0.965850i | \(0.583427\pi\) | |||||||
\(84\) | −4.86272 | −0.530566 | ||||||||
\(85\) | −6.24864 | −0.677760 | ||||||||
\(86\) | 14.2660 | 1.53834 | ||||||||
\(87\) | 1.66789 | 0.178816 | ||||||||
\(88\) | −15.0610 | −1.60551 | ||||||||
\(89\) | −0.813636 | −0.0862452 | −0.0431226 | − | 0.999070i | \(-0.513731\pi\) | ||||
−0.0431226 | + | 0.999070i | \(0.513731\pi\) | |||||||
\(90\) | 6.78229 | 0.714917 | ||||||||
\(91\) | 7.97694 | 0.836211 | ||||||||
\(92\) | −7.78303 | −0.811437 | ||||||||
\(93\) | −1.63954 | −0.170013 | ||||||||
\(94\) | −14.6861 | −1.51475 | ||||||||
\(95\) | 5.29043 | 0.542787 | ||||||||
\(96\) | 0.0135993 | 0.00138797 | ||||||||
\(97\) | 4.19973 | 0.426418 | 0.213209 | − | 0.977007i | \(-0.431608\pi\) | ||||
0.213209 | + | 0.977007i | \(0.431608\pi\) | |||||||
\(98\) | 1.41626 | 0.143064 | ||||||||
\(99\) | −8.52878 | −0.857175 | ||||||||
\(100\) | 3.99711 | 0.399711 | ||||||||
\(101\) | −12.4301 | −1.23684 | −0.618419 | − | 0.785848i | \(-0.712227\pi\) | ||||
−0.618419 | + | 0.785848i | \(0.712227\pi\) | |||||||
\(102\) | 7.34625 | 0.727387 | ||||||||
\(103\) | 11.4006 | 1.12333 | 0.561665 | − | 0.827365i | \(-0.310161\pi\) | ||||
0.561665 | + | 0.827365i | \(0.310161\pi\) | |||||||
\(104\) | 15.3952 | 1.50962 | ||||||||
\(105\) | −1.21656 | −0.118724 | ||||||||
\(106\) | 4.41785 | 0.429099 | ||||||||
\(107\) | 16.7562 | 1.61988 | 0.809939 | − | 0.586514i | \(-0.199500\pi\) | ||||
0.809939 | + | 0.586514i | \(0.199500\pi\) | |||||||
\(108\) | −11.0712 | −1.06533 | ||||||||
\(109\) | −5.12379 | −0.490770 | −0.245385 | − | 0.969426i | \(-0.578914\pi\) | ||||
−0.245385 | + | 0.969426i | \(0.578914\pi\) | |||||||
\(110\) | −7.54140 | −0.719045 | ||||||||
\(111\) | 3.85097 | 0.365517 | ||||||||
\(112\) | −10.0924 | −0.953645 | ||||||||
\(113\) | 16.7026 | 1.57125 | 0.785623 | − | 0.618705i | \(-0.212342\pi\) | ||||
0.785623 | + | 0.618705i | \(0.212342\pi\) | |||||||
\(114\) | −6.21973 | −0.582531 | ||||||||
\(115\) | −1.94717 | −0.181574 | ||||||||
\(116\) | 13.8868 | 1.28936 | ||||||||
\(117\) | 8.71803 | 0.805982 | ||||||||
\(118\) | −22.0583 | −2.03063 | ||||||||
\(119\) | 15.8347 | 1.45156 | ||||||||
\(120\) | −2.34791 | −0.214334 | ||||||||
\(121\) | −1.51663 | −0.137875 | ||||||||
\(122\) | −37.0708 | −3.35624 | ||||||||
\(123\) | 3.51294 | 0.316751 | ||||||||
\(124\) | −13.6508 | −1.22588 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −17.1870 | −1.53114 | ||||||||
\(127\) | 7.12946 | 0.632637 | 0.316318 | − | 0.948653i | \(-0.397553\pi\) | ||||
0.316318 | + | 0.948653i | \(0.397553\pi\) | |||||||
\(128\) | 19.6194 | 1.73413 | ||||||||
\(129\) | −2.79666 | −0.246232 | ||||||||
\(130\) | 7.70874 | 0.676101 | ||||||||
\(131\) | 9.41479 | 0.822574 | 0.411287 | − | 0.911506i | \(-0.365079\pi\) | ||||
0.411287 | + | 0.911506i | \(0.365079\pi\) | |||||||
\(132\) | 5.90930 | 0.514339 | ||||||||
\(133\) | −13.4065 | −1.16249 | ||||||||
\(134\) | 14.6555 | 1.26605 | ||||||||
\(135\) | −2.76981 | −0.238387 | ||||||||
\(136\) | 30.5603 | 2.62052 | ||||||||
\(137\) | 5.93827 | 0.507340 | 0.253670 | − | 0.967291i | \(-0.418362\pi\) | ||||
0.253670 | + | 0.967291i | \(0.418362\pi\) | |||||||
\(138\) | 2.28920 | 0.194869 | ||||||||
\(139\) | −18.9302 | −1.60564 | −0.802821 | − | 0.596220i | \(-0.796669\pi\) | ||||
−0.802821 | + | 0.596220i | \(0.796669\pi\) | |||||||
\(140\) | −10.1291 | −0.856063 | ||||||||
\(141\) | 2.87901 | 0.242457 | ||||||||
\(142\) | 36.3142 | 3.04742 | ||||||||
\(143\) | −9.69379 | −0.810636 | ||||||||
\(144\) | −11.0300 | −0.919170 | ||||||||
\(145\) | 3.47422 | 0.288519 | ||||||||
\(146\) | 8.21179 | 0.679612 | ||||||||
\(147\) | −0.277640 | −0.0228994 | ||||||||
\(148\) | 32.0631 | 2.63557 | ||||||||
\(149\) | −16.7069 | −1.36868 | −0.684341 | − | 0.729162i | \(-0.739910\pi\) | ||||
−0.684341 | + | 0.729162i | \(0.739910\pi\) | |||||||
\(150\) | −1.17566 | −0.0959919 | ||||||||
\(151\) | 10.4096 | 0.847121 | 0.423560 | − | 0.905868i | \(-0.360780\pi\) | ||||
0.423560 | + | 0.905868i | \(0.360780\pi\) | |||||||
\(152\) | −25.8740 | −2.09866 | ||||||||
\(153\) | 17.3058 | 1.39909 | ||||||||
\(154\) | 19.1107 | 1.53998 | ||||||||
\(155\) | −3.41518 | −0.274314 | ||||||||
\(156\) | −6.04042 | −0.483621 | ||||||||
\(157\) | −20.5357 | −1.63893 | −0.819465 | − | 0.573130i | \(-0.805729\pi\) | ||||
−0.819465 | + | 0.573130i | \(0.805729\pi\) | |||||||
\(158\) | −36.2153 | −2.88113 | ||||||||
\(159\) | −0.866062 | −0.0686832 | ||||||||
\(160\) | 0.0283274 | 0.00223948 | ||||||||
\(161\) | 4.93432 | 0.388879 | ||||||||
\(162\) | −17.0905 | −1.34276 | ||||||||
\(163\) | −20.8535 | −1.63337 | −0.816687 | − | 0.577081i | \(-0.804192\pi\) | ||||
−0.816687 | + | 0.577081i | \(0.804192\pi\) | |||||||
\(164\) | 29.2487 | 2.28394 | ||||||||
\(165\) | 1.47840 | 0.115093 | ||||||||
\(166\) | 11.5614 | 0.897338 | ||||||||
\(167\) | −2.78002 | −0.215124 | −0.107562 | − | 0.994198i | \(-0.534304\pi\) | ||||
−0.107562 | + | 0.994198i | \(0.534304\pi\) | |||||||
\(168\) | 5.94984 | 0.459040 | ||||||||
\(169\) | −3.09112 | −0.237778 | ||||||||
\(170\) | 15.3023 | 1.17363 | ||||||||
\(171\) | −14.6520 | −1.12047 | ||||||||
\(172\) | −23.2850 | −1.77547 | ||||||||
\(173\) | −6.18322 | −0.470102 | −0.235051 | − | 0.971983i | \(-0.575526\pi\) | ||||
−0.235051 | + | 0.971983i | \(0.575526\pi\) | |||||||
\(174\) | −4.08449 | −0.309644 | ||||||||
\(175\) | −2.53410 | −0.191560 | ||||||||
\(176\) | 12.2646 | 0.924478 | ||||||||
\(177\) | 4.32425 | 0.325031 | ||||||||
\(178\) | 1.99251 | 0.149345 | ||||||||
\(179\) | −1.39814 | −0.104502 | −0.0522511 | − | 0.998634i | \(-0.516640\pi\) | ||||
−0.0522511 | + | 0.998634i | \(0.516640\pi\) | |||||||
\(180\) | −11.0701 | −0.825116 | ||||||||
\(181\) | 3.58045 | 0.266133 | 0.133066 | − | 0.991107i | \(-0.457518\pi\) | ||||
0.133066 | + | 0.991107i | \(0.457518\pi\) | |||||||
\(182\) | −19.5347 | −1.44801 | ||||||||
\(183\) | 7.26726 | 0.537211 | ||||||||
\(184\) | 9.52303 | 0.702047 | ||||||||
\(185\) | 8.02159 | 0.589759 | ||||||||
\(186\) | 4.01508 | 0.294400 | ||||||||
\(187\) | −19.2427 | −1.40717 | ||||||||
\(188\) | 23.9707 | 1.74824 | ||||||||
\(189\) | 7.01897 | 0.510555 | ||||||||
\(190\) | −12.9557 | −0.939908 | ||||||||
\(191\) | −18.3633 | −1.32872 | −0.664360 | − | 0.747413i | \(-0.731296\pi\) | ||||
−0.664360 | + | 0.747413i | \(0.731296\pi\) | |||||||
\(192\) | −3.85724 | −0.278372 | ||||||||
\(193\) | −19.5531 | −1.40747 | −0.703733 | − | 0.710465i | \(-0.748485\pi\) | ||||
−0.703733 | + | 0.710465i | \(0.748485\pi\) | |||||||
\(194\) | −10.2847 | −0.738400 | ||||||||
\(195\) | −1.51120 | −0.108219 | ||||||||
\(196\) | −2.31163 | −0.165117 | ||||||||
\(197\) | −19.2963 | −1.37481 | −0.687403 | − | 0.726276i | \(-0.741249\pi\) | ||||
−0.687403 | + | 0.726276i | \(0.741249\pi\) | |||||||
\(198\) | 20.8861 | 1.48431 | ||||||||
\(199\) | −2.35278 | −0.166784 | −0.0833922 | − | 0.996517i | \(-0.526575\pi\) | ||||
−0.0833922 | + | 0.996517i | \(0.526575\pi\) | |||||||
\(200\) | −4.89071 | −0.345825 | ||||||||
\(201\) | −2.87303 | −0.202648 | ||||||||
\(202\) | 30.4400 | 2.14175 | ||||||||
\(203\) | −8.80404 | −0.617922 | ||||||||
\(204\) | −11.9906 | −0.839509 | ||||||||
\(205\) | 7.31748 | 0.511075 | ||||||||
\(206\) | −27.9188 | −1.94520 | ||||||||
\(207\) | 5.39273 | 0.374821 | ||||||||
\(208\) | −12.5367 | −0.869265 | ||||||||
\(209\) | 16.2919 | 1.12694 | ||||||||
\(210\) | 2.97923 | 0.205586 | ||||||||
\(211\) | 6.12434 | 0.421617 | 0.210809 | − | 0.977527i | \(-0.432390\pi\) | ||||
0.210809 | + | 0.977527i | \(0.432390\pi\) | |||||||
\(212\) | −7.21084 | −0.495242 | ||||||||
\(213\) | −7.11893 | −0.487781 | ||||||||
\(214\) | −41.0341 | −2.80504 | ||||||||
\(215\) | −5.82547 | −0.397294 | ||||||||
\(216\) | 13.5463 | 0.921711 | ||||||||
\(217\) | 8.65442 | 0.587500 | ||||||||
\(218\) | 12.5476 | 0.849834 | ||||||||
\(219\) | −1.60982 | −0.108781 | ||||||||
\(220\) | 12.3091 | 0.829881 | ||||||||
\(221\) | 19.6697 | 1.32313 | ||||||||
\(222\) | −9.43062 | −0.632942 | ||||||||
\(223\) | −0.391247 | −0.0261998 | −0.0130999 | − | 0.999914i | \(-0.504170\pi\) | ||||
−0.0130999 | + | 0.999914i | \(0.504170\pi\) | |||||||
\(224\) | −0.0717845 | −0.00479631 | ||||||||
\(225\) | −2.76953 | −0.184635 | ||||||||
\(226\) | −40.9029 | −2.72082 | ||||||||
\(227\) | −7.94013 | −0.527005 | −0.263503 | − | 0.964659i | \(-0.584878\pi\) | ||||
−0.263503 | + | 0.964659i | \(0.584878\pi\) | |||||||
\(228\) | 10.1519 | 0.672324 | ||||||||
\(229\) | −5.83068 | −0.385302 | −0.192651 | − | 0.981267i | \(-0.561709\pi\) | ||||
−0.192651 | + | 0.981267i | \(0.561709\pi\) | |||||||
\(230\) | 4.76842 | 0.314420 | ||||||||
\(231\) | −3.74640 | −0.246495 | ||||||||
\(232\) | −16.9914 | −1.11554 | ||||||||
\(233\) | −14.4254 | −0.945040 | −0.472520 | − | 0.881320i | \(-0.656656\pi\) | ||||
−0.472520 | + | 0.881320i | \(0.656656\pi\) | |||||||
\(234\) | −21.3496 | −1.39566 | ||||||||
\(235\) | 5.99700 | 0.391201 | ||||||||
\(236\) | 36.0037 | 2.34364 | ||||||||
\(237\) | 7.09953 | 0.461164 | ||||||||
\(238\) | −38.7776 | −2.51358 | ||||||||
\(239\) | −4.48985 | −0.290424 | −0.145212 | − | 0.989401i | \(-0.546386\pi\) | ||||
−0.145212 | + | 0.989401i | \(0.546386\pi\) | |||||||
\(240\) | 1.91197 | 0.123417 | ||||||||
\(241\) | −28.7805 | −1.85391 | −0.926957 | − | 0.375169i | \(-0.877585\pi\) | ||||
−0.926957 | + | 0.375169i | \(0.877585\pi\) | |||||||
\(242\) | 3.71407 | 0.238750 | ||||||||
\(243\) | 11.6598 | 0.747977 | ||||||||
\(244\) | 60.5072 | 3.87358 | ||||||||
\(245\) | −0.578326 | −0.0369479 | ||||||||
\(246\) | −8.60284 | −0.548497 | ||||||||
\(247\) | −16.6534 | −1.05963 | ||||||||
\(248\) | 16.7027 | 1.06062 | ||||||||
\(249\) | −2.26646 | −0.143631 | ||||||||
\(250\) | −2.44890 | −0.154882 | ||||||||
\(251\) | −10.1473 | −0.640490 | −0.320245 | − | 0.947335i | \(-0.603765\pi\) | ||||
−0.320245 | + | 0.947335i | \(0.603765\pi\) | |||||||
\(252\) | 28.0528 | 1.76716 | ||||||||
\(253\) | −5.99632 | −0.376985 | ||||||||
\(254\) | −17.4593 | −1.09549 | ||||||||
\(255\) | −2.99982 | −0.187856 | ||||||||
\(256\) | −31.9766 | −1.99854 | ||||||||
\(257\) | −10.2348 | −0.638428 | −0.319214 | − | 0.947683i | \(-0.603419\pi\) | ||||
−0.319214 | + | 0.947683i | \(0.603419\pi\) | |||||||
\(258\) | 6.84875 | 0.426384 | ||||||||
\(259\) | −20.3275 | −1.26309 | ||||||||
\(260\) | −12.5822 | −0.780318 | ||||||||
\(261\) | −9.62196 | −0.595585 | ||||||||
\(262\) | −23.0559 | −1.42440 | ||||||||
\(263\) | 4.78085 | 0.294800 | 0.147400 | − | 0.989077i | \(-0.452910\pi\) | ||||
0.147400 | + | 0.989077i | \(0.452910\pi\) | |||||||
\(264\) | −7.23040 | −0.445001 | ||||||||
\(265\) | −1.80401 | −0.110820 | ||||||||
\(266\) | 32.8312 | 2.01301 | ||||||||
\(267\) | −0.390606 | −0.0239047 | ||||||||
\(268\) | −23.9209 | −1.46120 | ||||||||
\(269\) | −14.7226 | −0.897652 | −0.448826 | − | 0.893619i | \(-0.648158\pi\) | ||||
−0.448826 | + | 0.893619i | \(0.648158\pi\) | |||||||
\(270\) | 6.78298 | 0.412799 | ||||||||
\(271\) | 6.47774 | 0.393495 | 0.196747 | − | 0.980454i | \(-0.436962\pi\) | ||||
0.196747 | + | 0.980454i | \(0.436962\pi\) | |||||||
\(272\) | −24.8861 | −1.50894 | ||||||||
\(273\) | 3.82953 | 0.231774 | ||||||||
\(274\) | −14.5422 | −0.878528 | ||||||||
\(275\) | 3.07951 | 0.185701 | ||||||||
\(276\) | −3.73644 | −0.224907 | ||||||||
\(277\) | 31.3309 | 1.88249 | 0.941246 | − | 0.337722i | \(-0.109656\pi\) | ||||
0.941246 | + | 0.337722i | \(0.109656\pi\) | |||||||
\(278\) | 46.3582 | 2.78038 | ||||||||
\(279\) | 9.45844 | 0.566262 | ||||||||
\(280\) | 12.3936 | 0.740657 | ||||||||
\(281\) | −14.1883 | −0.846401 | −0.423201 | − | 0.906036i | \(-0.639093\pi\) | ||||
−0.423201 | + | 0.906036i | \(0.639093\pi\) | |||||||
\(282\) | −7.05041 | −0.419846 | ||||||||
\(283\) | 22.4388 | 1.33385 | 0.666925 | − | 0.745124i | \(-0.267610\pi\) | ||||
0.666925 | + | 0.745124i | \(0.267610\pi\) | |||||||
\(284\) | −59.2723 | −3.51716 | ||||||||
\(285\) | 2.53980 | 0.150445 | ||||||||
\(286\) | 23.7391 | 1.40372 | ||||||||
\(287\) | −18.5432 | −1.09457 | ||||||||
\(288\) | −0.0784535 | −0.00462292 | ||||||||
\(289\) | 22.0455 | 1.29679 | ||||||||
\(290\) | −8.50803 | −0.499608 | ||||||||
\(291\) | 2.01619 | 0.118191 | ||||||||
\(292\) | −13.4033 | −0.784370 | ||||||||
\(293\) | −28.4697 | −1.66322 | −0.831610 | − | 0.555360i | \(-0.812580\pi\) | ||||
−0.831610 | + | 0.555360i | \(0.812580\pi\) | |||||||
\(294\) | 0.679913 | 0.0396533 | ||||||||
\(295\) | 9.00745 | 0.524434 | ||||||||
\(296\) | −39.2313 | −2.28027 | ||||||||
\(297\) | −8.52964 | −0.494940 | ||||||||
\(298\) | 40.9135 | 2.37005 | ||||||||
\(299\) | 6.12937 | 0.354470 | ||||||||
\(300\) | 1.91891 | 0.110788 | ||||||||
\(301\) | 14.7623 | 0.850887 | ||||||||
\(302\) | −25.4920 | −1.46690 | ||||||||
\(303\) | −5.96737 | −0.342816 | ||||||||
\(304\) | 21.0699 | 1.20844 | ||||||||
\(305\) | 15.1378 | 0.866786 | ||||||||
\(306\) | −42.3801 | −2.42271 | ||||||||
\(307\) | −14.3822 | −0.820838 | −0.410419 | − | 0.911897i | \(-0.634618\pi\) | ||||
−0.410419 | + | 0.911897i | \(0.634618\pi\) | |||||||
\(308\) | −31.1926 | −1.77736 | ||||||||
\(309\) | 5.47312 | 0.311355 | ||||||||
\(310\) | 8.36343 | 0.475011 | ||||||||
\(311\) | −2.07599 | −0.117719 | −0.0588593 | − | 0.998266i | \(-0.518746\pi\) | ||||
−0.0588593 | + | 0.998266i | \(0.518746\pi\) | |||||||
\(312\) | 7.39084 | 0.418424 | ||||||||
\(313\) | −15.8042 | −0.893308 | −0.446654 | − | 0.894707i | \(-0.647384\pi\) | ||||
−0.446654 | + | 0.894707i | \(0.647384\pi\) | |||||||
\(314\) | 50.2899 | 2.83802 | ||||||||
\(315\) | 7.01827 | 0.395435 | ||||||||
\(316\) | 59.1107 | 3.32524 | ||||||||
\(317\) | 30.4849 | 1.71220 | 0.856102 | − | 0.516807i | \(-0.172879\pi\) | ||||
0.856102 | + | 0.516807i | \(0.172879\pi\) | |||||||
\(318\) | 2.12090 | 0.118934 | ||||||||
\(319\) | 10.6989 | 0.599024 | ||||||||
\(320\) | −8.03466 | −0.449151 | ||||||||
\(321\) | 8.04421 | 0.448984 | ||||||||
\(322\) | −12.0837 | −0.673396 | ||||||||
\(323\) | −33.0580 | −1.83940 | ||||||||
\(324\) | 27.8953 | 1.54974 | ||||||||
\(325\) | −3.14784 | −0.174611 | ||||||||
\(326\) | 51.0681 | 2.82840 | ||||||||
\(327\) | −2.45980 | −0.136027 | ||||||||
\(328\) | −35.7877 | −1.97604 | ||||||||
\(329\) | −15.1970 | −0.837839 | ||||||||
\(330\) | −3.62044 | −0.199299 | ||||||||
\(331\) | 27.0037 | 1.48426 | 0.742129 | − | 0.670257i | \(-0.233816\pi\) | ||||
0.742129 | + | 0.670257i | \(0.233816\pi\) | |||||||
\(332\) | −18.8706 | −1.03566 | ||||||||
\(333\) | −22.2160 | −1.21743 | ||||||||
\(334\) | 6.80798 | 0.372516 | ||||||||
\(335\) | −5.98455 | −0.326971 | ||||||||
\(336\) | −4.84512 | −0.264323 | ||||||||
\(337\) | 13.0842 | 0.712740 | 0.356370 | − | 0.934345i | \(-0.384014\pi\) | ||||
0.356370 | + | 0.934345i | \(0.384014\pi\) | |||||||
\(338\) | 7.56983 | 0.411745 | ||||||||
\(339\) | 8.01849 | 0.435505 | ||||||||
\(340\) | −24.9765 | −1.35454 | ||||||||
\(341\) | −10.5171 | −0.569532 | ||||||||
\(342\) | 35.8813 | 1.94024 | ||||||||
\(343\) | 19.2043 | 1.03693 | ||||||||
\(344\) | 28.4907 | 1.53612 | ||||||||
\(345\) | −0.934786 | −0.0503272 | ||||||||
\(346\) | 15.1421 | 0.814044 | ||||||||
\(347\) | −12.4848 | −0.670218 | −0.335109 | − | 0.942179i | \(-0.608773\pi\) | ||||
−0.335109 | + | 0.942179i | \(0.608773\pi\) | |||||||
\(348\) | 6.66673 | 0.357374 | ||||||||
\(349\) | 11.1143 | 0.594936 | 0.297468 | − | 0.954732i | \(-0.403858\pi\) | ||||
0.297468 | + | 0.954732i | \(0.403858\pi\) | |||||||
\(350\) | 6.20576 | 0.331712 | ||||||||
\(351\) | 8.71890 | 0.465381 | ||||||||
\(352\) | 0.0872345 | 0.00464961 | ||||||||
\(353\) | 0.464677 | 0.0247323 | 0.0123661 | − | 0.999924i | \(-0.496064\pi\) | ||||
0.0123661 | + | 0.999924i | \(0.496064\pi\) | |||||||
\(354\) | −10.5897 | −0.562834 | ||||||||
\(355\) | −14.8288 | −0.787031 | ||||||||
\(356\) | −3.25219 | −0.172366 | ||||||||
\(357\) | 7.60184 | 0.402332 | ||||||||
\(358\) | 3.42391 | 0.180960 | ||||||||
\(359\) | −29.0602 | −1.53374 | −0.766869 | − | 0.641804i | \(-0.778186\pi\) | ||||
−0.766869 | + | 0.641804i | \(0.778186\pi\) | |||||||
\(360\) | 13.5450 | 0.713882 | ||||||||
\(361\) | 8.98868 | 0.473088 | ||||||||
\(362\) | −8.76817 | −0.460845 | ||||||||
\(363\) | −0.728096 | −0.0382151 | ||||||||
\(364\) | 31.8847 | 1.67121 | ||||||||
\(365\) | −3.35326 | −0.175518 | ||||||||
\(366\) | −17.7968 | −0.930253 | ||||||||
\(367\) | −18.5068 | −0.966048 | −0.483024 | − | 0.875607i | \(-0.660462\pi\) | ||||
−0.483024 | + | 0.875607i | \(0.660462\pi\) | |||||||
\(368\) | −7.75487 | −0.404251 | ||||||||
\(369\) | −20.2660 | −1.05500 | ||||||||
\(370\) | −19.6441 | −1.02125 | ||||||||
\(371\) | 4.57156 | 0.237343 | ||||||||
\(372\) | −6.55343 | −0.339779 | ||||||||
\(373\) | 1.30486 | 0.0675633 | 0.0337816 | − | 0.999429i | \(-0.489245\pi\) | ||||
0.0337816 | + | 0.999429i | \(0.489245\pi\) | |||||||
\(374\) | 47.1235 | 2.43670 | ||||||||
\(375\) | 0.480075 | 0.0247910 | ||||||||
\(376\) | −29.3296 | −1.51256 | ||||||||
\(377\) | −10.9363 | −0.563248 | ||||||||
\(378\) | −17.1888 | −0.884094 | ||||||||
\(379\) | −20.4798 | −1.05198 | −0.525989 | − | 0.850491i | \(-0.676305\pi\) | ||||
−0.525989 | + | 0.850491i | \(0.676305\pi\) | |||||||
\(380\) | 21.1464 | 1.08479 | ||||||||
\(381\) | 3.42267 | 0.175349 | ||||||||
\(382\) | 44.9698 | 2.30085 | ||||||||
\(383\) | −13.4409 | −0.686799 | −0.343400 | − | 0.939189i | \(-0.611579\pi\) | ||||
−0.343400 | + | 0.939189i | \(0.611579\pi\) | |||||||
\(384\) | 9.41879 | 0.480651 | ||||||||
\(385\) | −7.80379 | −0.397718 | ||||||||
\(386\) | 47.8837 | 2.43721 | ||||||||
\(387\) | 16.1338 | 0.820127 | ||||||||
\(388\) | 16.7868 | 0.852220 | ||||||||
\(389\) | −29.7978 | −1.51081 | −0.755405 | − | 0.655258i | \(-0.772560\pi\) | ||||
−0.755405 | + | 0.655258i | \(0.772560\pi\) | |||||||
\(390\) | 3.70077 | 0.187396 | ||||||||
\(391\) | 12.1671 | 0.615319 | ||||||||
\(392\) | 2.82843 | 0.142857 | ||||||||
\(393\) | 4.51980 | 0.227994 | ||||||||
\(394\) | 47.2547 | 2.38066 | ||||||||
\(395\) | 14.7884 | 0.744084 | ||||||||
\(396\) | −34.0905 | −1.71311 | ||||||||
\(397\) | −8.76087 | −0.439695 | −0.219848 | − | 0.975534i | \(-0.570556\pi\) | ||||
−0.219848 | + | 0.975534i | \(0.570556\pi\) | |||||||
\(398\) | 5.76173 | 0.288809 | ||||||||
\(399\) | −6.43613 | −0.322209 | ||||||||
\(400\) | 3.98264 | 0.199132 | ||||||||
\(401\) | 19.3033 | 0.963961 | 0.481980 | − | 0.876182i | \(-0.339918\pi\) | ||||
0.481980 | + | 0.876182i | \(0.339918\pi\) | |||||||
\(402\) | 7.03576 | 0.350912 | ||||||||
\(403\) | 10.7504 | 0.535517 | ||||||||
\(404\) | −49.6843 | −2.47189 | ||||||||
\(405\) | 6.97887 | 0.346783 | ||||||||
\(406\) | 21.5602 | 1.07001 | ||||||||
\(407\) | 24.7025 | 1.22446 | ||||||||
\(408\) | 14.6712 | 0.726334 | ||||||||
\(409\) | 32.6824 | 1.61604 | 0.808020 | − | 0.589155i | \(-0.200539\pi\) | ||||
0.808020 | + | 0.589155i | \(0.200539\pi\) | |||||||
\(410\) | −17.9198 | −0.884995 | ||||||||
\(411\) | 2.85081 | 0.140620 | ||||||||
\(412\) | 45.5692 | 2.24503 | ||||||||
\(413\) | −22.8258 | −1.12318 | ||||||||
\(414\) | −13.2063 | −0.649052 | ||||||||
\(415\) | −4.72106 | −0.231748 | ||||||||
\(416\) | −0.0891701 | −0.00437192 | ||||||||
\(417\) | −9.08794 | −0.445038 | ||||||||
\(418\) | −39.8973 | −1.95144 | ||||||||
\(419\) | −4.29147 | −0.209652 | −0.104826 | − | 0.994491i | \(-0.533429\pi\) | ||||
−0.104826 | + | 0.994491i | \(0.533429\pi\) | |||||||
\(420\) | −4.86272 | −0.237276 | ||||||||
\(421\) | −20.2011 | −0.984542 | −0.492271 | − | 0.870442i | \(-0.663833\pi\) | ||||
−0.492271 | + | 0.870442i | \(0.663833\pi\) | |||||||
\(422\) | −14.9979 | −0.730086 | ||||||||
\(423\) | −16.6089 | −0.807551 | ||||||||
\(424\) | 8.82291 | 0.428479 | ||||||||
\(425\) | −6.24864 | −0.303104 | ||||||||
\(426\) | 17.4335 | 0.844658 | ||||||||
\(427\) | −38.3606 | −1.85640 | ||||||||
\(428\) | 66.9761 | 3.23741 | ||||||||
\(429\) | −4.65375 | −0.224685 | ||||||||
\(430\) | 14.2660 | 0.687967 | ||||||||
\(431\) | −7.86199 | −0.378699 | −0.189349 | − | 0.981910i | \(-0.560638\pi\) | ||||
−0.189349 | + | 0.981910i | \(0.560638\pi\) | |||||||
\(432\) | −11.0312 | −0.530737 | ||||||||
\(433\) | 10.3456 | 0.497177 | 0.248588 | − | 0.968609i | \(-0.420033\pi\) | ||||
0.248588 | + | 0.968609i | \(0.420033\pi\) | |||||||
\(434\) | −21.1938 | −1.01733 | ||||||||
\(435\) | 1.66789 | 0.0799691 | ||||||||
\(436\) | −20.4803 | −0.980830 | ||||||||
\(437\) | −10.3014 | −0.492781 | ||||||||
\(438\) | 3.94228 | 0.188369 | ||||||||
\(439\) | 27.2229 | 1.29928 | 0.649638 | − | 0.760244i | \(-0.274920\pi\) | ||||
0.649638 | + | 0.760244i | \(0.274920\pi\) | |||||||
\(440\) | −15.0610 | −0.718004 | ||||||||
\(441\) | 1.60169 | 0.0762710 | ||||||||
\(442\) | −48.1691 | −2.29117 | ||||||||
\(443\) | −15.9815 | −0.759306 | −0.379653 | − | 0.925129i | \(-0.623957\pi\) | ||||
−0.379653 | + | 0.925129i | \(0.623957\pi\) | |||||||
\(444\) | 15.3927 | 0.730506 | ||||||||
\(445\) | −0.813636 | −0.0385700 | ||||||||
\(446\) | 0.958124 | 0.0453685 | ||||||||
\(447\) | −8.02056 | −0.379359 | ||||||||
\(448\) | 20.3606 | 0.961950 | ||||||||
\(449\) | −25.0695 | −1.18310 | −0.591551 | − | 0.806267i | \(-0.701484\pi\) | ||||
−0.591551 | + | 0.806267i | \(0.701484\pi\) | |||||||
\(450\) | 6.78229 | 0.319720 | ||||||||
\(451\) | 22.5342 | 1.06110 | ||||||||
\(452\) | 66.7620 | 3.14022 | ||||||||
\(453\) | 4.99739 | 0.234798 | ||||||||
\(454\) | 19.4446 | 0.912579 | ||||||||
\(455\) | 7.97694 | 0.373965 | ||||||||
\(456\) | −12.4215 | −0.581688 | ||||||||
\(457\) | 0.0485111 | 0.00226925 | 0.00113463 | − | 0.999999i | \(-0.499639\pi\) | ||||
0.00113463 | + | 0.999999i | \(0.499639\pi\) | |||||||
\(458\) | 14.2788 | 0.667202 | ||||||||
\(459\) | 17.3075 | 0.807846 | ||||||||
\(460\) | −7.78303 | −0.362886 | ||||||||
\(461\) | 25.8435 | 1.20365 | 0.601825 | − | 0.798628i | \(-0.294441\pi\) | ||||
0.601825 | + | 0.798628i | \(0.294441\pi\) | |||||||
\(462\) | 9.17457 | 0.426839 | ||||||||
\(463\) | −11.1217 | −0.516871 | −0.258436 | − | 0.966029i | \(-0.583207\pi\) | ||||
−0.258436 | + | 0.966029i | \(0.583207\pi\) | |||||||
\(464\) | 13.8366 | 0.642348 | ||||||||
\(465\) | −1.63954 | −0.0760320 | ||||||||
\(466\) | 35.3264 | 1.63646 | ||||||||
\(467\) | 8.33562 | 0.385726 | 0.192863 | − | 0.981226i | \(-0.438223\pi\) | ||||
0.192863 | + | 0.981226i | \(0.438223\pi\) | |||||||
\(468\) | 34.8469 | 1.61080 | ||||||||
\(469\) | 15.1654 | 0.700275 | ||||||||
\(470\) | −14.6861 | −0.677417 | ||||||||
\(471\) | −9.85869 | −0.454265 | ||||||||
\(472\) | −44.0528 | −2.02770 | ||||||||
\(473\) | −17.9396 | −0.824863 | ||||||||
\(474\) | −17.3860 | −0.798567 | ||||||||
\(475\) | 5.29043 | 0.242742 | ||||||||
\(476\) | 63.2929 | 2.90103 | ||||||||
\(477\) | 4.99627 | 0.228763 | ||||||||
\(478\) | 10.9952 | 0.502908 | ||||||||
\(479\) | −32.4588 | −1.48308 | −0.741541 | − | 0.670907i | \(-0.765905\pi\) | ||||
−0.741541 | + | 0.670907i | \(0.765905\pi\) | |||||||
\(480\) | 0.0135993 | 0.000620720 0 | ||||||||
\(481\) | −25.2507 | −1.15133 | ||||||||
\(482\) | 70.4805 | 3.21030 | ||||||||
\(483\) | 2.36884 | 0.107786 | ||||||||
\(484\) | −6.06213 | −0.275551 | ||||||||
\(485\) | 4.19973 | 0.190700 | ||||||||
\(486\) | −28.5537 | −1.29522 | ||||||||
\(487\) | 7.85528 | 0.355957 | 0.177978 | − | 0.984034i | \(-0.443044\pi\) | ||||
0.177978 | + | 0.984034i | \(0.443044\pi\) | |||||||
\(488\) | −74.0344 | −3.35138 | ||||||||
\(489\) | −10.0113 | −0.452724 | ||||||||
\(490\) | 1.41626 | 0.0639802 | ||||||||
\(491\) | 18.0957 | 0.816649 | 0.408325 | − | 0.912837i | \(-0.366113\pi\) | ||||
0.408325 | + | 0.912837i | \(0.366113\pi\) | |||||||
\(492\) | 14.0416 | 0.633044 | ||||||||
\(493\) | −21.7092 | −0.977732 | ||||||||
\(494\) | 40.7826 | 1.83489 | ||||||||
\(495\) | −8.52878 | −0.383340 | ||||||||
\(496\) | −13.6015 | −0.610723 | ||||||||
\(497\) | 37.5777 | 1.68559 | ||||||||
\(498\) | 5.55034 | 0.248717 | ||||||||
\(499\) | 23.0160 | 1.03034 | 0.515168 | − | 0.857089i | \(-0.327729\pi\) | ||||
0.515168 | + | 0.857089i | \(0.327729\pi\) | |||||||
\(500\) | 3.99711 | 0.178756 | ||||||||
\(501\) | −1.33462 | −0.0596263 | ||||||||
\(502\) | 24.8496 | 1.10909 | ||||||||
\(503\) | −11.3548 | −0.506285 | −0.253143 | − | 0.967429i | \(-0.581464\pi\) | ||||
−0.253143 | + | 0.967429i | \(0.581464\pi\) | |||||||
\(504\) | −34.3243 | −1.52893 | ||||||||
\(505\) | −12.4301 | −0.553131 | ||||||||
\(506\) | 14.6844 | 0.652800 | ||||||||
\(507\) | −1.48397 | −0.0659053 | ||||||||
\(508\) | 28.4972 | 1.26436 | ||||||||
\(509\) | 18.3028 | 0.811256 | 0.405628 | − | 0.914038i | \(-0.367053\pi\) | ||||
0.405628 | + | 0.914038i | \(0.367053\pi\) | |||||||
\(510\) | 7.34625 | 0.325297 | ||||||||
\(511\) | 8.49750 | 0.375907 | ||||||||
\(512\) | 39.0687 | 1.72661 | ||||||||
\(513\) | −14.6535 | −0.646967 | ||||||||
\(514\) | 25.0639 | 1.10552 | ||||||||
\(515\) | 11.4006 | 0.502369 | ||||||||
\(516\) | −11.1786 | −0.492109 | ||||||||
\(517\) | 18.4678 | 0.812214 | ||||||||
\(518\) | 49.7801 | 2.18721 | ||||||||
\(519\) | −2.96841 | −0.130299 | ||||||||
\(520\) | 15.3952 | 0.675123 | ||||||||
\(521\) | −7.18084 | −0.314598 | −0.157299 | − | 0.987551i | \(-0.550279\pi\) | ||||
−0.157299 | + | 0.987551i | \(0.550279\pi\) | |||||||
\(522\) | 23.5632 | 1.03133 | ||||||||
\(523\) | 11.9804 | 0.523867 | 0.261934 | − | 0.965086i | \(-0.415640\pi\) | ||||
0.261934 | + | 0.965086i | \(0.415640\pi\) | |||||||
\(524\) | 37.6319 | 1.64396 | ||||||||
\(525\) | −1.21656 | −0.0530950 | ||||||||
\(526\) | −11.7078 | −0.510485 | ||||||||
\(527\) | 21.3402 | 0.929595 | ||||||||
\(528\) | 5.88792 | 0.256239 | ||||||||
\(529\) | −19.2085 | −0.835154 | ||||||||
\(530\) | 4.41785 | 0.191899 | ||||||||
\(531\) | −24.9464 | −1.08258 | ||||||||
\(532\) | −53.5872 | −2.32330 | ||||||||
\(533\) | −23.0342 | −0.997724 | ||||||||
\(534\) | 0.956555 | 0.0413942 | ||||||||
\(535\) | 16.7562 | 0.724432 | ||||||||
\(536\) | 29.2687 | 1.26421 | ||||||||
\(537\) | −0.671214 | −0.0289650 | ||||||||
\(538\) | 36.0541 | 1.55440 | ||||||||
\(539\) | −1.78096 | −0.0767114 | ||||||||
\(540\) | −11.0712 | −0.476429 | ||||||||
\(541\) | 33.4557 | 1.43837 | 0.719186 | − | 0.694817i | \(-0.244515\pi\) | ||||
0.719186 | + | 0.694817i | \(0.244515\pi\) | |||||||
\(542\) | −15.8633 | −0.681388 | ||||||||
\(543\) | 1.71889 | 0.0737645 | ||||||||
\(544\) | −0.177008 | −0.00758915 | ||||||||
\(545\) | −5.12379 | −0.219479 | ||||||||
\(546\) | −9.37814 | −0.401347 | ||||||||
\(547\) | 44.9808 | 1.92324 | 0.961620 | − | 0.274384i | \(-0.0884739\pi\) | ||||
0.961620 | + | 0.274384i | \(0.0884739\pi\) | |||||||
\(548\) | 23.7359 | 1.01395 | ||||||||
\(549\) | −41.9245 | −1.78929 | ||||||||
\(550\) | −7.54140 | −0.321567 | ||||||||
\(551\) | 18.3802 | 0.783021 | ||||||||
\(552\) | 4.57177 | 0.194587 | ||||||||
\(553\) | −37.4753 | −1.59361 | ||||||||
\(554\) | −76.7262 | −3.25978 | ||||||||
\(555\) | 3.85097 | 0.163464 | ||||||||
\(556\) | −75.6662 | −3.20896 | ||||||||
\(557\) | 22.3691 | 0.947810 | 0.473905 | − | 0.880576i | \(-0.342844\pi\) | ||||
0.473905 | + | 0.880576i | \(0.342844\pi\) | |||||||
\(558\) | −23.1628 | −0.980558 | ||||||||
\(559\) | 18.3376 | 0.775599 | ||||||||
\(560\) | −10.0924 | −0.426483 | ||||||||
\(561\) | −9.23796 | −0.390027 | ||||||||
\(562\) | 34.7456 | 1.46566 | ||||||||
\(563\) | −11.8754 | −0.500487 | −0.250243 | − | 0.968183i | \(-0.580511\pi\) | ||||
−0.250243 | + | 0.968183i | \(0.580511\pi\) | |||||||
\(564\) | 11.5077 | 0.484562 | ||||||||
\(565\) | 16.7026 | 0.702683 | ||||||||
\(566\) | −54.9505 | −2.30974 | ||||||||
\(567\) | −17.6852 | −0.742707 | ||||||||
\(568\) | 72.5233 | 3.04301 | ||||||||
\(569\) | −20.5794 | −0.862734 | −0.431367 | − | 0.902177i | \(-0.641969\pi\) | ||||
−0.431367 | + | 0.902177i | \(0.641969\pi\) | |||||||
\(570\) | −6.21973 | −0.260516 | ||||||||
\(571\) | 30.1821 | 1.26308 | 0.631540 | − | 0.775343i | \(-0.282423\pi\) | ||||
0.631540 | + | 0.775343i | \(0.282423\pi\) | |||||||
\(572\) | −38.7471 | −1.62010 | ||||||||
\(573\) | −8.81575 | −0.368283 | ||||||||
\(574\) | 45.4105 | 1.89540 | ||||||||
\(575\) | −1.94717 | −0.0812025 | ||||||||
\(576\) | 22.2522 | 0.927176 | ||||||||
\(577\) | 35.0830 | 1.46052 | 0.730262 | − | 0.683168i | \(-0.239398\pi\) | ||||
0.730262 | + | 0.683168i | \(0.239398\pi\) | |||||||
\(578\) | −53.9872 | −2.24557 | ||||||||
\(579\) | −9.38698 | −0.390109 | ||||||||
\(580\) | 13.8868 | 0.576620 | ||||||||
\(581\) | 11.9636 | 0.496336 | ||||||||
\(582\) | −4.93744 | −0.204663 | ||||||||
\(583\) | −5.55548 | −0.230084 | ||||||||
\(584\) | 16.3998 | 0.678629 | ||||||||
\(585\) | 8.71803 | 0.360446 | ||||||||
\(586\) | 69.7195 | 2.88009 | ||||||||
\(587\) | −27.9304 | −1.15281 | −0.576406 | − | 0.817164i | \(-0.695545\pi\) | ||||
−0.576406 | + | 0.817164i | \(0.695545\pi\) | |||||||
\(588\) | −1.10976 | −0.0457656 | ||||||||
\(589\) | −18.0678 | −0.744470 | ||||||||
\(590\) | −22.0583 | −0.908128 | ||||||||
\(591\) | −9.26368 | −0.381057 | ||||||||
\(592\) | 31.9471 | 1.31302 | ||||||||
\(593\) | −25.5426 | −1.04891 | −0.524454 | − | 0.851439i | \(-0.675730\pi\) | ||||
−0.524454 | + | 0.851439i | \(0.675730\pi\) | |||||||
\(594\) | 20.8882 | 0.857055 | ||||||||
\(595\) | 15.8347 | 0.649159 | ||||||||
\(596\) | −66.7792 | −2.73538 | ||||||||
\(597\) | −1.12951 | −0.0462279 | ||||||||
\(598\) | −15.0102 | −0.613813 | ||||||||
\(599\) | 20.5384 | 0.839175 | 0.419588 | − | 0.907715i | \(-0.362175\pi\) | ||||
0.419588 | + | 0.907715i | \(0.362175\pi\) | |||||||
\(600\) | −2.34791 | −0.0958530 | ||||||||
\(601\) | 23.9576 | 0.977251 | 0.488626 | − | 0.872494i | \(-0.337498\pi\) | ||||
0.488626 | + | 0.872494i | \(0.337498\pi\) | |||||||
\(602\) | −36.1515 | −1.47342 | ||||||||
\(603\) | 16.5744 | 0.674960 | ||||||||
\(604\) | 41.6083 | 1.69302 | ||||||||
\(605\) | −1.51663 | −0.0616598 | ||||||||
\(606\) | 14.6135 | 0.593632 | ||||||||
\(607\) | 15.7703 | 0.640096 | 0.320048 | − | 0.947401i | \(-0.396301\pi\) | ||||
0.320048 | + | 0.947401i | \(0.396301\pi\) | |||||||
\(608\) | 0.149864 | 0.00607780 | ||||||||
\(609\) | −4.22660 | −0.171270 | ||||||||
\(610\) | −37.0708 | −1.50095 | ||||||||
\(611\) | −18.8776 | −0.763706 | ||||||||
\(612\) | 69.1730 | 2.79615 | ||||||||
\(613\) | −15.9706 | −0.645048 | −0.322524 | − | 0.946561i | \(-0.604531\pi\) | ||||
−0.322524 | + | 0.946561i | \(0.604531\pi\) | |||||||
\(614\) | 35.2207 | 1.42139 | ||||||||
\(615\) | 3.51294 | 0.141655 | ||||||||
\(616\) | 38.1661 | 1.53775 | ||||||||
\(617\) | −36.1786 | −1.45649 | −0.728247 | − | 0.685315i | \(-0.759665\pi\) | ||||
−0.728247 | + | 0.685315i | \(0.759665\pi\) | |||||||
\(618\) | −13.4031 | −0.539153 | ||||||||
\(619\) | −12.4216 | −0.499268 | −0.249634 | − | 0.968340i | \(-0.580310\pi\) | ||||
−0.249634 | + | 0.968340i | \(0.580310\pi\) | |||||||
\(620\) | −13.6508 | −0.548231 | ||||||||
\(621\) | 5.39328 | 0.216425 | ||||||||
\(622\) | 5.08389 | 0.203845 | ||||||||
\(623\) | 2.06184 | 0.0826057 | ||||||||
\(624\) | −6.01857 | −0.240936 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 38.7029 | 1.54688 | ||||||||
\(627\) | 7.82135 | 0.312355 | ||||||||
\(628\) | −82.0835 | −3.27549 | ||||||||
\(629\) | −50.1240 | −1.99858 | ||||||||
\(630\) | −17.1870 | −0.684747 | ||||||||
\(631\) | −35.9860 | −1.43258 | −0.716290 | − | 0.697803i | \(-0.754161\pi\) | ||||
−0.716290 | + | 0.697803i | \(0.754161\pi\) | |||||||
\(632\) | −72.3257 | −2.87696 | ||||||||
\(633\) | 2.94014 | 0.116860 | ||||||||
\(634\) | −74.6545 | −2.96491 | ||||||||
\(635\) | 7.12946 | 0.282924 | ||||||||
\(636\) | −3.46174 | −0.137267 | ||||||||
\(637\) | 1.82048 | 0.0721300 | ||||||||
\(638\) | −26.2005 | −1.03729 | ||||||||
\(639\) | 41.0688 | 1.62465 | ||||||||
\(640\) | 19.6194 | 0.775526 | ||||||||
\(641\) | −7.05860 | −0.278798 | −0.139399 | − | 0.990236i | \(-0.544517\pi\) | ||||
−0.139399 | + | 0.990236i | \(0.544517\pi\) | |||||||
\(642\) | −19.6995 | −0.777476 | ||||||||
\(643\) | 41.2621 | 1.62722 | 0.813610 | − | 0.581411i | \(-0.197499\pi\) | ||||
0.813610 | + | 0.581411i | \(0.197499\pi\) | |||||||
\(644\) | 19.7230 | 0.777195 | ||||||||
\(645\) | −2.79666 | −0.110119 | ||||||||
\(646\) | 80.9557 | 3.18516 | ||||||||
\(647\) | 19.5248 | 0.767601 | 0.383800 | − | 0.923416i | \(-0.374615\pi\) | ||||
0.383800 | + | 0.923416i | \(0.374615\pi\) | |||||||
\(648\) | −34.1316 | −1.34082 | ||||||||
\(649\) | 27.7385 | 1.08883 | ||||||||
\(650\) | 7.70874 | 0.302362 | ||||||||
\(651\) | 4.15477 | 0.162838 | ||||||||
\(652\) | −83.3537 | −3.26438 | ||||||||
\(653\) | −28.2209 | −1.10437 | −0.552185 | − | 0.833721i | \(-0.686206\pi\) | ||||
−0.552185 | + | 0.833721i | \(0.686206\pi\) | |||||||
\(654\) | 6.02381 | 0.235550 | ||||||||
\(655\) | 9.41479 | 0.367866 | ||||||||
\(656\) | 29.1429 | 1.13784 | ||||||||
\(657\) | 9.28694 | 0.362318 | ||||||||
\(658\) | 37.2160 | 1.45083 | ||||||||
\(659\) | −34.3936 | −1.33978 | −0.669891 | − | 0.742459i | \(-0.733659\pi\) | ||||
−0.669891 | + | 0.742459i | \(0.733659\pi\) | |||||||
\(660\) | 5.90930 | 0.230019 | ||||||||
\(661\) | 30.1511 | 1.17274 | 0.586370 | − | 0.810043i | \(-0.300556\pi\) | ||||
0.586370 | + | 0.810043i | \(0.300556\pi\) | |||||||
\(662\) | −66.1294 | −2.57019 | ||||||||
\(663\) | 9.44294 | 0.366733 | ||||||||
\(664\) | 23.0893 | 0.896040 | ||||||||
\(665\) | −13.4065 | −0.519882 | ||||||||
\(666\) | 54.4048 | 2.10814 | ||||||||
\(667\) | −6.76490 | −0.261938 | ||||||||
\(668\) | −11.1120 | −0.429937 | ||||||||
\(669\) | −0.187828 | −0.00726184 | ||||||||
\(670\) | 14.6555 | 0.566193 | ||||||||
\(671\) | 46.6169 | 1.79962 | ||||||||
\(672\) | −0.0344620 | −0.00132940 | ||||||||
\(673\) | −13.4327 | −0.517791 | −0.258896 | − | 0.965905i | \(-0.583359\pi\) | ||||
−0.258896 | + | 0.965905i | \(0.583359\pi\) | |||||||
\(674\) | −32.0418 | −1.23420 | ||||||||
\(675\) | −2.76981 | −0.106610 | ||||||||
\(676\) | −12.3555 | −0.475212 | ||||||||
\(677\) | 16.8522 | 0.647682 | 0.323841 | − | 0.946112i | \(-0.395026\pi\) | ||||
0.323841 | + | 0.946112i | \(0.395026\pi\) | |||||||
\(678\) | −19.6365 | −0.754134 | ||||||||
\(679\) | −10.6426 | −0.408424 | ||||||||
\(680\) | 30.5603 | 1.17193 | ||||||||
\(681\) | −3.81186 | −0.146071 | ||||||||
\(682\) | 25.7553 | 0.986220 | ||||||||
\(683\) | −19.5865 | −0.749457 | −0.374729 | − | 0.927135i | \(-0.622264\pi\) | ||||
−0.374729 | + | 0.927135i | \(0.622264\pi\) | |||||||
\(684\) | −58.5656 | −2.23931 | ||||||||
\(685\) | 5.93827 | 0.226890 | ||||||||
\(686\) | −47.0293 | −1.79559 | ||||||||
\(687\) | −2.79917 | −0.106795 | ||||||||
\(688\) | −23.2008 | −0.884521 | ||||||||
\(689\) | 5.67875 | 0.216343 | ||||||||
\(690\) | 2.28920 | 0.0871483 | ||||||||
\(691\) | 14.1480 | 0.538216 | 0.269108 | − | 0.963110i | \(-0.413271\pi\) | ||||
0.269108 | + | 0.963110i | \(0.413271\pi\) | |||||||
\(692\) | −24.7150 | −0.939523 | ||||||||
\(693\) | 21.6128 | 0.821003 | ||||||||
\(694\) | 30.5739 | 1.16057 | ||||||||
\(695\) | −18.9302 | −0.718065 | ||||||||
\(696\) | −8.15716 | −0.309196 | ||||||||
\(697\) | −45.7243 | −1.73193 | ||||||||
\(698\) | −27.2178 | −1.03021 | ||||||||
\(699\) | −6.92528 | −0.261938 | ||||||||
\(700\) | −10.1291 | −0.382843 | ||||||||
\(701\) | −2.25243 | −0.0850731 | −0.0425366 | − | 0.999095i | \(-0.513544\pi\) | ||||
−0.0425366 | + | 0.999095i | \(0.513544\pi\) | |||||||
\(702\) | −21.3517 | −0.805868 | ||||||||
\(703\) | 42.4377 | 1.60057 | ||||||||
\(704\) | −24.7428 | −0.932529 | ||||||||
\(705\) | 2.87901 | 0.108430 | ||||||||
\(706\) | −1.13795 | −0.0428272 | ||||||||
\(707\) | 31.4991 | 1.18464 | ||||||||
\(708\) | 17.2845 | 0.649591 | ||||||||
\(709\) | −35.7603 | −1.34301 | −0.671503 | − | 0.741002i | \(-0.734351\pi\) | ||||
−0.671503 | + | 0.741002i | \(0.734351\pi\) | |||||||
\(710\) | 36.3142 | 1.36285 | ||||||||
\(711\) | −40.9568 | −1.53600 | ||||||||
\(712\) | 3.97926 | 0.149129 | ||||||||
\(713\) | 6.64993 | 0.249042 | ||||||||
\(714\) | −18.6161 | −0.696692 | ||||||||
\(715\) | −9.69379 | −0.362527 | ||||||||
\(716\) | −5.58853 | −0.208853 | ||||||||
\(717\) | −2.15547 | −0.0804973 | ||||||||
\(718\) | 71.1654 | 2.65587 | ||||||||
\(719\) | −36.9321 | −1.37733 | −0.688667 | − | 0.725078i | \(-0.741804\pi\) | ||||
−0.688667 | + | 0.725078i | \(0.741804\pi\) | |||||||
\(720\) | −11.0300 | −0.411066 | ||||||||
\(721\) | −28.8902 | −1.07593 | ||||||||
\(722\) | −22.0124 | −0.819215 | ||||||||
\(723\) | −13.8168 | −0.513852 | ||||||||
\(724\) | 14.3114 | 0.531881 | ||||||||
\(725\) | 3.47422 | 0.129029 | ||||||||
\(726\) | 1.78303 | 0.0661746 | ||||||||
\(727\) | −42.9674 | −1.59357 | −0.796787 | − | 0.604261i | \(-0.793469\pi\) | ||||
−0.796787 | + | 0.604261i | \(0.793469\pi\) | |||||||
\(728\) | −39.0129 | −1.44592 | ||||||||
\(729\) | −15.3390 | −0.568112 | ||||||||
\(730\) | 8.21179 | 0.303932 | ||||||||
\(731\) | 36.4013 | 1.34635 | ||||||||
\(732\) | 29.0480 | 1.07365 | ||||||||
\(733\) | −47.0090 | −1.73632 | −0.868158 | − | 0.496289i | \(-0.834696\pi\) | ||||
−0.868158 | + | 0.496289i | \(0.834696\pi\) | |||||||
\(734\) | 45.3213 | 1.67284 | ||||||||
\(735\) | −0.277640 | −0.0102409 | ||||||||
\(736\) | −0.0551582 | −0.00203316 | ||||||||
\(737\) | −18.4295 | −0.678858 | ||||||||
\(738\) | 49.6293 | 1.82688 | ||||||||
\(739\) | −6.73634 | −0.247800 | −0.123900 | − | 0.992295i | \(-0.539540\pi\) | ||||
−0.123900 | + | 0.992295i | \(0.539540\pi\) | |||||||
\(740\) | 32.0631 | 1.17866 | ||||||||
\(741\) | −7.99489 | −0.293700 | ||||||||
\(742\) | −11.1953 | −0.410992 | ||||||||
\(743\) | 20.2609 | 0.743300 | 0.371650 | − | 0.928373i | \(-0.378792\pi\) | ||||
0.371650 | + | 0.928373i | \(0.378792\pi\) | |||||||
\(744\) | 8.01853 | 0.293974 | ||||||||
\(745\) | −16.7069 | −0.612093 | ||||||||
\(746\) | −3.19548 | −0.116995 | ||||||||
\(747\) | 13.0751 | 0.478393 | ||||||||
\(748\) | −76.9153 | −2.81230 | ||||||||
\(749\) | −42.4618 | −1.55152 | ||||||||
\(750\) | −1.17566 | −0.0429289 | ||||||||
\(751\) | −22.6504 | −0.826526 | −0.413263 | − | 0.910612i | \(-0.635611\pi\) | ||||
−0.413263 | + | 0.910612i | \(0.635611\pi\) | |||||||
\(752\) | 23.8839 | 0.870958 | ||||||||
\(753\) | −4.87145 | −0.177525 | ||||||||
\(754\) | 26.7819 | 0.975339 | ||||||||
\(755\) | 10.4096 | 0.378844 | ||||||||
\(756\) | 28.0556 | 1.02037 | ||||||||
\(757\) | 6.34454 | 0.230596 | 0.115298 | − | 0.993331i | \(-0.463218\pi\) | ||||
0.115298 | + | 0.993331i | \(0.463218\pi\) | |||||||
\(758\) | 50.1530 | 1.82164 | ||||||||
\(759\) | −2.87868 | −0.104490 | ||||||||
\(760\) | −25.8740 | −0.938548 | ||||||||
\(761\) | 1.28478 | 0.0465734 | 0.0232867 | − | 0.999729i | \(-0.492587\pi\) | ||||
0.0232867 | + | 0.999729i | \(0.492587\pi\) | |||||||
\(762\) | −8.38178 | −0.303640 | ||||||||
\(763\) | 12.9842 | 0.470060 | ||||||||
\(764\) | −73.3999 | −2.65552 | ||||||||
\(765\) | 17.3058 | 0.625692 | ||||||||
\(766\) | 32.9155 | 1.18928 | ||||||||
\(767\) | −28.3540 | −1.02380 | ||||||||
\(768\) | −15.3512 | −0.553938 | ||||||||
\(769\) | −21.2973 | −0.767999 | −0.383999 | − | 0.923333i | \(-0.625454\pi\) | ||||
−0.383999 | + | 0.923333i | \(0.625454\pi\) | |||||||
\(770\) | 19.1107 | 0.688701 | ||||||||
\(771\) | −4.91346 | −0.176954 | ||||||||
\(772\) | −78.1560 | −2.81290 | ||||||||
\(773\) | 11.7775 | 0.423605 | 0.211803 | − | 0.977312i | \(-0.432067\pi\) | ||||
0.211803 | + | 0.977312i | \(0.432067\pi\) | |||||||
\(774\) | −39.5101 | −1.42016 | ||||||||
\(775\) | −3.41518 | −0.122677 | ||||||||
\(776\) | −20.5397 | −0.737332 | ||||||||
\(777\) | −9.75874 | −0.350093 | ||||||||
\(778\) | 72.9719 | 2.61617 | ||||||||
\(779\) | 38.7126 | 1.38702 | ||||||||
\(780\) | −6.04042 | −0.216282 | ||||||||
\(781\) | −45.6654 | −1.63404 | ||||||||
\(782\) | −29.7961 | −1.06551 | ||||||||
\(783\) | −9.62293 | −0.343895 | ||||||||
\(784\) | −2.30327 | −0.0822596 | ||||||||
\(785\) | −20.5357 | −0.732952 | ||||||||
\(786\) | −11.0685 | −0.394802 | ||||||||
\(787\) | −21.7232 | −0.774350 | −0.387175 | − | 0.922006i | \(-0.626549\pi\) | ||||
−0.387175 | + | 0.922006i | \(0.626549\pi\) | |||||||
\(788\) | −77.1294 | −2.74762 | ||||||||
\(789\) | 2.29517 | 0.0817101 | ||||||||
\(790\) | −36.2153 | −1.28848 | ||||||||
\(791\) | −42.3260 | −1.50494 | ||||||||
\(792\) | 41.7118 | 1.48216 | ||||||||
\(793\) | −47.6512 | −1.69214 | ||||||||
\(794\) | 21.4545 | 0.761391 | ||||||||
\(795\) | −0.866062 | −0.0307161 | ||||||||
\(796\) | −9.40432 | −0.333327 | ||||||||
\(797\) | −24.0857 | −0.853160 | −0.426580 | − | 0.904450i | \(-0.640282\pi\) | ||||
−0.426580 | + | 0.904450i | \(0.640282\pi\) | |||||||
\(798\) | 15.7614 | 0.557948 | ||||||||
\(799\) | −37.4731 | −1.32570 | ||||||||
\(800\) | 0.0283274 | 0.00100153 | ||||||||
\(801\) | 2.25339 | 0.0796195 | ||||||||
\(802\) | −47.2718 | −1.66923 | ||||||||
\(803\) | −10.3264 | −0.364410 | ||||||||
\(804\) | −11.4838 | −0.405003 | ||||||||
\(805\) | 4.93432 | 0.173912 | ||||||||
\(806\) | −26.3267 | −0.927320 | ||||||||
\(807\) | −7.06795 | −0.248804 | ||||||||
\(808\) | 60.7919 | 2.13865 | ||||||||
\(809\) | −50.5780 | −1.77823 | −0.889114 | − | 0.457685i | \(-0.848679\pi\) | ||||
−0.889114 | + | 0.457685i | \(0.848679\pi\) | |||||||
\(810\) | −17.0905 | −0.600501 | ||||||||
\(811\) | 13.7040 | 0.481213 | 0.240606 | − | 0.970623i | \(-0.422654\pi\) | ||||
0.240606 | + | 0.970623i | \(0.422654\pi\) | |||||||
\(812\) | −35.1907 | −1.23495 | ||||||||
\(813\) | 3.10980 | 0.109065 | ||||||||
\(814\) | −60.4940 | −2.12032 | ||||||||
\(815\) | −20.8535 | −0.730467 | ||||||||
\(816\) | −11.9472 | −0.418236 | ||||||||
\(817\) | −30.8193 | −1.07823 | ||||||||
\(818\) | −80.0359 | −2.79839 | ||||||||
\(819\) | −22.0924 | −0.771970 | ||||||||
\(820\) | 29.2487 | 1.02141 | ||||||||
\(821\) | 13.6115 | 0.475044 | 0.237522 | − | 0.971382i | \(-0.423665\pi\) | ||||
0.237522 | + | 0.971382i | \(0.423665\pi\) | |||||||
\(822\) | −6.98136 | −0.243503 | ||||||||
\(823\) | −20.8170 | −0.725634 | −0.362817 | − | 0.931860i | \(-0.618185\pi\) | ||||
−0.362817 | + | 0.931860i | \(0.618185\pi\) | |||||||
\(824\) | −55.7568 | −1.94238 | ||||||||
\(825\) | 1.47840 | 0.0514711 | ||||||||
\(826\) | 55.8981 | 1.94494 | ||||||||
\(827\) | 0.749750 | 0.0260714 | 0.0130357 | − | 0.999915i | \(-0.495850\pi\) | ||||
0.0130357 | + | 0.999915i | \(0.495850\pi\) | |||||||
\(828\) | 21.5553 | 0.749099 | ||||||||
\(829\) | 26.0817 | 0.905856 | 0.452928 | − | 0.891547i | \(-0.350379\pi\) | ||||
0.452928 | + | 0.891547i | \(0.350379\pi\) | |||||||
\(830\) | 11.5614 | 0.401302 | ||||||||
\(831\) | 15.0412 | 0.521773 | ||||||||
\(832\) | 25.2918 | 0.876836 | ||||||||
\(833\) | 3.61375 | 0.125209 | ||||||||
\(834\) | 22.2554 | 0.770643 | ||||||||
\(835\) | −2.78002 | −0.0962065 | ||||||||
\(836\) | 65.1206 | 2.25224 | ||||||||
\(837\) | 9.45939 | 0.326964 | ||||||||
\(838\) | 10.5094 | 0.363040 | ||||||||
\(839\) | 2.31302 | 0.0798541 | 0.0399271 | − | 0.999203i | \(-0.487287\pi\) | ||||
0.0399271 | + | 0.999203i | \(0.487287\pi\) | |||||||
\(840\) | 5.94984 | 0.205289 | ||||||||
\(841\) | −16.9298 | −0.583785 | ||||||||
\(842\) | 49.4705 | 1.70487 | ||||||||
\(843\) | −6.81144 | −0.234598 | ||||||||
\(844\) | 24.4796 | 0.842624 | ||||||||
\(845\) | −3.09112 | −0.106338 | ||||||||
\(846\) | 40.6734 | 1.39838 | ||||||||
\(847\) | 3.84330 | 0.132057 | ||||||||
\(848\) | −7.18475 | −0.246725 | ||||||||
\(849\) | 10.7723 | 0.369705 | ||||||||
\(850\) | 15.3023 | 0.524864 | ||||||||
\(851\) | −15.6194 | −0.535425 | ||||||||
\(852\) | −28.4551 | −0.974857 | ||||||||
\(853\) | −6.18254 | −0.211686 | −0.105843 | − | 0.994383i | \(-0.533754\pi\) | ||||
−0.105843 | + | 0.994383i | \(0.533754\pi\) | |||||||
\(854\) | 93.9413 | 3.21461 | ||||||||
\(855\) | −14.6520 | −0.501088 | ||||||||
\(856\) | −81.9495 | −2.80098 | ||||||||
\(857\) | −26.5409 | −0.906621 | −0.453310 | − | 0.891353i | \(-0.649757\pi\) | ||||
−0.453310 | + | 0.891353i | \(0.649757\pi\) | |||||||
\(858\) | 11.3966 | 0.389072 | ||||||||
\(859\) | 35.6768 | 1.21728 | 0.608639 | − | 0.793447i | \(-0.291716\pi\) | ||||
0.608639 | + | 0.793447i | \(0.291716\pi\) | |||||||
\(860\) | −23.2850 | −0.794013 | ||||||||
\(861\) | −8.90215 | −0.303384 | ||||||||
\(862\) | 19.2532 | 0.655767 | ||||||||
\(863\) | −23.1008 | −0.786361 | −0.393180 | − | 0.919461i | \(-0.628625\pi\) | ||||
−0.393180 | + | 0.919461i | \(0.628625\pi\) | |||||||
\(864\) | −0.0784614 | −0.00266931 | ||||||||
\(865\) | −6.18322 | −0.210236 | ||||||||
\(866\) | −25.3353 | −0.860927 | ||||||||
\(867\) | 10.5835 | 0.359434 | ||||||||
\(868\) | 34.5926 | 1.17415 | ||||||||
\(869\) | 45.5409 | 1.54487 | ||||||||
\(870\) | −4.08449 | −0.138477 | ||||||||
\(871\) | 18.8384 | 0.638314 | ||||||||
\(872\) | 25.0590 | 0.848604 | ||||||||
\(873\) | −11.6313 | −0.393659 | ||||||||
\(874\) | 25.2270 | 0.853315 | ||||||||
\(875\) | −2.53410 | −0.0856683 | ||||||||
\(876\) | −6.43460 | −0.217405 | ||||||||
\(877\) | −30.7259 | −1.03754 | −0.518771 | − | 0.854913i | \(-0.673610\pi\) | ||||
−0.518771 | + | 0.854913i | \(0.673610\pi\) | |||||||
\(878\) | −66.6660 | −2.24987 | ||||||||
\(879\) | −13.6676 | −0.460997 | ||||||||
\(880\) | 12.2646 | 0.413439 | ||||||||
\(881\) | 13.9479 | 0.469915 | 0.234958 | − | 0.972006i | \(-0.424505\pi\) | ||||
0.234958 | + | 0.972006i | \(0.424505\pi\) | |||||||
\(882\) | −3.92238 | −0.132073 | ||||||||
\(883\) | 36.2623 | 1.22032 | 0.610161 | − | 0.792277i | \(-0.291105\pi\) | ||||
0.610161 | + | 0.792277i | \(0.291105\pi\) | |||||||
\(884\) | 78.6219 | 2.64434 | ||||||||
\(885\) | 4.32425 | 0.145358 | ||||||||
\(886\) | 39.1372 | 1.31484 | ||||||||
\(887\) | −54.9928 | −1.84648 | −0.923239 | − | 0.384225i | \(-0.874469\pi\) | ||||
−0.923239 | + | 0.384225i | \(0.874469\pi\) | |||||||
\(888\) | −18.8340 | −0.632026 | ||||||||
\(889\) | −18.0668 | −0.605940 | ||||||||
\(890\) | 1.99251 | 0.0667891 | ||||||||
\(891\) | 21.4915 | 0.719992 | ||||||||
\(892\) | −1.56385 | −0.0523617 | ||||||||
\(893\) | 31.7267 | 1.06170 | ||||||||
\(894\) | 19.6415 | 0.656911 | ||||||||
\(895\) | −1.39814 | −0.0467348 | ||||||||
\(896\) | −49.7176 | −1.66095 | ||||||||
\(897\) | 2.94256 | 0.0982491 | ||||||||
\(898\) | 61.3927 | 2.04870 | ||||||||
\(899\) | −11.8651 | −0.395723 | ||||||||
\(900\) | −11.0701 | −0.369003 | ||||||||
\(901\) | 11.2726 | 0.375546 | ||||||||
\(902\) | −55.1841 | −1.83743 | ||||||||
\(903\) | 7.08703 | 0.235842 | ||||||||
\(904\) | −81.6875 | −2.71689 | ||||||||
\(905\) | 3.58045 | 0.119018 | ||||||||
\(906\) | −12.2381 | −0.406584 | ||||||||
\(907\) | −25.7799 | −0.856009 | −0.428004 | − | 0.903777i | \(-0.640783\pi\) | ||||
−0.428004 | + | 0.903777i | \(0.640783\pi\) | |||||||
\(908\) | −31.7376 | −1.05325 | ||||||||
\(909\) | 34.4254 | 1.14182 | ||||||||
\(910\) | −19.5347 | −0.647570 | ||||||||
\(911\) | −2.23560 | −0.0740687 | −0.0370344 | − | 0.999314i | \(-0.511791\pi\) | ||||
−0.0370344 | + | 0.999314i | \(0.511791\pi\) | |||||||
\(912\) | 10.1151 | 0.334946 | ||||||||
\(913\) | −14.5385 | −0.481155 | ||||||||
\(914\) | −0.118799 | −0.00392952 | ||||||||
\(915\) | 7.26726 | 0.240248 | ||||||||
\(916\) | −23.3059 | −0.770047 | ||||||||
\(917\) | −23.8580 | −0.787862 | ||||||||
\(918\) | −42.3844 | −1.39889 | ||||||||
\(919\) | 17.7434 | 0.585300 | 0.292650 | − | 0.956220i | \(-0.405463\pi\) | ||||
0.292650 | + | 0.956220i | \(0.405463\pi\) | |||||||
\(920\) | 9.52303 | 0.313965 | ||||||||
\(921\) | −6.90456 | −0.227513 | ||||||||
\(922\) | −63.2880 | −2.08428 | ||||||||
\(923\) | 46.6786 | 1.53645 | ||||||||
\(924\) | −14.9748 | −0.492634 | ||||||||
\(925\) | 8.02159 | 0.263748 | ||||||||
\(926\) | 27.2360 | 0.895031 | ||||||||
\(927\) | −31.5742 | −1.03703 | ||||||||
\(928\) | 0.0984158 | 0.00323066 | ||||||||
\(929\) | −23.8895 | −0.783788 | −0.391894 | − | 0.920010i | \(-0.628180\pi\) | ||||
−0.391894 | + | 0.920010i | \(0.628180\pi\) | |||||||
\(930\) | 4.01508 | 0.131660 | ||||||||
\(931\) | −3.05960 | −0.100274 | ||||||||
\(932\) | −57.6599 | −1.88871 | ||||||||
\(933\) | −0.996632 | −0.0326283 | ||||||||
\(934\) | −20.4131 | −0.667937 | ||||||||
\(935\) | −19.2427 | −0.629305 | ||||||||
\(936\) | −42.6373 | −1.39365 | ||||||||
\(937\) | −19.1165 | −0.624509 | −0.312255 | − | 0.949998i | \(-0.601084\pi\) | ||||
−0.312255 | + | 0.949998i | \(0.601084\pi\) | |||||||
\(938\) | −37.1387 | −1.21262 | ||||||||
\(939\) | −7.58721 | −0.247599 | ||||||||
\(940\) | 23.9707 | 0.781837 | ||||||||
\(941\) | 25.1192 | 0.818861 | 0.409431 | − | 0.912341i | \(-0.365727\pi\) | ||||
0.409431 | + | 0.912341i | \(0.365727\pi\) | |||||||
\(942\) | 24.1429 | 0.786620 | ||||||||
\(943\) | −14.2484 | −0.463990 | ||||||||
\(944\) | 35.8735 | 1.16758 | ||||||||
\(945\) | 7.01897 | 0.228327 | ||||||||
\(946\) | 43.9322 | 1.42836 | ||||||||
\(947\) | 22.7177 | 0.738227 | 0.369114 | − | 0.929384i | \(-0.379661\pi\) | ||||
0.369114 | + | 0.929384i | \(0.379661\pi\) | |||||||
\(948\) | 28.3776 | 0.921661 | ||||||||
\(949\) | 10.5555 | 0.342646 | ||||||||
\(950\) | −12.9557 | −0.420340 | ||||||||
\(951\) | 14.6351 | 0.474574 | ||||||||
\(952\) | −77.4429 | −2.50994 | ||||||||
\(953\) | 45.5869 | 1.47670 | 0.738352 | − | 0.674416i | \(-0.235605\pi\) | ||||
0.738352 | + | 0.674416i | \(0.235605\pi\) | |||||||
\(954\) | −12.2354 | −0.396134 | ||||||||
\(955\) | −18.3633 | −0.594221 | ||||||||
\(956\) | −17.9464 | −0.580428 | ||||||||
\(957\) | 5.13628 | 0.166032 | ||||||||
\(958\) | 79.4884 | 2.56815 | ||||||||
\(959\) | −15.0482 | −0.485931 | ||||||||
\(960\) | −3.85724 | −0.124492 | ||||||||
\(961\) | −19.3365 | −0.623759 | ||||||||
\(962\) | 61.8363 | 1.99368 | ||||||||
\(963\) | −46.4066 | −1.49543 | ||||||||
\(964\) | −115.039 | −3.70514 | ||||||||
\(965\) | −19.5531 | −0.629438 | ||||||||
\(966\) | −5.80106 | −0.186646 | ||||||||
\(967\) | 32.6088 | 1.04863 | 0.524314 | − | 0.851525i | \(-0.324322\pi\) | ||||
0.524314 | + | 0.851525i | \(0.324322\pi\) | |||||||
\(968\) | 7.41740 | 0.238404 | ||||||||
\(969\) | −15.8703 | −0.509828 | ||||||||
\(970\) | −10.2847 | −0.330223 | ||||||||
\(971\) | 15.7664 | 0.505969 | 0.252984 | − | 0.967470i | \(-0.418588\pi\) | ||||
0.252984 | + | 0.967470i | \(0.418588\pi\) | |||||||
\(972\) | 46.6055 | 1.49487 | ||||||||
\(973\) | 47.9712 | 1.53788 | ||||||||
\(974\) | −19.2368 | −0.616386 | ||||||||
\(975\) | −1.51120 | −0.0483971 | ||||||||
\(976\) | 60.2883 | 1.92978 | ||||||||
\(977\) | 22.8696 | 0.731663 | 0.365831 | − | 0.930681i | \(-0.380785\pi\) | ||||
0.365831 | + | 0.930681i | \(0.380785\pi\) | |||||||
\(978\) | 24.5165 | 0.783953 | ||||||||
\(979\) | −2.50560 | −0.0800793 | ||||||||
\(980\) | −2.31163 | −0.0738424 | ||||||||
\(981\) | 14.1905 | 0.453067 | ||||||||
\(982\) | −44.3146 | −1.41414 | ||||||||
\(983\) | 24.5627 | 0.783430 | 0.391715 | − | 0.920087i | \(-0.371882\pi\) | ||||
0.391715 | + | 0.920087i | \(0.371882\pi\) | |||||||
\(984\) | −17.1808 | −0.547703 | ||||||||
\(985\) | −19.2963 | −0.614832 | ||||||||
\(986\) | 53.1636 | 1.69307 | ||||||||
\(987\) | −7.29571 | −0.232225 | ||||||||
\(988\) | −66.5655 | −2.11773 | ||||||||
\(989\) | 11.3432 | 0.360692 | ||||||||
\(990\) | 20.8861 | 0.663805 | ||||||||
\(991\) | 12.0385 | 0.382414 | 0.191207 | − | 0.981550i | \(-0.438760\pi\) | ||||
0.191207 | + | 0.981550i | \(0.438760\pi\) | |||||||
\(992\) | −0.0967432 | −0.00307160 | ||||||||
\(993\) | 12.9638 | 0.411394 | ||||||||
\(994\) | −92.0239 | −2.91882 | ||||||||
\(995\) | −2.35278 | −0.0745882 | ||||||||
\(996\) | −9.05929 | −0.287055 | ||||||||
\(997\) | 37.3739 | 1.18364 | 0.591822 | − | 0.806069i | \(-0.298409\pi\) | ||||
0.591822 | + | 0.806069i | \(0.298409\pi\) | |||||||
\(998\) | −56.3638 | −1.78417 | ||||||||
\(999\) | −22.2183 | −0.702954 |
(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 | 8005.2.a.e.1.12 | ✓ | 126 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8005.2.a.e.1.12 | ✓ | 126 | 1.1 | even | 1 | trivial |