Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8007,2,Mod(1,8007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8007, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8007 = 3 \cdot 17 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8007.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: | \(63.9362168984\) |
Analytic rank: | \(0\) |
Dimension: | \(64\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 8007.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.69942 | −1.90878 | −0.954391 | − | 0.298560i | \(-0.903494\pi\) | ||||
−0.954391 | + | 0.298560i | \(0.903494\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 5.28690 | 2.64345 | ||||||||
\(5\) | 3.29410 | 1.47317 | 0.736583 | − | 0.676347i | \(-0.236438\pi\) | ||||
0.736583 | + | 0.676347i | \(0.236438\pi\) | |||||||
\(6\) | 2.69942 | 1.10204 | ||||||||
\(7\) | 4.13717 | 1.56370 | 0.781851 | − | 0.623465i | \(-0.214276\pi\) | ||||
0.781851 | + | 0.623465i | \(0.214276\pi\) | |||||||
\(8\) | −8.87273 | −3.13698 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −8.89217 | −2.81195 | ||||||||
\(11\) | 1.26440 | 0.381232 | 0.190616 | − | 0.981665i | \(-0.438951\pi\) | ||||
0.190616 | + | 0.981665i | \(0.438951\pi\) | |||||||
\(12\) | −5.28690 | −1.52620 | ||||||||
\(13\) | 5.50466 | 1.52672 | 0.763359 | − | 0.645975i | \(-0.223549\pi\) | ||||
0.763359 | + | 0.645975i | \(0.223549\pi\) | |||||||
\(14\) | −11.1680 | −2.98477 | ||||||||
\(15\) | −3.29410 | −0.850532 | ||||||||
\(16\) | 13.3775 | 3.34437 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −2.69942 | −0.636261 | ||||||||
\(19\) | 3.75022 | 0.860359 | 0.430179 | − | 0.902743i | \(-0.358450\pi\) | ||||
0.430179 | + | 0.902743i | \(0.358450\pi\) | |||||||
\(20\) | 17.4156 | 3.89424 | ||||||||
\(21\) | −4.13717 | −0.902804 | ||||||||
\(22\) | −3.41316 | −0.727689 | ||||||||
\(23\) | −5.79289 | −1.20790 | −0.603951 | − | 0.797022i | \(-0.706408\pi\) | ||||
−0.603951 | + | 0.797022i | \(0.706408\pi\) | |||||||
\(24\) | 8.87273 | 1.81114 | ||||||||
\(25\) | 5.85108 | 1.17022 | ||||||||
\(26\) | −14.8594 | −2.91417 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 21.8728 | 4.13357 | ||||||||
\(29\) | 1.48332 | 0.275445 | 0.137723 | − | 0.990471i | \(-0.456022\pi\) | ||||
0.137723 | + | 0.990471i | \(0.456022\pi\) | |||||||
\(30\) | 8.89217 | 1.62348 | ||||||||
\(31\) | −5.62716 | −1.01067 | −0.505334 | − | 0.862924i | \(-0.668631\pi\) | ||||
−0.505334 | + | 0.862924i | \(0.668631\pi\) | |||||||
\(32\) | −18.3660 | −3.24668 | ||||||||
\(33\) | −1.26440 | −0.220105 | ||||||||
\(34\) | −2.69942 | −0.462948 | ||||||||
\(35\) | 13.6282 | 2.30359 | ||||||||
\(36\) | 5.28690 | 0.881149 | ||||||||
\(37\) | 9.89414 | 1.62659 | 0.813293 | − | 0.581854i | \(-0.197672\pi\) | ||||
0.813293 | + | 0.581854i | \(0.197672\pi\) | |||||||
\(38\) | −10.1234 | −1.64224 | ||||||||
\(39\) | −5.50466 | −0.881451 | ||||||||
\(40\) | −29.2276 | −4.62129 | ||||||||
\(41\) | 3.72683 | 0.582033 | 0.291017 | − | 0.956718i | \(-0.406007\pi\) | ||||
0.291017 | + | 0.956718i | \(0.406007\pi\) | |||||||
\(42\) | 11.1680 | 1.72326 | ||||||||
\(43\) | −3.23636 | −0.493541 | −0.246770 | − | 0.969074i | \(-0.579369\pi\) | ||||
−0.246770 | + | 0.969074i | \(0.579369\pi\) | |||||||
\(44\) | 6.68477 | 1.00777 | ||||||||
\(45\) | 3.29410 | 0.491055 | ||||||||
\(46\) | 15.6375 | 2.30562 | ||||||||
\(47\) | 1.75649 | 0.256210 | 0.128105 | − | 0.991761i | \(-0.459111\pi\) | ||||
0.128105 | + | 0.991761i | \(0.459111\pi\) | |||||||
\(48\) | −13.3775 | −1.93087 | ||||||||
\(49\) | 10.1162 | 1.44517 | ||||||||
\(50\) | −15.7946 | −2.23369 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | 29.1025 | 4.03580 | ||||||||
\(53\) | −6.58226 | −0.904143 | −0.452071 | − | 0.891982i | \(-0.649315\pi\) | ||||
−0.452071 | + | 0.891982i | \(0.649315\pi\) | |||||||
\(54\) | 2.69942 | 0.367345 | ||||||||
\(55\) | 4.16507 | 0.561618 | ||||||||
\(56\) | −36.7080 | −4.90531 | ||||||||
\(57\) | −3.75022 | −0.496728 | ||||||||
\(58\) | −4.00411 | −0.525765 | ||||||||
\(59\) | −13.0815 | −1.70307 | −0.851536 | − | 0.524296i | \(-0.824328\pi\) | ||||
−0.851536 | + | 0.524296i | \(0.824328\pi\) | |||||||
\(60\) | −17.4156 | −2.24834 | ||||||||
\(61\) | −1.45833 | −0.186721 | −0.0933603 | − | 0.995632i | \(-0.529761\pi\) | ||||
−0.0933603 | + | 0.995632i | \(0.529761\pi\) | |||||||
\(62\) | 15.1901 | 1.92915 | ||||||||
\(63\) | 4.13717 | 0.521234 | ||||||||
\(64\) | 22.8228 | 2.85285 | ||||||||
\(65\) | 18.1329 | 2.24911 | ||||||||
\(66\) | 3.41316 | 0.420132 | ||||||||
\(67\) | −15.7266 | −1.92131 | −0.960653 | − | 0.277751i | \(-0.910411\pi\) | ||||
−0.960653 | + | 0.277751i | \(0.910411\pi\) | |||||||
\(68\) | 5.28690 | 0.641130 | ||||||||
\(69\) | 5.79289 | 0.697382 | ||||||||
\(70\) | −36.7884 | −4.39706 | ||||||||
\(71\) | −0.751536 | −0.0891910 | −0.0445955 | − | 0.999005i | \(-0.514200\pi\) | ||||
−0.0445955 | + | 0.999005i | \(0.514200\pi\) | |||||||
\(72\) | −8.87273 | −1.04566 | ||||||||
\(73\) | 8.74535 | 1.02357 | 0.511783 | − | 0.859115i | \(-0.328985\pi\) | ||||
0.511783 | + | 0.859115i | \(0.328985\pi\) | |||||||
\(74\) | −26.7085 | −3.10480 | ||||||||
\(75\) | −5.85108 | −0.675625 | ||||||||
\(76\) | 19.8270 | 2.27431 | ||||||||
\(77\) | 5.23105 | 0.596134 | ||||||||
\(78\) | 14.8594 | 1.68250 | ||||||||
\(79\) | −8.70356 | −0.979227 | −0.489614 | − | 0.871939i | \(-0.662862\pi\) | ||||
−0.489614 | + | 0.871939i | \(0.662862\pi\) | |||||||
\(80\) | 44.0667 | 4.92681 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −10.0603 | −1.11097 | ||||||||
\(83\) | −8.79348 | −0.965210 | −0.482605 | − | 0.875838i | \(-0.660309\pi\) | ||||
−0.482605 | + | 0.875838i | \(0.660309\pi\) | |||||||
\(84\) | −21.8728 | −2.38652 | ||||||||
\(85\) | 3.29410 | 0.357295 | ||||||||
\(86\) | 8.73632 | 0.942062 | ||||||||
\(87\) | −1.48332 | −0.159029 | ||||||||
\(88\) | −11.2187 | −1.19592 | ||||||||
\(89\) | 4.33618 | 0.459634 | 0.229817 | − | 0.973234i | \(-0.426187\pi\) | ||||
0.229817 | + | 0.973234i | \(0.426187\pi\) | |||||||
\(90\) | −8.89217 | −0.937317 | ||||||||
\(91\) | 22.7737 | 2.38733 | ||||||||
\(92\) | −30.6264 | −3.19302 | ||||||||
\(93\) | 5.62716 | 0.583510 | ||||||||
\(94\) | −4.74151 | −0.489049 | ||||||||
\(95\) | 12.3536 | 1.26745 | ||||||||
\(96\) | 18.3660 | 1.87447 | ||||||||
\(97\) | 12.3848 | 1.25749 | 0.628744 | − | 0.777612i | \(-0.283569\pi\) | ||||
0.628744 | + | 0.777612i | \(0.283569\pi\) | |||||||
\(98\) | −27.3078 | −2.75851 | ||||||||
\(99\) | 1.26440 | 0.127077 | ||||||||
\(100\) | 30.9341 | 3.09341 | ||||||||
\(101\) | 9.24128 | 0.919542 | 0.459771 | − | 0.888038i | \(-0.347932\pi\) | ||||
0.459771 | + | 0.888038i | \(0.347932\pi\) | |||||||
\(102\) | 2.69942 | 0.267283 | ||||||||
\(103\) | −8.06351 | −0.794521 | −0.397261 | − | 0.917706i | \(-0.630039\pi\) | ||||
−0.397261 | + | 0.917706i | \(0.630039\pi\) | |||||||
\(104\) | −48.8413 | −4.78929 | ||||||||
\(105\) | −13.6282 | −1.32998 | ||||||||
\(106\) | 17.7683 | 1.72581 | ||||||||
\(107\) | 19.4006 | 1.87553 | 0.937763 | − | 0.347277i | \(-0.112894\pi\) | ||||
0.937763 | + | 0.347277i | \(0.112894\pi\) | |||||||
\(108\) | −5.28690 | −0.508732 | ||||||||
\(109\) | −8.87914 | −0.850467 | −0.425234 | − | 0.905084i | \(-0.639808\pi\) | ||||
−0.425234 | + | 0.905084i | \(0.639808\pi\) | |||||||
\(110\) | −11.2433 | −1.07201 | ||||||||
\(111\) | −9.89414 | −0.939110 | ||||||||
\(112\) | 55.3448 | 5.22960 | ||||||||
\(113\) | 12.5063 | 1.17650 | 0.588249 | − | 0.808680i | \(-0.299818\pi\) | ||||
0.588249 | + | 0.808680i | \(0.299818\pi\) | |||||||
\(114\) | 10.1234 | 0.948146 | ||||||||
\(115\) | −19.0824 | −1.77944 | ||||||||
\(116\) | 7.84215 | 0.728126 | ||||||||
\(117\) | 5.50466 | 0.508906 | ||||||||
\(118\) | 35.3126 | 3.25079 | ||||||||
\(119\) | 4.13717 | 0.379254 | ||||||||
\(120\) | 29.2276 | 2.66811 | ||||||||
\(121\) | −9.40128 | −0.854662 | ||||||||
\(122\) | 3.93666 | 0.356409 | ||||||||
\(123\) | −3.72683 | −0.336037 | ||||||||
\(124\) | −29.7502 | −2.67165 | ||||||||
\(125\) | 2.80355 | 0.250757 | ||||||||
\(126\) | −11.1680 | −0.994922 | ||||||||
\(127\) | 2.80959 | 0.249311 | 0.124655 | − | 0.992200i | \(-0.460217\pi\) | ||||
0.124655 | + | 0.992200i | \(0.460217\pi\) | |||||||
\(128\) | −24.8763 | −2.19877 | ||||||||
\(129\) | 3.23636 | 0.284946 | ||||||||
\(130\) | −48.9484 | −4.29305 | ||||||||
\(131\) | 13.3474 | 1.16617 | 0.583086 | − | 0.812410i | \(-0.301845\pi\) | ||||
0.583086 | + | 0.812410i | \(0.301845\pi\) | |||||||
\(132\) | −6.68477 | −0.581835 | ||||||||
\(133\) | 15.5153 | 1.34535 | ||||||||
\(134\) | 42.4527 | 3.66735 | ||||||||
\(135\) | −3.29410 | −0.283511 | ||||||||
\(136\) | −8.87273 | −0.760830 | ||||||||
\(137\) | −12.2063 | −1.04285 | −0.521426 | − | 0.853296i | \(-0.674600\pi\) | ||||
−0.521426 | + | 0.853296i | \(0.674600\pi\) | |||||||
\(138\) | −15.6375 | −1.33115 | ||||||||
\(139\) | 14.7339 | 1.24971 | 0.624856 | − | 0.780740i | \(-0.285158\pi\) | ||||
0.624856 | + | 0.780740i | \(0.285158\pi\) | |||||||
\(140\) | 72.0511 | 6.08943 | ||||||||
\(141\) | −1.75649 | −0.147923 | ||||||||
\(142\) | 2.02872 | 0.170246 | ||||||||
\(143\) | 6.96011 | 0.582034 | ||||||||
\(144\) | 13.3775 | 1.11479 | ||||||||
\(145\) | 4.88620 | 0.405777 | ||||||||
\(146\) | −23.6074 | −1.95376 | ||||||||
\(147\) | −10.1162 | −0.834367 | ||||||||
\(148\) | 52.3093 | 4.29980 | ||||||||
\(149\) | 3.66511 | 0.300257 | 0.150129 | − | 0.988666i | \(-0.452031\pi\) | ||||
0.150129 | + | 0.988666i | \(0.452031\pi\) | |||||||
\(150\) | 15.7946 | 1.28962 | ||||||||
\(151\) | 5.80463 | 0.472374 | 0.236187 | − | 0.971708i | \(-0.424102\pi\) | ||||
0.236187 | + | 0.971708i | \(0.424102\pi\) | |||||||
\(152\) | −33.2747 | −2.69893 | ||||||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | −14.1208 | −1.13789 | ||||||||
\(155\) | −18.5364 | −1.48888 | ||||||||
\(156\) | −29.1025 | −2.33007 | ||||||||
\(157\) | −1.00000 | −0.0798087 | ||||||||
\(158\) | 23.4946 | 1.86913 | ||||||||
\(159\) | 6.58226 | 0.522007 | ||||||||
\(160\) | −60.4995 | −4.78290 | ||||||||
\(161\) | −23.9662 | −1.88880 | ||||||||
\(162\) | −2.69942 | −0.212087 | ||||||||
\(163\) | 16.4903 | 1.29162 | 0.645812 | − | 0.763497i | \(-0.276519\pi\) | ||||
0.645812 | + | 0.763497i | \(0.276519\pi\) | |||||||
\(164\) | 19.7034 | 1.53857 | ||||||||
\(165\) | −4.16507 | −0.324250 | ||||||||
\(166\) | 23.7373 | 1.84238 | ||||||||
\(167\) | −2.85685 | −0.221070 | −0.110535 | − | 0.993872i | \(-0.535256\pi\) | ||||
−0.110535 | + | 0.993872i | \(0.535256\pi\) | |||||||
\(168\) | 36.7080 | 2.83208 | ||||||||
\(169\) | 17.3013 | 1.33087 | ||||||||
\(170\) | −8.89217 | −0.681998 | ||||||||
\(171\) | 3.75022 | 0.286786 | ||||||||
\(172\) | −17.1103 | −1.30465 | ||||||||
\(173\) | 24.1347 | 1.83493 | 0.917464 | − | 0.397819i | \(-0.130233\pi\) | ||||
0.917464 | + | 0.397819i | \(0.130233\pi\) | |||||||
\(174\) | 4.00411 | 0.303551 | ||||||||
\(175\) | 24.2069 | 1.82987 | ||||||||
\(176\) | 16.9145 | 1.27498 | ||||||||
\(177\) | 13.0815 | 0.983269 | ||||||||
\(178\) | −11.7052 | −0.877341 | ||||||||
\(179\) | −16.6698 | −1.24596 | −0.622978 | − | 0.782239i | \(-0.714077\pi\) | ||||
−0.622978 | + | 0.782239i | \(0.714077\pi\) | |||||||
\(180\) | 17.4156 | 1.29808 | ||||||||
\(181\) | 6.75382 | 0.502007 | 0.251004 | − | 0.967986i | \(-0.419239\pi\) | ||||
0.251004 | + | 0.967986i | \(0.419239\pi\) | |||||||
\(182\) | −61.4759 | −4.55690 | ||||||||
\(183\) | 1.45833 | 0.107803 | ||||||||
\(184\) | 51.3988 | 3.78917 | ||||||||
\(185\) | 32.5923 | 2.39623 | ||||||||
\(186\) | −15.1901 | −1.11379 | ||||||||
\(187\) | 1.26440 | 0.0924624 | ||||||||
\(188\) | 9.28637 | 0.677278 | ||||||||
\(189\) | −4.13717 | −0.300935 | ||||||||
\(190\) | −33.3476 | −2.41929 | ||||||||
\(191\) | 9.45313 | 0.684004 | 0.342002 | − | 0.939699i | \(-0.388895\pi\) | ||||
0.342002 | + | 0.939699i | \(0.388895\pi\) | |||||||
\(192\) | −22.8228 | −1.64709 | ||||||||
\(193\) | 12.3474 | 0.888786 | 0.444393 | − | 0.895832i | \(-0.353419\pi\) | ||||
0.444393 | + | 0.895832i | \(0.353419\pi\) | |||||||
\(194\) | −33.4319 | −2.40027 | ||||||||
\(195\) | −18.1329 | −1.29852 | ||||||||
\(196\) | 53.4831 | 3.82022 | ||||||||
\(197\) | 13.4501 | 0.958279 | 0.479140 | − | 0.877739i | \(-0.340949\pi\) | ||||
0.479140 | + | 0.877739i | \(0.340949\pi\) | |||||||
\(198\) | −3.41316 | −0.242563 | ||||||||
\(199\) | 11.4664 | 0.812830 | 0.406415 | − | 0.913689i | \(-0.366779\pi\) | ||||
0.406415 | + | 0.913689i | \(0.366779\pi\) | |||||||
\(200\) | −51.9151 | −3.67095 | ||||||||
\(201\) | 15.7266 | 1.10927 | ||||||||
\(202\) | −24.9461 | −1.75520 | ||||||||
\(203\) | 6.13674 | 0.430715 | ||||||||
\(204\) | −5.28690 | −0.370157 | ||||||||
\(205\) | 12.2765 | 0.857431 | ||||||||
\(206\) | 21.7668 | 1.51657 | ||||||||
\(207\) | −5.79289 | −0.402634 | ||||||||
\(208\) | 73.6384 | 5.10590 | ||||||||
\(209\) | 4.74179 | 0.327997 | ||||||||
\(210\) | 36.7884 | 2.53864 | ||||||||
\(211\) | −16.7940 | −1.15615 | −0.578074 | − | 0.815985i | \(-0.696195\pi\) | ||||
−0.578074 | + | 0.815985i | \(0.696195\pi\) | |||||||
\(212\) | −34.7997 | −2.39005 | ||||||||
\(213\) | 0.751536 | 0.0514944 | ||||||||
\(214\) | −52.3704 | −3.57997 | ||||||||
\(215\) | −10.6609 | −0.727067 | ||||||||
\(216\) | 8.87273 | 0.603713 | ||||||||
\(217\) | −23.2805 | −1.58038 | ||||||||
\(218\) | 23.9686 | 1.62336 | ||||||||
\(219\) | −8.74535 | −0.590956 | ||||||||
\(220\) | 22.0203 | 1.48461 | ||||||||
\(221\) | 5.50466 | 0.370283 | ||||||||
\(222\) | 26.7085 | 1.79256 | ||||||||
\(223\) | 12.6977 | 0.850299 | 0.425149 | − | 0.905123i | \(-0.360222\pi\) | ||||
0.425149 | + | 0.905123i | \(0.360222\pi\) | |||||||
\(224\) | −75.9833 | −5.07685 | ||||||||
\(225\) | 5.85108 | 0.390072 | ||||||||
\(226\) | −33.7599 | −2.24568 | ||||||||
\(227\) | 6.99675 | 0.464390 | 0.232195 | − | 0.972669i | \(-0.425409\pi\) | ||||
0.232195 | + | 0.972669i | \(0.425409\pi\) | |||||||
\(228\) | −19.8270 | −1.31308 | ||||||||
\(229\) | 23.4790 | 1.55154 | 0.775769 | − | 0.631017i | \(-0.217362\pi\) | ||||
0.775769 | + | 0.631017i | \(0.217362\pi\) | |||||||
\(230\) | 51.5114 | 3.39656 | ||||||||
\(231\) | −5.23105 | −0.344178 | ||||||||
\(232\) | −13.1611 | −0.864068 | ||||||||
\(233\) | −0.513616 | −0.0336481 | −0.0168240 | − | 0.999858i | \(-0.505356\pi\) | ||||
−0.0168240 | + | 0.999858i | \(0.505356\pi\) | |||||||
\(234\) | −14.8594 | −0.971390 | ||||||||
\(235\) | 5.78604 | 0.377440 | ||||||||
\(236\) | −69.1607 | −4.50198 | ||||||||
\(237\) | 8.70356 | 0.565357 | ||||||||
\(238\) | −11.1680 | −0.723912 | ||||||||
\(239\) | 1.99661 | 0.129150 | 0.0645750 | − | 0.997913i | \(-0.479431\pi\) | ||||
0.0645750 | + | 0.997913i | \(0.479431\pi\) | |||||||
\(240\) | −44.0667 | −2.84449 | ||||||||
\(241\) | 8.78995 | 0.566211 | 0.283105 | − | 0.959089i | \(-0.408635\pi\) | ||||
0.283105 | + | 0.959089i | \(0.408635\pi\) | |||||||
\(242\) | 25.3781 | 1.63136 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −7.71006 | −0.493586 | ||||||||
\(245\) | 33.3236 | 2.12897 | ||||||||
\(246\) | 10.0603 | 0.641421 | ||||||||
\(247\) | 20.6437 | 1.31352 | ||||||||
\(248\) | 49.9283 | 3.17045 | ||||||||
\(249\) | 8.79348 | 0.557264 | ||||||||
\(250\) | −7.56797 | −0.478640 | ||||||||
\(251\) | 15.1706 | 0.957559 | 0.478780 | − | 0.877935i | \(-0.341079\pi\) | ||||
0.478780 | + | 0.877935i | \(0.341079\pi\) | |||||||
\(252\) | 21.8728 | 1.37786 | ||||||||
\(253\) | −7.32456 | −0.460491 | ||||||||
\(254\) | −7.58428 | −0.475880 | ||||||||
\(255\) | −3.29410 | −0.206284 | ||||||||
\(256\) | 21.5061 | 1.34413 | ||||||||
\(257\) | −6.41622 | −0.400233 | −0.200116 | − | 0.979772i | \(-0.564132\pi\) | ||||
−0.200116 | + | 0.979772i | \(0.564132\pi\) | |||||||
\(258\) | −8.73632 | −0.543900 | ||||||||
\(259\) | 40.9337 | 2.54350 | ||||||||
\(260\) | 95.8666 | 5.94540 | ||||||||
\(261\) | 1.48332 | 0.0918152 | ||||||||
\(262\) | −36.0304 | −2.22597 | ||||||||
\(263\) | −13.0807 | −0.806588 | −0.403294 | − | 0.915070i | \(-0.632135\pi\) | ||||
−0.403294 | + | 0.915070i | \(0.632135\pi\) | |||||||
\(264\) | 11.2187 | 0.690464 | ||||||||
\(265\) | −21.6826 | −1.33195 | ||||||||
\(266\) | −41.8823 | −2.56797 | ||||||||
\(267\) | −4.33618 | −0.265370 | ||||||||
\(268\) | −83.1447 | −5.07887 | ||||||||
\(269\) | −23.3216 | −1.42194 | −0.710971 | − | 0.703221i | \(-0.751744\pi\) | ||||
−0.710971 | + | 0.703221i | \(0.751744\pi\) | |||||||
\(270\) | 8.89217 | 0.541160 | ||||||||
\(271\) | 14.2253 | 0.864125 | 0.432062 | − | 0.901844i | \(-0.357786\pi\) | ||||
0.432062 | + | 0.901844i | \(0.357786\pi\) | |||||||
\(272\) | 13.3775 | 0.811128 | ||||||||
\(273\) | −22.7737 | −1.37833 | ||||||||
\(274\) | 32.9499 | 1.99058 | ||||||||
\(275\) | 7.39813 | 0.446124 | ||||||||
\(276\) | 30.6264 | 1.84349 | ||||||||
\(277\) | −14.6727 | −0.881598 | −0.440799 | − | 0.897606i | \(-0.645305\pi\) | ||||
−0.440799 | + | 0.897606i | \(0.645305\pi\) | |||||||
\(278\) | −39.7730 | −2.38543 | ||||||||
\(279\) | −5.62716 | −0.336889 | ||||||||
\(280\) | −120.920 | −7.22633 | ||||||||
\(281\) | −21.5555 | −1.28589 | −0.642946 | − | 0.765912i | \(-0.722288\pi\) | ||||
−0.642946 | + | 0.765912i | \(0.722288\pi\) | |||||||
\(282\) | 4.74151 | 0.282353 | ||||||||
\(283\) | 23.2166 | 1.38008 | 0.690042 | − | 0.723769i | \(-0.257592\pi\) | ||||
0.690042 | + | 0.723769i | \(0.257592\pi\) | |||||||
\(284\) | −3.97329 | −0.235772 | ||||||||
\(285\) | −12.3536 | −0.731763 | ||||||||
\(286\) | −18.7883 | −1.11098 | ||||||||
\(287\) | 15.4185 | 0.910127 | ||||||||
\(288\) | −18.3660 | −1.08223 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −13.1899 | −0.774539 | ||||||||
\(291\) | −12.3848 | −0.726011 | ||||||||
\(292\) | 46.2357 | 2.70574 | ||||||||
\(293\) | −26.1234 | −1.52615 | −0.763073 | − | 0.646312i | \(-0.776310\pi\) | ||||
−0.763073 | + | 0.646312i | \(0.776310\pi\) | |||||||
\(294\) | 27.3078 | 1.59262 | ||||||||
\(295\) | −43.0919 | −2.50891 | ||||||||
\(296\) | −87.7880 | −5.10257 | ||||||||
\(297\) | −1.26440 | −0.0733682 | ||||||||
\(298\) | −9.89368 | −0.573126 | ||||||||
\(299\) | −31.8879 | −1.84412 | ||||||||
\(300\) | −30.9341 | −1.78598 | ||||||||
\(301\) | −13.3894 | −0.771751 | ||||||||
\(302\) | −15.6692 | −0.901659 | ||||||||
\(303\) | −9.24128 | −0.530898 | ||||||||
\(304\) | 50.1684 | 2.87736 | ||||||||
\(305\) | −4.80390 | −0.275070 | ||||||||
\(306\) | −2.69942 | −0.154316 | ||||||||
\(307\) | 25.8888 | 1.47755 | 0.738776 | − | 0.673951i | \(-0.235404\pi\) | ||||
0.738776 | + | 0.673951i | \(0.235404\pi\) | |||||||
\(308\) | 27.6560 | 1.57585 | ||||||||
\(309\) | 8.06351 | 0.458717 | ||||||||
\(310\) | 50.0377 | 2.84195 | ||||||||
\(311\) | −6.70284 | −0.380083 | −0.190041 | − | 0.981776i | \(-0.560862\pi\) | ||||
−0.190041 | + | 0.981776i | \(0.560862\pi\) | |||||||
\(312\) | 48.8413 | 2.76510 | ||||||||
\(313\) | 10.8671 | 0.614243 | 0.307121 | − | 0.951670i | \(-0.400634\pi\) | ||||
0.307121 | + | 0.951670i | \(0.400634\pi\) | |||||||
\(314\) | 2.69942 | 0.152337 | ||||||||
\(315\) | 13.6282 | 0.767864 | ||||||||
\(316\) | −46.0148 | −2.58854 | ||||||||
\(317\) | 21.2873 | 1.19561 | 0.597806 | − | 0.801641i | \(-0.296039\pi\) | ||||
0.597806 | + | 0.801641i | \(0.296039\pi\) | |||||||
\(318\) | −17.7683 | −0.996397 | ||||||||
\(319\) | 1.87552 | 0.105009 | ||||||||
\(320\) | 75.1804 | 4.20271 | ||||||||
\(321\) | −19.4006 | −1.08283 | ||||||||
\(322\) | 64.6949 | 3.60530 | ||||||||
\(323\) | 3.75022 | 0.208668 | ||||||||
\(324\) | 5.28690 | 0.293716 | ||||||||
\(325\) | 32.2082 | 1.78659 | ||||||||
\(326\) | −44.5144 | −2.46543 | ||||||||
\(327\) | 8.87914 | 0.491018 | ||||||||
\(328\) | −33.0672 | −1.82583 | ||||||||
\(329\) | 7.26689 | 0.400636 | ||||||||
\(330\) | 11.2433 | 0.618923 | ||||||||
\(331\) | 6.85976 | 0.377047 | 0.188523 | − | 0.982069i | \(-0.439630\pi\) | ||||
0.188523 | + | 0.982069i | \(0.439630\pi\) | |||||||
\(332\) | −46.4902 | −2.55148 | ||||||||
\(333\) | 9.89414 | 0.542196 | ||||||||
\(334\) | 7.71185 | 0.421974 | ||||||||
\(335\) | −51.8049 | −2.83040 | ||||||||
\(336\) | −55.3448 | −3.01931 | ||||||||
\(337\) | −17.9501 | −0.977802 | −0.488901 | − | 0.872339i | \(-0.662602\pi\) | ||||
−0.488901 | + | 0.872339i | \(0.662602\pi\) | |||||||
\(338\) | −46.7034 | −2.54033 | ||||||||
\(339\) | −12.5063 | −0.679251 | ||||||||
\(340\) | 17.4156 | 0.944491 | ||||||||
\(341\) | −7.11501 | −0.385299 | ||||||||
\(342\) | −10.1234 | −0.547412 | ||||||||
\(343\) | 12.8921 | 0.696108 | ||||||||
\(344\) | 28.7154 | 1.54823 | ||||||||
\(345\) | 19.0824 | 1.02736 | ||||||||
\(346\) | −65.1498 | −3.50248 | ||||||||
\(347\) | 12.8958 | 0.692280 | 0.346140 | − | 0.938183i | \(-0.387492\pi\) | ||||
0.346140 | + | 0.938183i | \(0.387492\pi\) | |||||||
\(348\) | −7.84215 | −0.420384 | ||||||||
\(349\) | −24.5721 | −1.31531 | −0.657657 | − | 0.753317i | \(-0.728453\pi\) | ||||
−0.657657 | + | 0.753317i | \(0.728453\pi\) | |||||||
\(350\) | −65.3447 | −3.49282 | ||||||||
\(351\) | −5.50466 | −0.293817 | ||||||||
\(352\) | −23.2221 | −1.23774 | ||||||||
\(353\) | 16.8630 | 0.897525 | 0.448762 | − | 0.893651i | \(-0.351865\pi\) | ||||
0.448762 | + | 0.893651i | \(0.351865\pi\) | |||||||
\(354\) | −35.3126 | −1.87685 | ||||||||
\(355\) | −2.47563 | −0.131393 | ||||||||
\(356\) | 22.9249 | 1.21502 | ||||||||
\(357\) | −4.13717 | −0.218962 | ||||||||
\(358\) | 44.9988 | 2.37826 | ||||||||
\(359\) | −32.0361 | −1.69080 | −0.845400 | − | 0.534133i | \(-0.820638\pi\) | ||||
−0.845400 | + | 0.534133i | \(0.820638\pi\) | |||||||
\(360\) | −29.2276 | −1.54043 | ||||||||
\(361\) | −4.93587 | −0.259783 | ||||||||
\(362\) | −18.2314 | −0.958222 | ||||||||
\(363\) | 9.40128 | 0.493439 | ||||||||
\(364\) | 120.402 | 6.31079 | ||||||||
\(365\) | 28.8080 | 1.50788 | ||||||||
\(366\) | −3.93666 | −0.205773 | ||||||||
\(367\) | −6.99587 | −0.365181 | −0.182591 | − | 0.983189i | \(-0.558448\pi\) | ||||
−0.182591 | + | 0.983189i | \(0.558448\pi\) | |||||||
\(368\) | −77.4942 | −4.03967 | ||||||||
\(369\) | 3.72683 | 0.194011 | ||||||||
\(370\) | −87.9804 | −4.57388 | ||||||||
\(371\) | −27.2319 | −1.41381 | ||||||||
\(372\) | 29.7502 | 1.54248 | ||||||||
\(373\) | −13.1290 | −0.679796 | −0.339898 | − | 0.940462i | \(-0.610393\pi\) | ||||
−0.339898 | + | 0.940462i | \(0.610393\pi\) | |||||||
\(374\) | −3.41316 | −0.176491 | ||||||||
\(375\) | −2.80355 | −0.144775 | ||||||||
\(376\) | −15.5848 | −0.803727 | ||||||||
\(377\) | 8.16516 | 0.420527 | ||||||||
\(378\) | 11.1680 | 0.574419 | ||||||||
\(379\) | −14.3639 | −0.737822 | −0.368911 | − | 0.929465i | \(-0.620269\pi\) | ||||
−0.368911 | + | 0.929465i | \(0.620269\pi\) | |||||||
\(380\) | 65.3121 | 3.35044 | ||||||||
\(381\) | −2.80959 | −0.143940 | ||||||||
\(382\) | −25.5180 | −1.30562 | ||||||||
\(383\) | −15.1396 | −0.773598 | −0.386799 | − | 0.922164i | \(-0.626419\pi\) | ||||
−0.386799 | + | 0.922164i | \(0.626419\pi\) | |||||||
\(384\) | 24.8763 | 1.26946 | ||||||||
\(385\) | 17.2316 | 0.878204 | ||||||||
\(386\) | −33.3309 | −1.69650 | ||||||||
\(387\) | −3.23636 | −0.164514 | ||||||||
\(388\) | 65.4772 | 3.32410 | ||||||||
\(389\) | −10.9027 | −0.552790 | −0.276395 | − | 0.961044i | \(-0.589140\pi\) | ||||
−0.276395 | + | 0.961044i | \(0.589140\pi\) | |||||||
\(390\) | 48.9484 | 2.47860 | ||||||||
\(391\) | −5.79289 | −0.292959 | ||||||||
\(392\) | −89.7580 | −4.53346 | ||||||||
\(393\) | −13.3474 | −0.673290 | ||||||||
\(394\) | −36.3075 | −1.82915 | ||||||||
\(395\) | −28.6704 | −1.44256 | ||||||||
\(396\) | 6.68477 | 0.335923 | ||||||||
\(397\) | −33.6495 | −1.68882 | −0.844409 | − | 0.535699i | \(-0.820048\pi\) | ||||
−0.844409 | + | 0.535699i | \(0.820048\pi\) | |||||||
\(398\) | −30.9526 | −1.55151 | ||||||||
\(399\) | −15.5153 | −0.776736 | ||||||||
\(400\) | 78.2727 | 3.91363 | ||||||||
\(401\) | 15.4442 | 0.771244 | 0.385622 | − | 0.922657i | \(-0.373987\pi\) | ||||
0.385622 | + | 0.922657i | \(0.373987\pi\) | |||||||
\(402\) | −42.4527 | −2.11735 | ||||||||
\(403\) | −30.9756 | −1.54300 | ||||||||
\(404\) | 48.8577 | 2.43076 | ||||||||
\(405\) | 3.29410 | 0.163685 | ||||||||
\(406\) | −16.5657 | −0.822141 | ||||||||
\(407\) | 12.5102 | 0.620107 | ||||||||
\(408\) | 8.87273 | 0.439265 | ||||||||
\(409\) | −34.8077 | −1.72113 | −0.860565 | − | 0.509340i | \(-0.829890\pi\) | ||||
−0.860565 | + | 0.509340i | \(0.829890\pi\) | |||||||
\(410\) | −33.1396 | −1.63665 | ||||||||
\(411\) | 12.2063 | 0.602091 | ||||||||
\(412\) | −42.6309 | −2.10028 | ||||||||
\(413\) | −54.1205 | −2.66310 | ||||||||
\(414\) | 15.6375 | 0.768540 | ||||||||
\(415\) | −28.9666 | −1.42191 | ||||||||
\(416\) | −101.099 | −4.95677 | ||||||||
\(417\) | −14.7339 | −0.721521 | ||||||||
\(418\) | −12.8001 | −0.626074 | ||||||||
\(419\) | −23.5329 | −1.14966 | −0.574829 | − | 0.818273i | \(-0.694932\pi\) | ||||
−0.574829 | + | 0.818273i | \(0.694932\pi\) | |||||||
\(420\) | −72.0511 | −3.51573 | ||||||||
\(421\) | 0.165111 | 0.00804701 | 0.00402350 | − | 0.999992i | \(-0.498719\pi\) | ||||
0.00402350 | + | 0.999992i | \(0.498719\pi\) | |||||||
\(422\) | 45.3342 | 2.20683 | ||||||||
\(423\) | 1.75649 | 0.0854034 | ||||||||
\(424\) | 58.4026 | 2.83628 | ||||||||
\(425\) | 5.85108 | 0.283819 | ||||||||
\(426\) | −2.02872 | −0.0982916 | ||||||||
\(427\) | −6.03337 | −0.291975 | ||||||||
\(428\) | 102.569 | 4.95785 | ||||||||
\(429\) | −6.96011 | −0.336037 | ||||||||
\(430\) | 28.7783 | 1.38781 | ||||||||
\(431\) | 16.3564 | 0.787859 | 0.393929 | − | 0.919141i | \(-0.371115\pi\) | ||||
0.393929 | + | 0.919141i | \(0.371115\pi\) | |||||||
\(432\) | −13.3775 | −0.643624 | ||||||||
\(433\) | −21.1189 | −1.01491 | −0.507454 | − | 0.861679i | \(-0.669413\pi\) | ||||
−0.507454 | + | 0.861679i | \(0.669413\pi\) | |||||||
\(434\) | 62.8440 | 3.01661 | ||||||||
\(435\) | −4.88620 | −0.234275 | ||||||||
\(436\) | −46.9431 | −2.24817 | ||||||||
\(437\) | −21.7246 | −1.03923 | ||||||||
\(438\) | 23.6074 | 1.12801 | ||||||||
\(439\) | −7.14242 | −0.340889 | −0.170445 | − | 0.985367i | \(-0.554520\pi\) | ||||
−0.170445 | + | 0.985367i | \(0.554520\pi\) | |||||||
\(440\) | −36.9555 | −1.76179 | ||||||||
\(441\) | 10.1162 | 0.481722 | ||||||||
\(442\) | −14.8594 | −0.706790 | ||||||||
\(443\) | 22.1067 | 1.05032 | 0.525159 | − | 0.851004i | \(-0.324006\pi\) | ||||
0.525159 | + | 0.851004i | \(0.324006\pi\) | |||||||
\(444\) | −52.3093 | −2.48249 | ||||||||
\(445\) | 14.2838 | 0.677117 | ||||||||
\(446\) | −34.2764 | −1.62303 | ||||||||
\(447\) | −3.66511 | −0.173354 | ||||||||
\(448\) | 94.4216 | 4.46100 | ||||||||
\(449\) | 8.84021 | 0.417195 | 0.208598 | − | 0.978002i | \(-0.433110\pi\) | ||||
0.208598 | + | 0.978002i | \(0.433110\pi\) | |||||||
\(450\) | −15.7946 | −0.744563 | ||||||||
\(451\) | 4.71222 | 0.221890 | ||||||||
\(452\) | 66.1197 | 3.11001 | ||||||||
\(453\) | −5.80463 | −0.272725 | ||||||||
\(454\) | −18.8872 | −0.886420 | ||||||||
\(455\) | 75.0188 | 3.51693 | ||||||||
\(456\) | 33.2747 | 1.55823 | ||||||||
\(457\) | 7.66476 | 0.358542 | 0.179271 | − | 0.983800i | \(-0.442626\pi\) | ||||
0.179271 | + | 0.983800i | \(0.442626\pi\) | |||||||
\(458\) | −63.3799 | −2.96155 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | −100.886 | −4.70385 | ||||||||
\(461\) | 35.1633 | 1.63772 | 0.818860 | − | 0.573994i | \(-0.194607\pi\) | ||||
0.818860 | + | 0.573994i | \(0.194607\pi\) | |||||||
\(462\) | 14.1208 | 0.656961 | ||||||||
\(463\) | 19.5807 | 0.909992 | 0.454996 | − | 0.890493i | \(-0.349641\pi\) | ||||
0.454996 | + | 0.890493i | \(0.349641\pi\) | |||||||
\(464\) | 19.8431 | 0.921191 | ||||||||
\(465\) | 18.5364 | 0.859606 | ||||||||
\(466\) | 1.38647 | 0.0642268 | ||||||||
\(467\) | 13.9284 | 0.644532 | 0.322266 | − | 0.946649i | \(-0.395556\pi\) | ||||
0.322266 | + | 0.946649i | \(0.395556\pi\) | |||||||
\(468\) | 29.1025 | 1.34527 | ||||||||
\(469\) | −65.0635 | −3.00435 | ||||||||
\(470\) | −15.6190 | −0.720450 | ||||||||
\(471\) | 1.00000 | 0.0460776 | ||||||||
\(472\) | 116.069 | 5.34251 | ||||||||
\(473\) | −4.09207 | −0.188154 | ||||||||
\(474\) | −23.4946 | −1.07914 | ||||||||
\(475\) | 21.9428 | 1.00681 | ||||||||
\(476\) | 21.8728 | 1.00254 | ||||||||
\(477\) | −6.58226 | −0.301381 | ||||||||
\(478\) | −5.38970 | −0.246519 | ||||||||
\(479\) | 24.4521 | 1.11725 | 0.558623 | − | 0.829422i | \(-0.311330\pi\) | ||||
0.558623 | + | 0.829422i | \(0.311330\pi\) | |||||||
\(480\) | 60.4995 | 2.76141 | ||||||||
\(481\) | 54.4639 | 2.48334 | ||||||||
\(482\) | −23.7278 | −1.08077 | ||||||||
\(483\) | 23.9662 | 1.09050 | ||||||||
\(484\) | −49.7036 | −2.25925 | ||||||||
\(485\) | 40.7968 | 1.85249 | ||||||||
\(486\) | 2.69942 | 0.122448 | ||||||||
\(487\) | −23.0199 | −1.04313 | −0.521566 | − | 0.853211i | \(-0.674652\pi\) | ||||
−0.521566 | + | 0.853211i | \(0.674652\pi\) | |||||||
\(488\) | 12.9394 | 0.585739 | ||||||||
\(489\) | −16.4903 | −0.745719 | ||||||||
\(490\) | −89.9547 | −4.06374 | ||||||||
\(491\) | 41.0352 | 1.85189 | 0.925947 | − | 0.377654i | \(-0.123269\pi\) | ||||
0.925947 | + | 0.377654i | \(0.123269\pi\) | |||||||
\(492\) | −19.7034 | −0.888296 | ||||||||
\(493\) | 1.48332 | 0.0668053 | ||||||||
\(494\) | −55.7260 | −2.50723 | ||||||||
\(495\) | 4.16507 | 0.187206 | ||||||||
\(496\) | −75.2772 | −3.38005 | ||||||||
\(497\) | −3.10923 | −0.139468 | ||||||||
\(498\) | −23.7373 | −1.06370 | ||||||||
\(499\) | −39.1034 | −1.75051 | −0.875254 | − | 0.483663i | \(-0.839306\pi\) | ||||
−0.875254 | + | 0.483663i | \(0.839306\pi\) | |||||||
\(500\) | 14.8221 | 0.662863 | ||||||||
\(501\) | 2.85685 | 0.127635 | ||||||||
\(502\) | −40.9519 | −1.82777 | ||||||||
\(503\) | 0.772059 | 0.0344244 | 0.0172122 | − | 0.999852i | \(-0.494521\pi\) | ||||
0.0172122 | + | 0.999852i | \(0.494521\pi\) | |||||||
\(504\) | −36.7080 | −1.63510 | ||||||||
\(505\) | 30.4417 | 1.35464 | ||||||||
\(506\) | 19.7721 | 0.878977 | ||||||||
\(507\) | −17.3013 | −0.768376 | ||||||||
\(508\) | 14.8540 | 0.659040 | ||||||||
\(509\) | −36.1631 | −1.60290 | −0.801450 | − | 0.598061i | \(-0.795938\pi\) | ||||
−0.801450 | + | 0.598061i | \(0.795938\pi\) | |||||||
\(510\) | 8.89217 | 0.393752 | ||||||||
\(511\) | 36.1810 | 1.60055 | ||||||||
\(512\) | −8.30164 | −0.366884 | ||||||||
\(513\) | −3.75022 | −0.165576 | ||||||||
\(514\) | 17.3201 | 0.763957 | ||||||||
\(515\) | −26.5620 | −1.17046 | ||||||||
\(516\) | 17.1103 | 0.753240 | ||||||||
\(517\) | 2.22091 | 0.0976756 | ||||||||
\(518\) | −110.498 | −4.85498 | ||||||||
\(519\) | −24.1347 | −1.05940 | ||||||||
\(520\) | −160.888 | −7.05541 | ||||||||
\(521\) | 15.7118 | 0.688346 | 0.344173 | − | 0.938906i | \(-0.388159\pi\) | ||||
0.344173 | + | 0.938906i | \(0.388159\pi\) | |||||||
\(522\) | −4.00411 | −0.175255 | ||||||||
\(523\) | 35.2225 | 1.54017 | 0.770087 | − | 0.637939i | \(-0.220213\pi\) | ||||
0.770087 | + | 0.637939i | \(0.220213\pi\) | |||||||
\(524\) | 70.5666 | 3.08271 | ||||||||
\(525\) | −24.2069 | −1.05648 | ||||||||
\(526\) | 35.3103 | 1.53960 | ||||||||
\(527\) | −5.62716 | −0.245123 | ||||||||
\(528\) | −16.9145 | −0.736111 | ||||||||
\(529\) | 10.5576 | 0.459026 | ||||||||
\(530\) | 58.5306 | 2.54240 | ||||||||
\(531\) | −13.0815 | −0.567691 | ||||||||
\(532\) | 82.0277 | 3.55635 | ||||||||
\(533\) | 20.5149 | 0.888600 | ||||||||
\(534\) | 11.7052 | 0.506533 | ||||||||
\(535\) | 63.9074 | 2.76296 | ||||||||
\(536\) | 139.538 | 6.02710 | ||||||||
\(537\) | 16.6698 | 0.719353 | ||||||||
\(538\) | 62.9549 | 2.71418 | ||||||||
\(539\) | 12.7909 | 0.550944 | ||||||||
\(540\) | −17.4156 | −0.749446 | ||||||||
\(541\) | −18.0113 | −0.774367 | −0.387183 | − | 0.922003i | \(-0.626552\pi\) | ||||
−0.387183 | + | 0.922003i | \(0.626552\pi\) | |||||||
\(542\) | −38.4001 | −1.64943 | ||||||||
\(543\) | −6.75382 | −0.289834 | ||||||||
\(544\) | −18.3660 | −0.787437 | ||||||||
\(545\) | −29.2488 | −1.25288 | ||||||||
\(546\) | 61.4759 | 2.63092 | ||||||||
\(547\) | 19.9297 | 0.852133 | 0.426066 | − | 0.904692i | \(-0.359899\pi\) | ||||
0.426066 | + | 0.904692i | \(0.359899\pi\) | |||||||
\(548\) | −64.5333 | −2.75673 | ||||||||
\(549\) | −1.45833 | −0.0622402 | ||||||||
\(550\) | −19.9707 | −0.851554 | ||||||||
\(551\) | 5.56277 | 0.236982 | ||||||||
\(552\) | −51.3988 | −2.18768 | ||||||||
\(553\) | −36.0081 | −1.53122 | ||||||||
\(554\) | 39.6079 | 1.68278 | ||||||||
\(555\) | −32.5923 | −1.38346 | ||||||||
\(556\) | 77.8965 | 3.30355 | ||||||||
\(557\) | −12.8291 | −0.543586 | −0.271793 | − | 0.962356i | \(-0.587617\pi\) | ||||
−0.271793 | + | 0.962356i | \(0.587617\pi\) | |||||||
\(558\) | 15.1901 | 0.643048 | ||||||||
\(559\) | −17.8151 | −0.753497 | ||||||||
\(560\) | 182.311 | 7.70406 | ||||||||
\(561\) | −1.26440 | −0.0533832 | ||||||||
\(562\) | 58.1874 | 2.45449 | ||||||||
\(563\) | −26.8621 | −1.13210 | −0.566052 | − | 0.824370i | \(-0.691530\pi\) | ||||
−0.566052 | + | 0.824370i | \(0.691530\pi\) | |||||||
\(564\) | −9.28637 | −0.391027 | ||||||||
\(565\) | 41.1971 | 1.73318 | ||||||||
\(566\) | −62.6715 | −2.63428 | ||||||||
\(567\) | 4.13717 | 0.173745 | ||||||||
\(568\) | 6.66818 | 0.279790 | ||||||||
\(569\) | −11.9965 | −0.502920 | −0.251460 | − | 0.967868i | \(-0.580911\pi\) | ||||
−0.251460 | + | 0.967868i | \(0.580911\pi\) | |||||||
\(570\) | 33.3476 | 1.39678 | ||||||||
\(571\) | 9.73093 | 0.407227 | 0.203613 | − | 0.979051i | \(-0.434731\pi\) | ||||
0.203613 | + | 0.979051i | \(0.434731\pi\) | |||||||
\(572\) | 36.7974 | 1.53858 | ||||||||
\(573\) | −9.45313 | −0.394910 | ||||||||
\(574\) | −41.6212 | −1.73723 | ||||||||
\(575\) | −33.8947 | −1.41351 | ||||||||
\(576\) | 22.8228 | 0.950948 | ||||||||
\(577\) | 44.0985 | 1.83584 | 0.917922 | − | 0.396760i | \(-0.129865\pi\) | ||||
0.917922 | + | 0.396760i | \(0.129865\pi\) | |||||||
\(578\) | −2.69942 | −0.112281 | ||||||||
\(579\) | −12.3474 | −0.513141 | ||||||||
\(580\) | 25.8328 | 1.07265 | ||||||||
\(581\) | −36.3801 | −1.50930 | ||||||||
\(582\) | 33.4319 | 1.38580 | ||||||||
\(583\) | −8.32264 | −0.344688 | ||||||||
\(584\) | −77.5951 | −3.21091 | ||||||||
\(585\) | 18.1329 | 0.749702 | ||||||||
\(586\) | 70.5182 | 2.91308 | ||||||||
\(587\) | −6.53569 | −0.269757 | −0.134878 | − | 0.990862i | \(-0.543064\pi\) | ||||
−0.134878 | + | 0.990862i | \(0.543064\pi\) | |||||||
\(588\) | −53.4831 | −2.20561 | ||||||||
\(589\) | −21.1031 | −0.869537 | ||||||||
\(590\) | 116.323 | 4.78895 | ||||||||
\(591\) | −13.4501 | −0.553263 | ||||||||
\(592\) | 132.359 | 5.43990 | ||||||||
\(593\) | 31.7624 | 1.30432 | 0.652162 | − | 0.758080i | \(-0.273862\pi\) | ||||
0.652162 | + | 0.758080i | \(0.273862\pi\) | |||||||
\(594\) | 3.41316 | 0.140044 | ||||||||
\(595\) | 13.6282 | 0.558703 | ||||||||
\(596\) | 19.3770 | 0.793714 | ||||||||
\(597\) | −11.4664 | −0.469287 | ||||||||
\(598\) | 86.0790 | 3.52003 | ||||||||
\(599\) | −15.8996 | −0.649640 | −0.324820 | − | 0.945776i | \(-0.605304\pi\) | ||||
−0.324820 | + | 0.945776i | \(0.605304\pi\) | |||||||
\(600\) | 51.9151 | 2.11942 | ||||||||
\(601\) | 21.8923 | 0.893006 | 0.446503 | − | 0.894782i | \(-0.352669\pi\) | ||||
0.446503 | + | 0.894782i | \(0.352669\pi\) | |||||||
\(602\) | 36.1436 | 1.47310 | ||||||||
\(603\) | −15.7266 | −0.640435 | ||||||||
\(604\) | 30.6885 | 1.24870 | ||||||||
\(605\) | −30.9687 | −1.25906 | ||||||||
\(606\) | 24.9461 | 1.01337 | ||||||||
\(607\) | −39.9993 | −1.62352 | −0.811761 | − | 0.583990i | \(-0.801491\pi\) | ||||
−0.811761 | + | 0.583990i | \(0.801491\pi\) | |||||||
\(608\) | −68.8766 | −2.79331 | ||||||||
\(609\) | −6.13674 | −0.248673 | ||||||||
\(610\) | 12.9678 | 0.525049 | ||||||||
\(611\) | 9.66886 | 0.391160 | ||||||||
\(612\) | 5.28690 | 0.213710 | ||||||||
\(613\) | 10.2120 | 0.412458 | 0.206229 | − | 0.978504i | \(-0.433881\pi\) | ||||
0.206229 | + | 0.978504i | \(0.433881\pi\) | |||||||
\(614\) | −69.8849 | −2.82032 | ||||||||
\(615\) | −12.2765 | −0.495038 | ||||||||
\(616\) | −46.4137 | −1.87006 | ||||||||
\(617\) | 23.5999 | 0.950096 | 0.475048 | − | 0.879960i | \(-0.342431\pi\) | ||||
0.475048 | + | 0.879960i | \(0.342431\pi\) | |||||||
\(618\) | −21.7668 | −0.875591 | ||||||||
\(619\) | 13.6338 | 0.547988 | 0.273994 | − | 0.961731i | \(-0.411655\pi\) | ||||
0.273994 | + | 0.961731i | \(0.411655\pi\) | |||||||
\(620\) | −98.0001 | −3.93578 | ||||||||
\(621\) | 5.79289 | 0.232461 | ||||||||
\(622\) | 18.0938 | 0.725495 | ||||||||
\(623\) | 17.9395 | 0.718731 | ||||||||
\(624\) | −73.6384 | −2.94789 | ||||||||
\(625\) | −20.0202 | −0.800810 | ||||||||
\(626\) | −29.3348 | −1.17246 | ||||||||
\(627\) | −4.74179 | −0.189369 | ||||||||
\(628\) | −5.28690 | −0.210970 | ||||||||
\(629\) | 9.89414 | 0.394505 | ||||||||
\(630\) | −36.7884 | −1.46569 | ||||||||
\(631\) | −45.5123 | −1.81182 | −0.905909 | − | 0.423472i | \(-0.860811\pi\) | ||||
−0.905909 | + | 0.423472i | \(0.860811\pi\) | |||||||
\(632\) | 77.2243 | 3.07182 | ||||||||
\(633\) | 16.7940 | 0.667502 | ||||||||
\(634\) | −57.4634 | −2.28216 | ||||||||
\(635\) | 9.25507 | 0.367276 | ||||||||
\(636\) | 34.7997 | 1.37990 | ||||||||
\(637\) | 55.6860 | 2.20636 | ||||||||
\(638\) | −5.06281 | −0.200439 | ||||||||
\(639\) | −0.751536 | −0.0297303 | ||||||||
\(640\) | −81.9449 | −3.23916 | ||||||||
\(641\) | −33.4518 | −1.32127 | −0.660633 | − | 0.750709i | \(-0.729712\pi\) | ||||
−0.660633 | + | 0.750709i | \(0.729712\pi\) | |||||||
\(642\) | 52.3704 | 2.06690 | ||||||||
\(643\) | 7.51082 | 0.296198 | 0.148099 | − | 0.988973i | \(-0.452685\pi\) | ||||
0.148099 | + | 0.988973i | \(0.452685\pi\) | |||||||
\(644\) | −126.707 | −4.99294 | ||||||||
\(645\) | 10.6609 | 0.419773 | ||||||||
\(646\) | −10.1234 | −0.398301 | ||||||||
\(647\) | −16.9500 | −0.666374 | −0.333187 | − | 0.942861i | \(-0.608124\pi\) | ||||
−0.333187 | + | 0.942861i | \(0.608124\pi\) | |||||||
\(648\) | −8.87273 | −0.348554 | ||||||||
\(649\) | −16.5404 | −0.649266 | ||||||||
\(650\) | −86.9436 | −3.41021 | ||||||||
\(651\) | 23.2805 | 0.912436 | ||||||||
\(652\) | 87.1827 | 3.41434 | ||||||||
\(653\) | −32.0471 | −1.25410 | −0.627049 | − | 0.778980i | \(-0.715738\pi\) | ||||
−0.627049 | + | 0.778980i | \(0.715738\pi\) | |||||||
\(654\) | −23.9686 | −0.937245 | ||||||||
\(655\) | 43.9678 | 1.71796 | ||||||||
\(656\) | 49.8556 | 1.94653 | ||||||||
\(657\) | 8.74535 | 0.341188 | ||||||||
\(658\) | −19.6164 | −0.764728 | ||||||||
\(659\) | 12.3092 | 0.479497 | 0.239749 | − | 0.970835i | \(-0.422935\pi\) | ||||
0.239749 | + | 0.970835i | \(0.422935\pi\) | |||||||
\(660\) | −22.0203 | −0.857139 | ||||||||
\(661\) | −17.5377 | −0.682138 | −0.341069 | − | 0.940038i | \(-0.610789\pi\) | ||||
−0.341069 | + | 0.940038i | \(0.610789\pi\) | |||||||
\(662\) | −18.5174 | −0.719700 | ||||||||
\(663\) | −5.50466 | −0.213783 | ||||||||
\(664\) | 78.0222 | 3.02785 | ||||||||
\(665\) | 51.1089 | 1.98192 | ||||||||
\(666\) | −26.7085 | −1.03493 | ||||||||
\(667\) | −8.59271 | −0.332711 | ||||||||
\(668\) | −15.1039 | −0.584386 | ||||||||
\(669\) | −12.6977 | −0.490920 | ||||||||
\(670\) | 139.843 | 5.40262 | ||||||||
\(671\) | −1.84392 | −0.0711839 | ||||||||
\(672\) | 75.9833 | 2.93112 | ||||||||
\(673\) | −10.9126 | −0.420648 | −0.210324 | − | 0.977632i | \(-0.567452\pi\) | ||||
−0.210324 | + | 0.977632i | \(0.567452\pi\) | |||||||
\(674\) | 48.4548 | 1.86641 | ||||||||
\(675\) | −5.85108 | −0.225208 | ||||||||
\(676\) | 91.4699 | 3.51807 | ||||||||
\(677\) | 16.7562 | 0.643994 | 0.321997 | − | 0.946741i | \(-0.395646\pi\) | ||||
0.321997 | + | 0.946741i | \(0.395646\pi\) | |||||||
\(678\) | 33.7599 | 1.29654 | ||||||||
\(679\) | 51.2381 | 1.96634 | ||||||||
\(680\) | −29.2276 | −1.12083 | ||||||||
\(681\) | −6.99675 | −0.268116 | ||||||||
\(682\) | 19.2064 | 0.735452 | ||||||||
\(683\) | 43.1298 | 1.65031 | 0.825157 | − | 0.564903i | \(-0.191086\pi\) | ||||
0.825157 | + | 0.564903i | \(0.191086\pi\) | |||||||
\(684\) | 19.8270 | 0.758105 | ||||||||
\(685\) | −40.2087 | −1.53629 | ||||||||
\(686\) | −34.8013 | −1.32872 | ||||||||
\(687\) | −23.4790 | −0.895781 | ||||||||
\(688\) | −43.2944 | −1.65058 | ||||||||
\(689\) | −36.2331 | −1.38037 | ||||||||
\(690\) | −51.5114 | −1.96101 | ||||||||
\(691\) | 28.0457 | 1.06691 | 0.533455 | − | 0.845829i | \(-0.320893\pi\) | ||||
0.533455 | + | 0.845829i | \(0.320893\pi\) | |||||||
\(692\) | 127.598 | 4.85054 | ||||||||
\(693\) | 5.23105 | 0.198711 | ||||||||
\(694\) | −34.8111 | −1.32141 | ||||||||
\(695\) | 48.5348 | 1.84103 | ||||||||
\(696\) | 13.1611 | 0.498870 | ||||||||
\(697\) | 3.72683 | 0.141164 | ||||||||
\(698\) | 66.3306 | 2.51065 | ||||||||
\(699\) | 0.513616 | 0.0194267 | ||||||||
\(700\) | 127.979 | 4.83717 | ||||||||
\(701\) | −47.0710 | −1.77785 | −0.888924 | − | 0.458056i | \(-0.848546\pi\) | ||||
−0.888924 | + | 0.458056i | \(0.848546\pi\) | |||||||
\(702\) | 14.8594 | 0.560832 | ||||||||
\(703\) | 37.1052 | 1.39945 | ||||||||
\(704\) | 28.8572 | 1.08760 | ||||||||
\(705\) | −5.78604 | −0.217915 | ||||||||
\(706\) | −45.5203 | −1.71318 | ||||||||
\(707\) | 38.2327 | 1.43789 | ||||||||
\(708\) | 69.1607 | 2.59922 | ||||||||
\(709\) | 47.8561 | 1.79727 | 0.898637 | − | 0.438693i | \(-0.144558\pi\) | ||||
0.898637 | + | 0.438693i | \(0.144558\pi\) | |||||||
\(710\) | 6.68279 | 0.250801 | ||||||||
\(711\) | −8.70356 | −0.326409 | ||||||||
\(712\) | −38.4737 | −1.44186 | ||||||||
\(713\) | 32.5975 | 1.22079 | ||||||||
\(714\) | 11.1680 | 0.417951 | ||||||||
\(715\) | 22.9273 | 0.857432 | ||||||||
\(716\) | −88.1313 | −3.29362 | ||||||||
\(717\) | −1.99661 | −0.0745648 | ||||||||
\(718\) | 86.4790 | 3.22737 | ||||||||
\(719\) | −36.5954 | −1.36478 | −0.682389 | − | 0.730989i | \(-0.739059\pi\) | ||||
−0.682389 | + | 0.730989i | \(0.739059\pi\) | |||||||
\(720\) | 44.0667 | 1.64227 | ||||||||
\(721\) | −33.3601 | −1.24240 | ||||||||
\(722\) | 13.3240 | 0.495868 | ||||||||
\(723\) | −8.78995 | −0.326902 | ||||||||
\(724\) | 35.7067 | 1.32703 | ||||||||
\(725\) | 8.67902 | 0.322331 | ||||||||
\(726\) | −25.3781 | −0.941868 | ||||||||
\(727\) | −47.6172 | −1.76602 | −0.883011 | − | 0.469352i | \(-0.844488\pi\) | ||||
−0.883011 | + | 0.469352i | \(0.844488\pi\) | |||||||
\(728\) | −202.065 | −7.48902 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −77.7651 | −2.87822 | ||||||||
\(731\) | −3.23636 | −0.119701 | ||||||||
\(732\) | 7.71006 | 0.284972 | ||||||||
\(733\) | 24.2235 | 0.894714 | 0.447357 | − | 0.894355i | \(-0.352365\pi\) | ||||
0.447357 | + | 0.894355i | \(0.352365\pi\) | |||||||
\(734\) | 18.8848 | 0.697051 | ||||||||
\(735\) | −33.3236 | −1.22916 | ||||||||
\(736\) | 106.392 | 3.92168 | ||||||||
\(737\) | −19.8847 | −0.732464 | ||||||||
\(738\) | −10.0603 | −0.370325 | ||||||||
\(739\) | −22.0238 | −0.810160 | −0.405080 | − | 0.914281i | \(-0.632756\pi\) | ||||
−0.405080 | + | 0.914281i | \(0.632756\pi\) | |||||||
\(740\) | 172.312 | 6.33431 | ||||||||
\(741\) | −20.6437 | −0.758364 | ||||||||
\(742\) | 73.5105 | 2.69866 | ||||||||
\(743\) | −35.8856 | −1.31652 | −0.658258 | − | 0.752792i | \(-0.728707\pi\) | ||||
−0.658258 | + | 0.752792i | \(0.728707\pi\) | |||||||
\(744\) | −49.9283 | −1.83046 | ||||||||
\(745\) | 12.0732 | 0.442329 | ||||||||
\(746\) | 35.4409 | 1.29758 | ||||||||
\(747\) | −8.79348 | −0.321737 | ||||||||
\(748\) | 6.68477 | 0.244420 | ||||||||
\(749\) | 80.2635 | 2.93276 | ||||||||
\(750\) | 7.56797 | 0.276343 | ||||||||
\(751\) | −5.11360 | −0.186598 | −0.0932989 | − | 0.995638i | \(-0.529741\pi\) | ||||
−0.0932989 | + | 0.995638i | \(0.529741\pi\) | |||||||
\(752\) | 23.4974 | 0.856861 | ||||||||
\(753\) | −15.1706 | −0.552847 | ||||||||
\(754\) | −22.0412 | −0.802695 | ||||||||
\(755\) | 19.1210 | 0.695885 | ||||||||
\(756\) | −21.8728 | −0.795505 | ||||||||
\(757\) | 38.7193 | 1.40728 | 0.703638 | − | 0.710558i | \(-0.251557\pi\) | ||||
0.703638 | + | 0.710558i | \(0.251557\pi\) | |||||||
\(758\) | 38.7742 | 1.40834 | ||||||||
\(759\) | 7.32456 | 0.265865 | ||||||||
\(760\) | −109.610 | −3.97597 | ||||||||
\(761\) | 15.8585 | 0.574870 | 0.287435 | − | 0.957800i | \(-0.407198\pi\) | ||||
0.287435 | + | 0.957800i | \(0.407198\pi\) | |||||||
\(762\) | 7.58428 | 0.274749 | ||||||||
\(763\) | −36.7345 | −1.32988 | ||||||||
\(764\) | 49.9777 | 1.80813 | ||||||||
\(765\) | 3.29410 | 0.119098 | ||||||||
\(766\) | 40.8682 | 1.47663 | ||||||||
\(767\) | −72.0094 | −2.60011 | ||||||||
\(768\) | −21.5061 | −0.776036 | ||||||||
\(769\) | 14.1488 | 0.510221 | 0.255110 | − | 0.966912i | \(-0.417888\pi\) | ||||
0.255110 | + | 0.966912i | \(0.417888\pi\) | |||||||
\(770\) | −46.5154 | −1.67630 | ||||||||
\(771\) | 6.41622 | 0.231074 | ||||||||
\(772\) | 65.2795 | 2.34946 | ||||||||
\(773\) | −51.4829 | −1.85171 | −0.925855 | − | 0.377879i | \(-0.876654\pi\) | ||||
−0.925855 | + | 0.377879i | \(0.876654\pi\) | |||||||
\(774\) | 8.73632 | 0.314021 | ||||||||
\(775\) | −32.9250 | −1.18270 | ||||||||
\(776\) | −109.887 | −3.94472 | ||||||||
\(777\) | −40.9337 | −1.46849 | ||||||||
\(778\) | 29.4311 | 1.05515 | ||||||||
\(779\) | 13.9764 | 0.500757 | ||||||||
\(780\) | −95.8666 | −3.43258 | ||||||||
\(781\) | −0.950246 | −0.0340025 | ||||||||
\(782\) | 15.6375 | 0.559195 | ||||||||
\(783\) | −1.48332 | −0.0530095 | ||||||||
\(784\) | 135.329 | 4.83317 | ||||||||
\(785\) | −3.29410 | −0.117571 | ||||||||
\(786\) | 36.0304 | 1.28516 | ||||||||
\(787\) | 22.7733 | 0.811782 | 0.405891 | − | 0.913922i | \(-0.366961\pi\) | ||||
0.405891 | + | 0.913922i | \(0.366961\pi\) | |||||||
\(788\) | 71.1092 | 2.53316 | ||||||||
\(789\) | 13.0807 | 0.465684 | ||||||||
\(790\) | 77.3936 | 2.75354 | ||||||||
\(791\) | 51.7408 | 1.83969 | ||||||||
\(792\) | −11.2187 | −0.398640 | ||||||||
\(793\) | −8.02763 | −0.285069 | ||||||||
\(794\) | 90.8342 | 3.22358 | ||||||||
\(795\) | 21.6826 | 0.769003 | ||||||||
\(796\) | 60.6215 | 2.14867 | ||||||||
\(797\) | −25.9350 | −0.918667 | −0.459333 | − | 0.888264i | \(-0.651912\pi\) | ||||
−0.459333 | + | 0.888264i | \(0.651912\pi\) | |||||||
\(798\) | 41.8823 | 1.48262 | ||||||||
\(799\) | 1.75649 | 0.0621401 | ||||||||
\(800\) | −107.461 | −3.79932 | ||||||||
\(801\) | 4.33618 | 0.153211 | ||||||||
\(802\) | −41.6903 | −1.47214 | ||||||||
\(803\) | 11.0577 | 0.390216 | ||||||||
\(804\) | 83.1447 | 2.93229 | ||||||||
\(805\) | −78.9469 | −2.78251 | ||||||||
\(806\) | 83.6163 | 2.94526 | ||||||||
\(807\) | 23.3216 | 0.820958 | ||||||||
\(808\) | −81.9954 | −2.88459 | ||||||||
\(809\) | −35.4632 | −1.24682 | −0.623410 | − | 0.781895i | \(-0.714253\pi\) | ||||
−0.623410 | + | 0.781895i | \(0.714253\pi\) | |||||||
\(810\) | −8.89217 | −0.312439 | ||||||||
\(811\) | −16.2439 | −0.570399 | −0.285200 | − | 0.958468i | \(-0.592060\pi\) | ||||
−0.285200 | + | 0.958468i | \(0.592060\pi\) | |||||||
\(812\) | 32.4443 | 1.13857 | ||||||||
\(813\) | −14.2253 | −0.498903 | ||||||||
\(814\) | −33.7703 | −1.18365 | ||||||||
\(815\) | 54.3208 | 1.90277 | ||||||||
\(816\) | −13.3775 | −0.468305 | ||||||||
\(817\) | −12.1371 | −0.424622 | ||||||||
\(818\) | 93.9608 | 3.28526 | ||||||||
\(819\) | 22.7737 | 0.795777 | ||||||||
\(820\) | 64.9048 | 2.26657 | ||||||||
\(821\) | −15.2862 | −0.533491 | −0.266745 | − | 0.963767i | \(-0.585948\pi\) | ||||
−0.266745 | + | 0.963767i | \(0.585948\pi\) | |||||||
\(822\) | −32.9499 | −1.14926 | ||||||||
\(823\) | 54.5763 | 1.90241 | 0.951204 | − | 0.308562i | \(-0.0998477\pi\) | ||||
0.951204 | + | 0.308562i | \(0.0998477\pi\) | |||||||
\(824\) | 71.5453 | 2.49240 | ||||||||
\(825\) | −7.39813 | −0.257570 | ||||||||
\(826\) | 146.094 | 5.08327 | ||||||||
\(827\) | −29.6884 | −1.03237 | −0.516184 | − | 0.856478i | \(-0.672648\pi\) | ||||
−0.516184 | + | 0.856478i | \(0.672648\pi\) | |||||||
\(828\) | −30.6264 | −1.06434 | ||||||||
\(829\) | −20.6662 | −0.717767 | −0.358884 | − | 0.933382i | \(-0.616842\pi\) | ||||
−0.358884 | + | 0.933382i | \(0.616842\pi\) | |||||||
\(830\) | 78.1931 | 2.71412 | ||||||||
\(831\) | 14.6727 | 0.508991 | ||||||||
\(832\) | 125.631 | 4.35549 | ||||||||
\(833\) | 10.1162 | 0.350504 | ||||||||
\(834\) | 39.7730 | 1.37723 | ||||||||
\(835\) | −9.41074 | −0.325672 | ||||||||
\(836\) | 25.0694 | 0.867042 | ||||||||
\(837\) | 5.62716 | 0.194503 | ||||||||
\(838\) | 63.5254 | 2.19445 | ||||||||
\(839\) | −4.74449 | −0.163798 | −0.0818990 | − | 0.996641i | \(-0.526098\pi\) | ||||
−0.0818990 | + | 0.996641i | \(0.526098\pi\) | |||||||
\(840\) | 120.920 | 4.17212 | ||||||||
\(841\) | −26.7998 | −0.924130 | ||||||||
\(842\) | −0.445704 | −0.0153600 | ||||||||
\(843\) | 21.5555 | 0.742410 | ||||||||
\(844\) | −88.7881 | −3.05621 | ||||||||
\(845\) | 56.9920 | 1.96059 | ||||||||
\(846\) | −4.74151 | −0.163016 | ||||||||
\(847\) | −38.8947 | −1.33644 | ||||||||
\(848\) | −88.0540 | −3.02379 | ||||||||
\(849\) | −23.2166 | −0.796792 | ||||||||
\(850\) | −15.7946 | −0.541749 | ||||||||
\(851\) | −57.3157 | −1.96476 | ||||||||
\(852\) | 3.97329 | 0.136123 | ||||||||
\(853\) | 51.6619 | 1.76887 | 0.884434 | − | 0.466664i | \(-0.154544\pi\) | ||||
0.884434 | + | 0.466664i | \(0.154544\pi\) | |||||||
\(854\) | 16.2866 | 0.557317 | ||||||||
\(855\) | 12.3536 | 0.422484 | ||||||||
\(856\) | −172.136 | −5.88349 | ||||||||
\(857\) | 3.30949 | 0.113050 | 0.0565250 | − | 0.998401i | \(-0.481998\pi\) | ||||
0.0565250 | + | 0.998401i | \(0.481998\pi\) | |||||||
\(858\) | 18.7883 | 0.641422 | ||||||||
\(859\) | 9.46105 | 0.322807 | 0.161403 | − | 0.986889i | \(-0.448398\pi\) | ||||
0.161403 | + | 0.986889i | \(0.448398\pi\) | |||||||
\(860\) | −56.3631 | −1.92196 | ||||||||
\(861\) | −15.4185 | −0.525462 | ||||||||
\(862\) | −44.1528 | −1.50385 | ||||||||
\(863\) | −32.3737 | −1.10201 | −0.551007 | − | 0.834501i | \(-0.685756\pi\) | ||||
−0.551007 | + | 0.834501i | \(0.685756\pi\) | |||||||
\(864\) | 18.3660 | 0.624825 | ||||||||
\(865\) | 79.5021 | 2.70315 | ||||||||
\(866\) | 57.0088 | 1.93724 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | −123.082 | −4.17766 | ||||||||
\(869\) | −11.0048 | −0.373313 | ||||||||
\(870\) | 13.1899 | 0.447180 | ||||||||
\(871\) | −86.5694 | −2.93329 | ||||||||
\(872\) | 78.7822 | 2.66790 | ||||||||
\(873\) | 12.3848 | 0.419163 | ||||||||
\(874\) | 58.6439 | 1.98366 | ||||||||
\(875\) | 11.5988 | 0.392109 | ||||||||
\(876\) | −46.2357 | −1.56216 | ||||||||
\(877\) | 28.0649 | 0.947683 | 0.473842 | − | 0.880610i | \(-0.342867\pi\) | ||||
0.473842 | + | 0.880610i | \(0.342867\pi\) | |||||||
\(878\) | 19.2804 | 0.650683 | ||||||||
\(879\) | 26.1234 | 0.881121 | ||||||||
\(880\) | 55.7181 | 1.87826 | ||||||||
\(881\) | 11.9638 | 0.403072 | 0.201536 | − | 0.979481i | \(-0.435407\pi\) | ||||
0.201536 | + | 0.979481i | \(0.435407\pi\) | |||||||
\(882\) | −27.3078 | −0.919502 | ||||||||
\(883\) | 37.9825 | 1.27821 | 0.639107 | − | 0.769118i | \(-0.279304\pi\) | ||||
0.639107 | + | 0.769118i | \(0.279304\pi\) | |||||||
\(884\) | 29.1025 | 0.978825 | ||||||||
\(885\) | 43.0919 | 1.44852 | ||||||||
\(886\) | −59.6753 | −2.00483 | ||||||||
\(887\) | 47.2865 | 1.58772 | 0.793862 | − | 0.608098i | \(-0.208067\pi\) | ||||
0.793862 | + | 0.608098i | \(0.208067\pi\) | |||||||
\(888\) | 87.7880 | 2.94597 | ||||||||
\(889\) | 11.6238 | 0.389848 | ||||||||
\(890\) | −38.5580 | −1.29247 | ||||||||
\(891\) | 1.26440 | 0.0423591 | ||||||||
\(892\) | 67.1312 | 2.24772 | ||||||||
\(893\) | 6.58721 | 0.220433 | ||||||||
\(894\) | 9.89368 | 0.330894 | ||||||||
\(895\) | −54.9118 | −1.83550 | ||||||||
\(896\) | −102.917 | −3.43823 | ||||||||
\(897\) | 31.8879 | 1.06471 | ||||||||
\(898\) | −23.8635 | −0.796335 | ||||||||
\(899\) | −8.34688 | −0.278384 | ||||||||
\(900\) | 30.9341 | 1.03114 | ||||||||
\(901\) | −6.58226 | −0.219287 | ||||||||
\(902\) | −12.7203 | −0.423539 | ||||||||
\(903\) | 13.3894 | 0.445571 | ||||||||
\(904\) | −110.965 | −3.69065 | ||||||||
\(905\) | 22.2477 | 0.739540 | ||||||||
\(906\) | 15.6692 | 0.520573 | ||||||||
\(907\) | −31.8598 | −1.05789 | −0.528943 | − | 0.848657i | \(-0.677412\pi\) | ||||
−0.528943 | + | 0.848657i | \(0.677412\pi\) | |||||||
\(908\) | 36.9911 | 1.22759 | ||||||||
\(909\) | 9.24128 | 0.306514 | ||||||||
\(910\) | −202.508 | −6.71306 | ||||||||
\(911\) | 47.7384 | 1.58164 | 0.790822 | − | 0.612046i | \(-0.209653\pi\) | ||||
0.790822 | + | 0.612046i | \(0.209653\pi\) | |||||||
\(912\) | −50.1684 | −1.66124 | ||||||||
\(913\) | −11.1185 | −0.367969 | ||||||||
\(914\) | −20.6904 | −0.684379 | ||||||||
\(915\) | 4.80390 | 0.158812 | ||||||||
\(916\) | 124.131 | 4.10141 | ||||||||
\(917\) | 55.2206 | 1.82355 | ||||||||
\(918\) | 2.69942 | 0.0890943 | ||||||||
\(919\) | −52.6185 | −1.73573 | −0.867863 | − | 0.496804i | \(-0.834507\pi\) | ||||
−0.867863 | + | 0.496804i | \(0.834507\pi\) | |||||||
\(920\) | 169.313 | 5.58207 | ||||||||
\(921\) | −25.8888 | −0.853065 | ||||||||
\(922\) | −94.9208 | −3.12605 | ||||||||
\(923\) | −4.13695 | −0.136169 | ||||||||
\(924\) | −27.6560 | −0.909817 | ||||||||
\(925\) | 57.8914 | 1.90346 | ||||||||
\(926\) | −52.8566 | −1.73698 | ||||||||
\(927\) | −8.06351 | −0.264840 | ||||||||
\(928\) | −27.2427 | −0.894285 | ||||||||
\(929\) | −4.06466 | −0.133357 | −0.0666786 | − | 0.997775i | \(-0.521240\pi\) | ||||
−0.0666786 | + | 0.997775i | \(0.521240\pi\) | |||||||
\(930\) | −50.0377 | −1.64080 | ||||||||
\(931\) | 37.9378 | 1.24336 | ||||||||
\(932\) | −2.71543 | −0.0889469 | ||||||||
\(933\) | 6.70284 | 0.219441 | ||||||||
\(934\) | −37.5988 | −1.23027 | ||||||||
\(935\) | 4.16507 | 0.136212 | ||||||||
\(936\) | −48.8413 | −1.59643 | ||||||||
\(937\) | −31.1634 | −1.01807 | −0.509033 | − | 0.860747i | \(-0.669997\pi\) | ||||
−0.509033 | + | 0.860747i | \(0.669997\pi\) | |||||||
\(938\) | 175.634 | 5.73465 | ||||||||
\(939\) | −10.8671 | −0.354633 | ||||||||
\(940\) | 30.5902 | 0.997743 | ||||||||
\(941\) | 23.8033 | 0.775965 | 0.387983 | − | 0.921667i | \(-0.373172\pi\) | ||||
0.387983 | + | 0.921667i | \(0.373172\pi\) | |||||||
\(942\) | −2.69942 | −0.0879520 | ||||||||
\(943\) | −21.5891 | −0.703039 | ||||||||
\(944\) | −174.998 | −5.69570 | ||||||||
\(945\) | −13.6282 | −0.443327 | ||||||||
\(946\) | 11.0462 | 0.359144 | ||||||||
\(947\) | 23.4461 | 0.761895 | 0.380948 | − | 0.924597i | \(-0.375598\pi\) | ||||
0.380948 | + | 0.924597i | \(0.375598\pi\) | |||||||
\(948\) | 46.0148 | 1.49449 | ||||||||
\(949\) | 48.1401 | 1.56269 | ||||||||
\(950\) | −59.2330 | −1.92177 | ||||||||
\(951\) | −21.2873 | −0.690287 | ||||||||
\(952\) | −36.7080 | −1.18971 | ||||||||
\(953\) | 10.6565 | 0.345197 | 0.172599 | − | 0.984992i | \(-0.444784\pi\) | ||||
0.172599 | + | 0.984992i | \(0.444784\pi\) | |||||||
\(954\) | 17.7683 | 0.575270 | ||||||||
\(955\) | 31.1395 | 1.00765 | ||||||||
\(956\) | 10.5559 | 0.341401 | ||||||||
\(957\) | −1.87552 | −0.0606268 | ||||||||
\(958\) | −66.0066 | −2.13258 | ||||||||
\(959\) | −50.4994 | −1.63071 | ||||||||
\(960\) | −75.1804 | −2.42644 | ||||||||
\(961\) | 0.664961 | 0.0214504 | ||||||||
\(962\) | −147.021 | −4.74015 | ||||||||
\(963\) | 19.4006 | 0.625175 | ||||||||
\(964\) | 46.4716 | 1.49675 | ||||||||
\(965\) | 40.6736 | 1.30933 | ||||||||
\(966\) | −64.6949 | −2.08152 | ||||||||
\(967\) | 5.48941 | 0.176528 | 0.0882638 | − | 0.996097i | \(-0.471868\pi\) | ||||
0.0882638 | + | 0.996097i | \(0.471868\pi\) | |||||||
\(968\) | 83.4150 | 2.68106 | ||||||||
\(969\) | −3.75022 | −0.120474 | ||||||||
\(970\) | −110.128 | −3.53599 | ||||||||
\(971\) | −42.0415 | −1.34918 | −0.674588 | − | 0.738195i | \(-0.735679\pi\) | ||||
−0.674588 | + | 0.738195i | \(0.735679\pi\) | |||||||
\(972\) | −5.28690 | −0.169577 | ||||||||
\(973\) | 60.9566 | 1.95418 | ||||||||
\(974\) | 62.1405 | 1.99111 | ||||||||
\(975\) | −32.2082 | −1.03149 | ||||||||
\(976\) | −19.5088 | −0.624462 | ||||||||
\(977\) | 50.2521 | 1.60771 | 0.803854 | − | 0.594827i | \(-0.202779\pi\) | ||||
0.803854 | + | 0.594827i | \(0.202779\pi\) | |||||||
\(978\) | 44.5144 | 1.42341 | ||||||||
\(979\) | 5.48268 | 0.175227 | ||||||||
\(980\) | 176.179 | 5.62782 | ||||||||
\(981\) | −8.87914 | −0.283489 | ||||||||
\(982\) | −110.772 | −3.53486 | ||||||||
\(983\) | 23.2261 | 0.740797 | 0.370398 | − | 0.928873i | \(-0.379221\pi\) | ||||
0.370398 | + | 0.928873i | \(0.379221\pi\) | |||||||
\(984\) | 33.0672 | 1.05414 | ||||||||
\(985\) | 44.3059 | 1.41170 | ||||||||
\(986\) | −4.00411 | −0.127517 | ||||||||
\(987\) | −7.26689 | −0.231308 | ||||||||
\(988\) | 109.141 | 3.47223 | ||||||||
\(989\) | 18.7479 | 0.596149 | ||||||||
\(990\) | −11.2433 | −0.357336 | ||||||||
\(991\) | −35.1600 | −1.11689 | −0.558447 | − | 0.829540i | \(-0.688603\pi\) | ||||
−0.558447 | + | 0.829540i | \(0.688603\pi\) | |||||||
\(992\) | 103.349 | 3.28132 | ||||||||
\(993\) | −6.85976 | −0.217688 | ||||||||
\(994\) | 8.39314 | 0.266214 | ||||||||
\(995\) | 37.7714 | 1.19743 | ||||||||
\(996\) | 46.4902 | 1.47310 | ||||||||
\(997\) | −46.4104 | −1.46983 | −0.734917 | − | 0.678157i | \(-0.762779\pi\) | ||||
−0.734917 | + | 0.678157i | \(0.762779\pi\) | |||||||
\(998\) | 105.557 | 3.34134 | ||||||||
\(999\) | −9.89414 | −0.313037 |
(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 | 8007.2.a.j.1.2 | ✓ | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8007.2.a.j.1.2 | ✓ | 64 | 1.1 | even | 1 | trivial |