Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4017,2,Mod(1,4017)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4017, 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("4017.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4017 = 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4017.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: | \(32.0759064919\) |
Analytic rank: | \(0\) |
Dimension: | \(25\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 4017.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.97968 | −1.39984 | −0.699922 | − | 0.714219i | \(-0.746782\pi\) | ||||
−0.699922 | + | 0.714219i | \(0.746782\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.91913 | 0.959564 | ||||||||
\(5\) | 2.16016 | 0.966051 | 0.483026 | − | 0.875606i | \(-0.339538\pi\) | ||||
0.483026 | + | 0.875606i | \(0.339538\pi\) | |||||||
\(6\) | 1.97968 | 0.808201 | ||||||||
\(7\) | 5.12656 | 1.93766 | 0.968828 | − | 0.247733i | \(-0.0796855\pi\) | ||||
0.968828 | + | 0.247733i | \(0.0796855\pi\) | |||||||
\(8\) | 0.160099 | 0.0566036 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −4.27642 | −1.35232 | ||||||||
\(11\) | 5.28339 | 1.59300 | 0.796501 | − | 0.604637i | \(-0.206682\pi\) | ||||
0.796501 | + | 0.604637i | \(0.206682\pi\) | |||||||
\(12\) | −1.91913 | −0.554005 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | −10.1489 | −2.71242 | ||||||||
\(15\) | −2.16016 | −0.557750 | ||||||||
\(16\) | −4.15520 | −1.03880 | ||||||||
\(17\) | −0.0913774 | −0.0221623 | −0.0110811 | − | 0.999939i | \(-0.503527\pi\) | ||||
−0.0110811 | + | 0.999939i | \(0.503527\pi\) | |||||||
\(18\) | −1.97968 | −0.466615 | ||||||||
\(19\) | −3.04801 | −0.699262 | −0.349631 | − | 0.936887i | \(-0.613693\pi\) | ||||
−0.349631 | + | 0.936887i | \(0.613693\pi\) | |||||||
\(20\) | 4.14562 | 0.926988 | ||||||||
\(21\) | −5.12656 | −1.11871 | ||||||||
\(22\) | −10.4594 | −2.22995 | ||||||||
\(23\) | 0.448356 | 0.0934886 | 0.0467443 | − | 0.998907i | \(-0.485115\pi\) | ||||
0.0467443 | + | 0.998907i | \(0.485115\pi\) | |||||||
\(24\) | −0.160099 | −0.0326801 | ||||||||
\(25\) | −0.333725 | −0.0667449 | ||||||||
\(26\) | −1.97968 | −0.388247 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 9.83852 | 1.85931 | ||||||||
\(29\) | −2.04909 | −0.380507 | −0.190254 | − | 0.981735i | \(-0.560931\pi\) | ||||
−0.190254 | + | 0.981735i | \(0.560931\pi\) | |||||||
\(30\) | 4.27642 | 0.780763 | ||||||||
\(31\) | 10.1345 | 1.82020 | 0.910101 | − | 0.414386i | \(-0.136004\pi\) | ||||
0.910101 | + | 0.414386i | \(0.136004\pi\) | |||||||
\(32\) | 7.90577 | 1.39756 | ||||||||
\(33\) | −5.28339 | −0.919720 | ||||||||
\(34\) | 0.180898 | 0.0310237 | ||||||||
\(35\) | 11.0742 | 1.87188 | ||||||||
\(36\) | 1.91913 | 0.319855 | ||||||||
\(37\) | 3.51047 | 0.577117 | 0.288558 | − | 0.957462i | \(-0.406824\pi\) | ||||
0.288558 | + | 0.957462i | \(0.406824\pi\) | |||||||
\(38\) | 6.03409 | 0.978858 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 0.345839 | 0.0546820 | ||||||||
\(41\) | −5.08046 | −0.793434 | −0.396717 | − | 0.917941i | \(-0.629851\pi\) | ||||
−0.396717 | + | 0.917941i | \(0.629851\pi\) | |||||||
\(42\) | 10.1489 | 1.56602 | ||||||||
\(43\) | −2.08433 | −0.317857 | −0.158928 | − | 0.987290i | \(-0.550804\pi\) | ||||
−0.158928 | + | 0.987290i | \(0.550804\pi\) | |||||||
\(44\) | 10.1395 | 1.52859 | ||||||||
\(45\) | 2.16016 | 0.322017 | ||||||||
\(46\) | −0.887600 | −0.130870 | ||||||||
\(47\) | 2.87315 | 0.419092 | 0.209546 | − | 0.977799i | \(-0.432801\pi\) | ||||
0.209546 | + | 0.977799i | \(0.432801\pi\) | |||||||
\(48\) | 4.15520 | 0.599752 | ||||||||
\(49\) | 19.2816 | 2.75451 | ||||||||
\(50\) | 0.660668 | 0.0934325 | ||||||||
\(51\) | 0.0913774 | 0.0127954 | ||||||||
\(52\) | 1.91913 | 0.266135 | ||||||||
\(53\) | 12.1242 | 1.66539 | 0.832694 | − | 0.553733i | \(-0.186797\pi\) | ||||
0.832694 | + | 0.553733i | \(0.186797\pi\) | |||||||
\(54\) | 1.97968 | 0.269400 | ||||||||
\(55\) | 11.4129 | 1.53892 | ||||||||
\(56\) | 0.820758 | 0.109678 | ||||||||
\(57\) | 3.04801 | 0.403719 | ||||||||
\(58\) | 4.05655 | 0.532651 | ||||||||
\(59\) | −4.87431 | −0.634581 | −0.317290 | − | 0.948328i | \(-0.602773\pi\) | ||||
−0.317290 | + | 0.948328i | \(0.602773\pi\) | |||||||
\(60\) | −4.14562 | −0.535197 | ||||||||
\(61\) | 9.71819 | 1.24429 | 0.622144 | − | 0.782903i | \(-0.286262\pi\) | ||||
0.622144 | + | 0.782903i | \(0.286262\pi\) | |||||||
\(62\) | −20.0630 | −2.54800 | ||||||||
\(63\) | 5.12656 | 0.645886 | ||||||||
\(64\) | −7.34048 | −0.917560 | ||||||||
\(65\) | 2.16016 | 0.267934 | ||||||||
\(66\) | 10.4594 | 1.28746 | ||||||||
\(67\) | −14.5811 | −1.78137 | −0.890683 | − | 0.454625i | \(-0.849773\pi\) | ||||
−0.890683 | + | 0.454625i | \(0.849773\pi\) | |||||||
\(68\) | −0.175365 | −0.0212661 | ||||||||
\(69\) | −0.448356 | −0.0539757 | ||||||||
\(70\) | −21.9233 | −2.62033 | ||||||||
\(71\) | 11.2128 | 1.33071 | 0.665357 | − | 0.746525i | \(-0.268279\pi\) | ||||
0.665357 | + | 0.746525i | \(0.268279\pi\) | |||||||
\(72\) | 0.160099 | 0.0188679 | ||||||||
\(73\) | −15.2353 | −1.78315 | −0.891577 | − | 0.452870i | \(-0.850400\pi\) | ||||
−0.891577 | + | 0.452870i | \(0.850400\pi\) | |||||||
\(74\) | −6.94959 | −0.807874 | ||||||||
\(75\) | 0.333725 | 0.0385352 | ||||||||
\(76\) | −5.84953 | −0.670987 | ||||||||
\(77\) | 27.0856 | 3.08669 | ||||||||
\(78\) | 1.97968 | 0.224154 | ||||||||
\(79\) | −15.7024 | −1.76665 | −0.883327 | − | 0.468757i | \(-0.844702\pi\) | ||||
−0.883327 | + | 0.468757i | \(0.844702\pi\) | |||||||
\(80\) | −8.97589 | −1.00353 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 10.0577 | 1.11068 | ||||||||
\(83\) | 3.47805 | 0.381766 | 0.190883 | − | 0.981613i | \(-0.438865\pi\) | ||||
0.190883 | + | 0.981613i | \(0.438865\pi\) | |||||||
\(84\) | −9.83852 | −1.07347 | ||||||||
\(85\) | −0.197389 | −0.0214099 | ||||||||
\(86\) | 4.12630 | 0.444950 | ||||||||
\(87\) | 2.04909 | 0.219686 | ||||||||
\(88\) | 0.845867 | 0.0901697 | ||||||||
\(89\) | 11.6302 | 1.23280 | 0.616400 | − | 0.787433i | \(-0.288590\pi\) | ||||
0.616400 | + | 0.787433i | \(0.288590\pi\) | |||||||
\(90\) | −4.27642 | −0.450774 | ||||||||
\(91\) | 5.12656 | 0.537409 | ||||||||
\(92\) | 0.860452 | 0.0897083 | ||||||||
\(93\) | −10.1345 | −1.05089 | ||||||||
\(94\) | −5.68791 | −0.586663 | ||||||||
\(95\) | −6.58418 | −0.675523 | ||||||||
\(96\) | −7.90577 | −0.806879 | ||||||||
\(97\) | 5.69283 | 0.578019 | 0.289010 | − | 0.957326i | \(-0.406674\pi\) | ||||
0.289010 | + | 0.957326i | \(0.406674\pi\) | |||||||
\(98\) | −38.1714 | −3.85589 | ||||||||
\(99\) | 5.28339 | 0.531001 | ||||||||
\(100\) | −0.640461 | −0.0640461 | ||||||||
\(101\) | 7.43844 | 0.740153 | 0.370076 | − | 0.929001i | \(-0.379332\pi\) | ||||
0.370076 | + | 0.929001i | \(0.379332\pi\) | |||||||
\(102\) | −0.180898 | −0.0179116 | ||||||||
\(103\) | −1.00000 | −0.0985329 | ||||||||
\(104\) | 0.160099 | 0.0156990 | ||||||||
\(105\) | −11.0742 | −1.08073 | ||||||||
\(106\) | −24.0020 | −2.33128 | ||||||||
\(107\) | −7.26779 | −0.702604 | −0.351302 | − | 0.936262i | \(-0.614261\pi\) | ||||
−0.351302 | + | 0.936262i | \(0.614261\pi\) | |||||||
\(108\) | −1.91913 | −0.184668 | ||||||||
\(109\) | −15.9411 | −1.52688 | −0.763440 | − | 0.645879i | \(-0.776491\pi\) | ||||
−0.763440 | + | 0.645879i | \(0.776491\pi\) | |||||||
\(110\) | −22.5940 | −2.15425 | ||||||||
\(111\) | −3.51047 | −0.333199 | ||||||||
\(112\) | −21.3019 | −2.01284 | ||||||||
\(113\) | 3.13608 | 0.295017 | 0.147509 | − | 0.989061i | \(-0.452875\pi\) | ||||
0.147509 | + | 0.989061i | \(0.452875\pi\) | |||||||
\(114\) | −6.03409 | −0.565144 | ||||||||
\(115\) | 0.968518 | 0.0903148 | ||||||||
\(116\) | −3.93248 | −0.365121 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | 9.64957 | 0.888314 | ||||||||
\(119\) | −0.468451 | −0.0429429 | ||||||||
\(120\) | −0.345839 | −0.0315707 | ||||||||
\(121\) | 16.9142 | 1.53765 | ||||||||
\(122\) | −19.2389 | −1.74181 | ||||||||
\(123\) | 5.08046 | 0.458090 | ||||||||
\(124\) | 19.4493 | 1.74660 | ||||||||
\(125\) | −11.5217 | −1.03053 | ||||||||
\(126\) | −10.1489 | −0.904139 | ||||||||
\(127\) | −2.59501 | −0.230270 | −0.115135 | − | 0.993350i | \(-0.536730\pi\) | ||||
−0.115135 | + | 0.993350i | \(0.536730\pi\) | |||||||
\(128\) | −1.27975 | −0.113115 | ||||||||
\(129\) | 2.08433 | 0.183515 | ||||||||
\(130\) | −4.27642 | −0.375066 | ||||||||
\(131\) | 1.84777 | 0.161441 | 0.0807203 | − | 0.996737i | \(-0.474278\pi\) | ||||
0.0807203 | + | 0.996737i | \(0.474278\pi\) | |||||||
\(132\) | −10.1395 | −0.882531 | ||||||||
\(133\) | −15.6258 | −1.35493 | ||||||||
\(134\) | 28.8659 | 2.49363 | ||||||||
\(135\) | −2.16016 | −0.185917 | ||||||||
\(136\) | −0.0146294 | −0.00125446 | ||||||||
\(137\) | 17.0567 | 1.45726 | 0.728628 | − | 0.684910i | \(-0.240158\pi\) | ||||
0.728628 | + | 0.684910i | \(0.240158\pi\) | |||||||
\(138\) | 0.887600 | 0.0755576 | ||||||||
\(139\) | −0.625326 | −0.0530394 | −0.0265197 | − | 0.999648i | \(-0.508442\pi\) | ||||
−0.0265197 | + | 0.999648i | \(0.508442\pi\) | |||||||
\(140\) | 21.2528 | 1.79619 | ||||||||
\(141\) | −2.87315 | −0.241963 | ||||||||
\(142\) | −22.1977 | −1.86279 | ||||||||
\(143\) | 5.28339 | 0.441819 | ||||||||
\(144\) | −4.15520 | −0.346267 | ||||||||
\(145\) | −4.42636 | −0.367590 | ||||||||
\(146\) | 30.1609 | 2.49614 | ||||||||
\(147\) | −19.2816 | −1.59032 | ||||||||
\(148\) | 6.73703 | 0.553781 | ||||||||
\(149\) | 8.04548 | 0.659111 | 0.329556 | − | 0.944136i | \(-0.393101\pi\) | ||||
0.329556 | + | 0.944136i | \(0.393101\pi\) | |||||||
\(150\) | −0.660668 | −0.0539433 | ||||||||
\(151\) | −7.47406 | −0.608230 | −0.304115 | − | 0.952635i | \(-0.598361\pi\) | ||||
−0.304115 | + | 0.952635i | \(0.598361\pi\) | |||||||
\(152\) | −0.487984 | −0.0395808 | ||||||||
\(153\) | −0.0913774 | −0.00738742 | ||||||||
\(154\) | −53.6208 | −4.32089 | ||||||||
\(155\) | 21.8920 | 1.75841 | ||||||||
\(156\) | −1.91913 | −0.153653 | ||||||||
\(157\) | 12.1690 | 0.971194 | 0.485597 | − | 0.874183i | \(-0.338602\pi\) | ||||
0.485597 | + | 0.874183i | \(0.338602\pi\) | |||||||
\(158\) | 31.0856 | 2.47304 | ||||||||
\(159\) | −12.1242 | −0.961512 | ||||||||
\(160\) | 17.0777 | 1.35011 | ||||||||
\(161\) | 2.29852 | 0.181149 | ||||||||
\(162\) | −1.97968 | −0.155538 | ||||||||
\(163\) | −12.7052 | −0.995148 | −0.497574 | − | 0.867422i | \(-0.665776\pi\) | ||||
−0.497574 | + | 0.867422i | \(0.665776\pi\) | |||||||
\(164\) | −9.75005 | −0.761351 | ||||||||
\(165\) | −11.4129 | −0.888497 | ||||||||
\(166\) | −6.88542 | −0.534413 | ||||||||
\(167\) | −21.3271 | −1.65034 | −0.825170 | − | 0.564885i | \(-0.808921\pi\) | ||||
−0.825170 | + | 0.564885i | \(0.808921\pi\) | |||||||
\(168\) | −0.820758 | −0.0633228 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0.390768 | 0.0299705 | ||||||||
\(171\) | −3.04801 | −0.233087 | ||||||||
\(172\) | −4.00009 | −0.305004 | ||||||||
\(173\) | 10.4525 | 0.794691 | 0.397345 | − | 0.917669i | \(-0.369932\pi\) | ||||
0.397345 | + | 0.917669i | \(0.369932\pi\) | |||||||
\(174\) | −4.05655 | −0.307526 | ||||||||
\(175\) | −1.71086 | −0.129329 | ||||||||
\(176\) | −21.9536 | −1.65481 | ||||||||
\(177\) | 4.87431 | 0.366375 | ||||||||
\(178\) | −23.0241 | −1.72573 | ||||||||
\(179\) | 6.88247 | 0.514420 | 0.257210 | − | 0.966356i | \(-0.417197\pi\) | ||||
0.257210 | + | 0.966356i | \(0.417197\pi\) | |||||||
\(180\) | 4.14562 | 0.308996 | ||||||||
\(181\) | −22.4316 | −1.66733 | −0.833665 | − | 0.552271i | \(-0.813762\pi\) | ||||
−0.833665 | + | 0.552271i | \(0.813762\pi\) | |||||||
\(182\) | −10.1489 | −0.752289 | ||||||||
\(183\) | −9.71819 | −0.718390 | ||||||||
\(184\) | 0.0717814 | 0.00529179 | ||||||||
\(185\) | 7.58315 | 0.557525 | ||||||||
\(186\) | 20.0630 | 1.47109 | ||||||||
\(187\) | −0.482782 | −0.0353045 | ||||||||
\(188\) | 5.51394 | 0.402146 | ||||||||
\(189\) | −5.12656 | −0.372902 | ||||||||
\(190\) | 13.0346 | 0.945627 | ||||||||
\(191\) | 3.33637 | 0.241411 | 0.120706 | − | 0.992688i | \(-0.461484\pi\) | ||||
0.120706 | + | 0.992688i | \(0.461484\pi\) | |||||||
\(192\) | 7.34048 | 0.529753 | ||||||||
\(193\) | −4.05623 | −0.291974 | −0.145987 | − | 0.989287i | \(-0.546636\pi\) | ||||
−0.145987 | + | 0.989287i | \(0.546636\pi\) | |||||||
\(194\) | −11.2700 | −0.809137 | ||||||||
\(195\) | −2.16016 | −0.154692 | ||||||||
\(196\) | 37.0039 | 2.64313 | ||||||||
\(197\) | 9.74945 | 0.694619 | 0.347310 | − | 0.937750i | \(-0.387095\pi\) | ||||
0.347310 | + | 0.937750i | \(0.387095\pi\) | |||||||
\(198\) | −10.4594 | −0.743318 | ||||||||
\(199\) | 12.2267 | 0.866730 | 0.433365 | − | 0.901218i | \(-0.357326\pi\) | ||||
0.433365 | + | 0.901218i | \(0.357326\pi\) | |||||||
\(200\) | −0.0534291 | −0.00377800 | ||||||||
\(201\) | 14.5811 | 1.02847 | ||||||||
\(202\) | −14.7257 | −1.03610 | ||||||||
\(203\) | −10.5048 | −0.737292 | ||||||||
\(204\) | 0.175365 | 0.0122780 | ||||||||
\(205\) | −10.9746 | −0.766498 | ||||||||
\(206\) | 1.97968 | 0.137931 | ||||||||
\(207\) | 0.448356 | 0.0311629 | ||||||||
\(208\) | −4.15520 | −0.288111 | ||||||||
\(209\) | −16.1038 | −1.11393 | ||||||||
\(210\) | 21.9233 | 1.51285 | ||||||||
\(211\) | −4.52040 | −0.311197 | −0.155599 | − | 0.987820i | \(-0.549731\pi\) | ||||
−0.155599 | + | 0.987820i | \(0.549731\pi\) | |||||||
\(212\) | 23.2679 | 1.59805 | ||||||||
\(213\) | −11.2128 | −0.768288 | ||||||||
\(214\) | 14.3879 | 0.983536 | ||||||||
\(215\) | −4.50247 | −0.307066 | ||||||||
\(216\) | −0.160099 | −0.0108934 | ||||||||
\(217\) | 51.9549 | 3.52693 | ||||||||
\(218\) | 31.5582 | 2.13739 | ||||||||
\(219\) | 15.2353 | 1.02950 | ||||||||
\(220\) | 21.9029 | 1.47669 | ||||||||
\(221\) | −0.0913774 | −0.00614671 | ||||||||
\(222\) | 6.94959 | 0.466426 | ||||||||
\(223\) | 16.1875 | 1.08399 | 0.541997 | − | 0.840380i | \(-0.317668\pi\) | ||||
0.541997 | + | 0.840380i | \(0.317668\pi\) | |||||||
\(224\) | 40.5294 | 2.70798 | ||||||||
\(225\) | −0.333725 | −0.0222483 | ||||||||
\(226\) | −6.20843 | −0.412978 | ||||||||
\(227\) | 21.7928 | 1.44644 | 0.723220 | − | 0.690617i | \(-0.242661\pi\) | ||||
0.723220 | + | 0.690617i | \(0.242661\pi\) | |||||||
\(228\) | 5.84953 | 0.387394 | ||||||||
\(229\) | −26.4450 | −1.74754 | −0.873769 | − | 0.486342i | \(-0.838331\pi\) | ||||
−0.873769 | + | 0.486342i | \(0.838331\pi\) | |||||||
\(230\) | −1.91736 | −0.126427 | ||||||||
\(231\) | −27.0856 | −1.78210 | ||||||||
\(232\) | −0.328058 | −0.0215381 | ||||||||
\(233\) | −15.3338 | −1.00455 | −0.502274 | − | 0.864709i | \(-0.667503\pi\) | ||||
−0.502274 | + | 0.864709i | \(0.667503\pi\) | |||||||
\(234\) | −1.97968 | −0.129416 | ||||||||
\(235\) | 6.20645 | 0.404864 | ||||||||
\(236\) | −9.35442 | −0.608921 | ||||||||
\(237\) | 15.7024 | 1.01998 | ||||||||
\(238\) | 0.927383 | 0.0601133 | ||||||||
\(239\) | −9.50354 | −0.614733 | −0.307366 | − | 0.951591i | \(-0.599448\pi\) | ||||
−0.307366 | + | 0.951591i | \(0.599448\pi\) | |||||||
\(240\) | 8.97589 | 0.579391 | ||||||||
\(241\) | 8.61404 | 0.554879 | 0.277440 | − | 0.960743i | \(-0.410514\pi\) | ||||
0.277440 | + | 0.960743i | \(0.410514\pi\) | |||||||
\(242\) | −33.4847 | −2.15248 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 18.6505 | 1.19397 | ||||||||
\(245\) | 41.6513 | 2.66100 | ||||||||
\(246\) | −10.0577 | −0.641254 | ||||||||
\(247\) | −3.04801 | −0.193940 | ||||||||
\(248\) | 1.62252 | 0.103030 | ||||||||
\(249\) | −3.47805 | −0.220413 | ||||||||
\(250\) | 22.8092 | 1.44258 | ||||||||
\(251\) | −6.34058 | −0.400214 | −0.200107 | − | 0.979774i | \(-0.564129\pi\) | ||||
−0.200107 | + | 0.979774i | \(0.564129\pi\) | |||||||
\(252\) | 9.83852 | 0.619769 | ||||||||
\(253\) | 2.36884 | 0.148928 | ||||||||
\(254\) | 5.13729 | 0.322342 | ||||||||
\(255\) | 0.197389 | 0.0123610 | ||||||||
\(256\) | 17.2144 | 1.07590 | ||||||||
\(257\) | −11.6725 | −0.728111 | −0.364056 | − | 0.931377i | \(-0.618608\pi\) | ||||
−0.364056 | + | 0.931377i | \(0.618608\pi\) | |||||||
\(258\) | −4.12630 | −0.256892 | ||||||||
\(259\) | 17.9966 | 1.11825 | ||||||||
\(260\) | 4.14562 | 0.257100 | ||||||||
\(261\) | −2.04909 | −0.126836 | ||||||||
\(262\) | −3.65800 | −0.225992 | ||||||||
\(263\) | −13.0002 | −0.801624 | −0.400812 | − | 0.916160i | \(-0.631272\pi\) | ||||
−0.400812 | + | 0.916160i | \(0.631272\pi\) | |||||||
\(264\) | −0.845867 | −0.0520595 | ||||||||
\(265\) | 26.1902 | 1.60885 | ||||||||
\(266\) | 30.9341 | 1.89669 | ||||||||
\(267\) | −11.6302 | −0.711758 | ||||||||
\(268\) | −27.9830 | −1.70934 | ||||||||
\(269\) | −23.2091 | −1.41509 | −0.707543 | − | 0.706670i | \(-0.750196\pi\) | ||||
−0.707543 | + | 0.706670i | \(0.750196\pi\) | |||||||
\(270\) | 4.27642 | 0.260254 | ||||||||
\(271\) | 12.6090 | 0.765944 | 0.382972 | − | 0.923760i | \(-0.374901\pi\) | ||||
0.382972 | + | 0.923760i | \(0.374901\pi\) | |||||||
\(272\) | 0.379691 | 0.0230222 | ||||||||
\(273\) | −5.12656 | −0.310273 | ||||||||
\(274\) | −33.7669 | −2.03993 | ||||||||
\(275\) | −1.76320 | −0.106325 | ||||||||
\(276\) | −0.860452 | −0.0517931 | ||||||||
\(277\) | 8.68645 | 0.521918 | 0.260959 | − | 0.965350i | \(-0.415961\pi\) | ||||
0.260959 | + | 0.965350i | \(0.415961\pi\) | |||||||
\(278\) | 1.23794 | 0.0742469 | ||||||||
\(279\) | 10.1345 | 0.606734 | ||||||||
\(280\) | 1.77297 | 0.105955 | ||||||||
\(281\) | −16.8805 | −1.00701 | −0.503503 | − | 0.863993i | \(-0.667956\pi\) | ||||
−0.503503 | + | 0.863993i | \(0.667956\pi\) | |||||||
\(282\) | 5.68791 | 0.338710 | ||||||||
\(283\) | 10.4162 | 0.619177 | 0.309589 | − | 0.950871i | \(-0.399809\pi\) | ||||
0.309589 | + | 0.950871i | \(0.399809\pi\) | |||||||
\(284\) | 21.5188 | 1.27691 | ||||||||
\(285\) | 6.58418 | 0.390013 | ||||||||
\(286\) | −10.4594 | −0.618478 | ||||||||
\(287\) | −26.0453 | −1.53740 | ||||||||
\(288\) | 7.90577 | 0.465852 | ||||||||
\(289\) | −16.9917 | −0.999509 | ||||||||
\(290\) | 8.76278 | 0.514568 | ||||||||
\(291\) | −5.69283 | −0.333720 | ||||||||
\(292\) | −29.2384 | −1.71105 | ||||||||
\(293\) | −28.7560 | −1.67995 | −0.839973 | − | 0.542629i | \(-0.817429\pi\) | ||||
−0.839973 | + | 0.542629i | \(0.817429\pi\) | |||||||
\(294\) | 38.1714 | 2.22620 | ||||||||
\(295\) | −10.5293 | −0.613038 | ||||||||
\(296\) | 0.562023 | 0.0326669 | ||||||||
\(297\) | −5.28339 | −0.306573 | ||||||||
\(298\) | −15.9275 | −0.922653 | ||||||||
\(299\) | 0.448356 | 0.0259291 | ||||||||
\(300\) | 0.640461 | 0.0369770 | ||||||||
\(301\) | −10.6854 | −0.615897 | ||||||||
\(302\) | 14.7962 | 0.851427 | ||||||||
\(303\) | −7.43844 | −0.427327 | ||||||||
\(304\) | 12.6651 | 0.726394 | ||||||||
\(305\) | 20.9928 | 1.20205 | ||||||||
\(306\) | 0.180898 | 0.0103412 | ||||||||
\(307\) | −26.0150 | −1.48475 | −0.742377 | − | 0.669983i | \(-0.766302\pi\) | ||||
−0.742377 | + | 0.669983i | \(0.766302\pi\) | |||||||
\(308\) | 51.9808 | 2.96188 | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | −43.3392 | −2.46150 | ||||||||
\(311\) | 27.5881 | 1.56438 | 0.782189 | − | 0.623041i | \(-0.214103\pi\) | ||||
0.782189 | + | 0.623041i | \(0.214103\pi\) | |||||||
\(312\) | −0.160099 | −0.00906383 | ||||||||
\(313\) | 2.05595 | 0.116209 | 0.0581045 | − | 0.998311i | \(-0.481494\pi\) | ||||
0.0581045 | + | 0.998311i | \(0.481494\pi\) | |||||||
\(314\) | −24.0908 | −1.35952 | ||||||||
\(315\) | 11.0742 | 0.623959 | ||||||||
\(316\) | −30.1349 | −1.69522 | ||||||||
\(317\) | 29.8820 | 1.67834 | 0.839169 | − | 0.543871i | \(-0.183042\pi\) | ||||
0.839169 | + | 0.543871i | \(0.183042\pi\) | |||||||
\(318\) | 24.0020 | 1.34597 | ||||||||
\(319\) | −10.8262 | −0.606149 | ||||||||
\(320\) | −15.8566 | −0.886410 | ||||||||
\(321\) | 7.26779 | 0.405648 | ||||||||
\(322\) | −4.55033 | −0.253580 | ||||||||
\(323\) | 0.278519 | 0.0154972 | ||||||||
\(324\) | 1.91913 | 0.106618 | ||||||||
\(325\) | −0.333725 | −0.0185117 | ||||||||
\(326\) | 25.1522 | 1.39305 | ||||||||
\(327\) | 15.9411 | 0.881544 | ||||||||
\(328\) | −0.813378 | −0.0449113 | ||||||||
\(329\) | 14.7294 | 0.812056 | ||||||||
\(330\) | 22.5940 | 1.24376 | ||||||||
\(331\) | −12.4074 | −0.681972 | −0.340986 | − | 0.940068i | \(-0.610761\pi\) | ||||
−0.340986 | + | 0.940068i | \(0.610761\pi\) | |||||||
\(332\) | 6.67483 | 0.366329 | ||||||||
\(333\) | 3.51047 | 0.192372 | ||||||||
\(334\) | 42.2208 | 2.31022 | ||||||||
\(335\) | −31.4975 | −1.72089 | ||||||||
\(336\) | 21.3019 | 1.16211 | ||||||||
\(337\) | −28.0923 | −1.53028 | −0.765142 | − | 0.643862i | \(-0.777331\pi\) | ||||
−0.765142 | + | 0.643862i | \(0.777331\pi\) | |||||||
\(338\) | −1.97968 | −0.107680 | ||||||||
\(339\) | −3.13608 | −0.170328 | ||||||||
\(340\) | −0.378816 | −0.0205442 | ||||||||
\(341\) | 53.5443 | 2.89959 | ||||||||
\(342\) | 6.03409 | 0.326286 | ||||||||
\(343\) | 62.9623 | 3.39965 | ||||||||
\(344\) | −0.333699 | −0.0179918 | ||||||||
\(345\) | −0.968518 | −0.0521433 | ||||||||
\(346\) | −20.6926 | −1.11244 | ||||||||
\(347\) | 17.8851 | 0.960121 | 0.480060 | − | 0.877235i | \(-0.340615\pi\) | ||||
0.480060 | + | 0.877235i | \(0.340615\pi\) | |||||||
\(348\) | 3.93248 | 0.210803 | ||||||||
\(349\) | −23.2235 | −1.24312 | −0.621562 | − | 0.783365i | \(-0.713501\pi\) | ||||
−0.621562 | + | 0.783365i | \(0.713501\pi\) | |||||||
\(350\) | 3.38695 | 0.181040 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 41.7693 | 2.22631 | ||||||||
\(353\) | 7.43361 | 0.395651 | 0.197826 | − | 0.980237i | \(-0.436612\pi\) | ||||
0.197826 | + | 0.980237i | \(0.436612\pi\) | |||||||
\(354\) | −9.64957 | −0.512869 | ||||||||
\(355\) | 24.2214 | 1.28554 | ||||||||
\(356\) | 22.3199 | 1.18295 | ||||||||
\(357\) | 0.468451 | 0.0247931 | ||||||||
\(358\) | −13.6251 | −0.720108 | ||||||||
\(359\) | −20.8797 | −1.10199 | −0.550995 | − | 0.834509i | \(-0.685752\pi\) | ||||
−0.550995 | + | 0.834509i | \(0.685752\pi\) | |||||||
\(360\) | 0.345839 | 0.0182273 | ||||||||
\(361\) | −9.70962 | −0.511033 | ||||||||
\(362\) | 44.4074 | 2.33400 | ||||||||
\(363\) | −16.9142 | −0.887765 | ||||||||
\(364\) | 9.83852 | 0.515679 | ||||||||
\(365\) | −32.9106 | −1.72262 | ||||||||
\(366\) | 19.2389 | 1.00563 | ||||||||
\(367\) | −20.6683 | −1.07888 | −0.539438 | − | 0.842025i | \(-0.681363\pi\) | ||||
−0.539438 | + | 0.842025i | \(0.681363\pi\) | |||||||
\(368\) | −1.86301 | −0.0971160 | ||||||||
\(369\) | −5.08046 | −0.264478 | ||||||||
\(370\) | −15.0122 | −0.780448 | ||||||||
\(371\) | 62.1555 | 3.22695 | ||||||||
\(372\) | −19.4493 | −1.00840 | ||||||||
\(373\) | 2.22158 | 0.115029 | 0.0575145 | − | 0.998345i | \(-0.481682\pi\) | ||||
0.0575145 | + | 0.998345i | \(0.481682\pi\) | |||||||
\(374\) | 0.955754 | 0.0494209 | ||||||||
\(375\) | 11.5217 | 0.594977 | ||||||||
\(376\) | 0.459989 | 0.0237221 | ||||||||
\(377\) | −2.04909 | −0.105534 | ||||||||
\(378\) | 10.1489 | 0.522005 | ||||||||
\(379\) | 30.4795 | 1.56563 | 0.782814 | − | 0.622256i | \(-0.213784\pi\) | ||||
0.782814 | + | 0.622256i | \(0.213784\pi\) | |||||||
\(380\) | −12.6359 | −0.648208 | ||||||||
\(381\) | 2.59501 | 0.132946 | ||||||||
\(382\) | −6.60494 | −0.337938 | ||||||||
\(383\) | 25.2787 | 1.29168 | 0.645841 | − | 0.763472i | \(-0.276507\pi\) | ||||
0.645841 | + | 0.763472i | \(0.276507\pi\) | |||||||
\(384\) | 1.27975 | 0.0653068 | ||||||||
\(385\) | 58.5091 | 2.98190 | ||||||||
\(386\) | 8.03003 | 0.408718 | ||||||||
\(387\) | −2.08433 | −0.105952 | ||||||||
\(388\) | 10.9253 | 0.554647 | ||||||||
\(389\) | −12.7487 | −0.646385 | −0.323192 | − | 0.946333i | \(-0.604756\pi\) | ||||
−0.323192 | + | 0.946333i | \(0.604756\pi\) | |||||||
\(390\) | 4.27642 | 0.216545 | ||||||||
\(391\) | −0.0409696 | −0.00207192 | ||||||||
\(392\) | 3.08697 | 0.155915 | ||||||||
\(393\) | −1.84777 | −0.0932078 | ||||||||
\(394\) | −19.3008 | −0.972359 | ||||||||
\(395\) | −33.9196 | −1.70668 | ||||||||
\(396\) | 10.1395 | 0.509529 | ||||||||
\(397\) | −6.30062 | −0.316219 | −0.158109 | − | 0.987422i | \(-0.550540\pi\) | ||||
−0.158109 | + | 0.987422i | \(0.550540\pi\) | |||||||
\(398\) | −24.2050 | −1.21329 | ||||||||
\(399\) | 15.6258 | 0.782269 | ||||||||
\(400\) | 1.38669 | 0.0693347 | ||||||||
\(401\) | −18.1355 | −0.905643 | −0.452821 | − | 0.891601i | \(-0.649583\pi\) | ||||
−0.452821 | + | 0.891601i | \(0.649583\pi\) | |||||||
\(402\) | −28.8659 | −1.43970 | ||||||||
\(403\) | 10.1345 | 0.504833 | ||||||||
\(404\) | 14.2753 | 0.710224 | ||||||||
\(405\) | 2.16016 | 0.107339 | ||||||||
\(406\) | 20.7961 | 1.03209 | ||||||||
\(407\) | 18.5472 | 0.919348 | ||||||||
\(408\) | 0.0146294 | 0.000724265 0 | ||||||||
\(409\) | −13.8925 | −0.686939 | −0.343469 | − | 0.939164i | \(-0.611602\pi\) | ||||
−0.343469 | + | 0.939164i | \(0.611602\pi\) | |||||||
\(410\) | 21.7262 | 1.07298 | ||||||||
\(411\) | −17.0567 | −0.841347 | ||||||||
\(412\) | −1.91913 | −0.0945487 | ||||||||
\(413\) | −24.9884 | −1.22960 | ||||||||
\(414\) | −0.887600 | −0.0436232 | ||||||||
\(415\) | 7.51313 | 0.368805 | ||||||||
\(416\) | 7.90577 | 0.387612 | ||||||||
\(417\) | 0.625326 | 0.0306223 | ||||||||
\(418\) | 31.8804 | 1.55932 | ||||||||
\(419\) | 3.59714 | 0.175732 | 0.0878660 | − | 0.996132i | \(-0.471995\pi\) | ||||
0.0878660 | + | 0.996132i | \(0.471995\pi\) | |||||||
\(420\) | −21.2528 | −1.03703 | ||||||||
\(421\) | 10.9094 | 0.531690 | 0.265845 | − | 0.964016i | \(-0.414349\pi\) | ||||
0.265845 | + | 0.964016i | \(0.414349\pi\) | |||||||
\(422\) | 8.94894 | 0.435628 | ||||||||
\(423\) | 2.87315 | 0.139697 | ||||||||
\(424\) | 1.94108 | 0.0942670 | ||||||||
\(425\) | 0.0304949 | 0.00147922 | ||||||||
\(426\) | 22.1977 | 1.07548 | ||||||||
\(427\) | 49.8209 | 2.41100 | ||||||||
\(428\) | −13.9478 | −0.674193 | ||||||||
\(429\) | −5.28339 | −0.255084 | ||||||||
\(430\) | 8.91345 | 0.429845 | ||||||||
\(431\) | 9.50082 | 0.457638 | 0.228819 | − | 0.973469i | \(-0.426514\pi\) | ||||
0.228819 | + | 0.973469i | \(0.426514\pi\) | |||||||
\(432\) | 4.15520 | 0.199917 | ||||||||
\(433\) | 35.4532 | 1.70377 | 0.851885 | − | 0.523729i | \(-0.175460\pi\) | ||||
0.851885 | + | 0.523729i | \(0.175460\pi\) | |||||||
\(434\) | −102.854 | −4.93715 | ||||||||
\(435\) | 4.42636 | 0.212228 | ||||||||
\(436\) | −30.5930 | −1.46514 | ||||||||
\(437\) | −1.36659 | −0.0653730 | ||||||||
\(438\) | −30.1609 | −1.44115 | ||||||||
\(439\) | 18.9769 | 0.905716 | 0.452858 | − | 0.891583i | \(-0.350404\pi\) | ||||
0.452858 | + | 0.891583i | \(0.350404\pi\) | |||||||
\(440\) | 1.82720 | 0.0871085 | ||||||||
\(441\) | 19.2816 | 0.918171 | ||||||||
\(442\) | 0.180898 | 0.00860443 | ||||||||
\(443\) | −13.0402 | −0.619559 | −0.309779 | − | 0.950809i | \(-0.600255\pi\) | ||||
−0.309779 | + | 0.950809i | \(0.600255\pi\) | |||||||
\(444\) | −6.73703 | −0.319726 | ||||||||
\(445\) | 25.1231 | 1.19095 | ||||||||
\(446\) | −32.0460 | −1.51742 | ||||||||
\(447\) | −8.04548 | −0.380538 | ||||||||
\(448\) | −37.6314 | −1.77792 | ||||||||
\(449\) | 24.1258 | 1.13857 | 0.569284 | − | 0.822141i | \(-0.307221\pi\) | ||||
0.569284 | + | 0.822141i | \(0.307221\pi\) | |||||||
\(450\) | 0.660668 | 0.0311442 | ||||||||
\(451\) | −26.8420 | −1.26394 | ||||||||
\(452\) | 6.01854 | 0.283088 | ||||||||
\(453\) | 7.47406 | 0.351162 | ||||||||
\(454\) | −43.1428 | −2.02479 | ||||||||
\(455\) | 11.0742 | 0.519165 | ||||||||
\(456\) | 0.487984 | 0.0228520 | ||||||||
\(457\) | −7.45454 | −0.348709 | −0.174354 | − | 0.984683i | \(-0.555784\pi\) | ||||
−0.174354 | + | 0.984683i | \(0.555784\pi\) | |||||||
\(458\) | 52.3527 | 2.44628 | ||||||||
\(459\) | 0.0913774 | 0.00426513 | ||||||||
\(460\) | 1.85871 | 0.0866629 | ||||||||
\(461\) | −31.8700 | −1.48433 | −0.742166 | − | 0.670216i | \(-0.766201\pi\) | ||||
−0.742166 | + | 0.670216i | \(0.766201\pi\) | |||||||
\(462\) | 53.6208 | 2.49467 | ||||||||
\(463\) | 39.3231 | 1.82750 | 0.913750 | − | 0.406277i | \(-0.133173\pi\) | ||||
0.913750 | + | 0.406277i | \(0.133173\pi\) | |||||||
\(464\) | 8.51440 | 0.395271 | ||||||||
\(465\) | −21.8920 | −1.01522 | ||||||||
\(466\) | 30.3559 | 1.40621 | ||||||||
\(467\) | 20.9344 | 0.968726 | 0.484363 | − | 0.874867i | \(-0.339051\pi\) | ||||
0.484363 | + | 0.874867i | \(0.339051\pi\) | |||||||
\(468\) | 1.91913 | 0.0887118 | ||||||||
\(469\) | −74.7509 | −3.45168 | ||||||||
\(470\) | −12.2868 | −0.566747 | ||||||||
\(471\) | −12.1690 | −0.560719 | ||||||||
\(472\) | −0.780373 | −0.0359196 | ||||||||
\(473\) | −11.0123 | −0.506346 | ||||||||
\(474\) | −31.0856 | −1.42781 | ||||||||
\(475\) | 1.01720 | 0.0466722 | ||||||||
\(476\) | −0.899018 | −0.0412064 | ||||||||
\(477\) | 12.1242 | 0.555129 | ||||||||
\(478\) | 18.8140 | 0.860530 | ||||||||
\(479\) | −5.51990 | −0.252211 | −0.126105 | − | 0.992017i | \(-0.540248\pi\) | ||||
−0.126105 | + | 0.992017i | \(0.540248\pi\) | |||||||
\(480\) | −17.0777 | −0.779487 | ||||||||
\(481\) | 3.51047 | 0.160063 | ||||||||
\(482\) | −17.0530 | −0.776744 | ||||||||
\(483\) | −2.29852 | −0.104586 | ||||||||
\(484\) | 32.4605 | 1.47548 | ||||||||
\(485\) | 12.2974 | 0.558396 | ||||||||
\(486\) | 1.97968 | 0.0898001 | ||||||||
\(487\) | −22.9136 | −1.03832 | −0.519158 | − | 0.854678i | \(-0.673754\pi\) | ||||
−0.519158 | + | 0.854678i | \(0.673754\pi\) | |||||||
\(488\) | 1.55588 | 0.0704312 | ||||||||
\(489\) | 12.7052 | 0.574549 | ||||||||
\(490\) | −82.4561 | −3.72499 | ||||||||
\(491\) | 30.4097 | 1.37237 | 0.686185 | − | 0.727427i | \(-0.259284\pi\) | ||||
0.686185 | + | 0.727427i | \(0.259284\pi\) | |||||||
\(492\) | 9.75005 | 0.439566 | ||||||||
\(493\) | 0.187241 | 0.00843290 | ||||||||
\(494\) | 6.03409 | 0.271486 | ||||||||
\(495\) | 11.4129 | 0.512974 | ||||||||
\(496\) | −42.1107 | −1.89083 | ||||||||
\(497\) | 57.4830 | 2.57847 | ||||||||
\(498\) | 6.88542 | 0.308543 | ||||||||
\(499\) | 26.0427 | 1.16583 | 0.582916 | − | 0.812532i | \(-0.301911\pi\) | ||||
0.582916 | + | 0.812532i | \(0.301911\pi\) | |||||||
\(500\) | −22.1116 | −0.988860 | ||||||||
\(501\) | 21.3271 | 0.952824 | ||||||||
\(502\) | 12.5523 | 0.560237 | ||||||||
\(503\) | 0.894332 | 0.0398763 | 0.0199381 | − | 0.999801i | \(-0.493653\pi\) | ||||
0.0199381 | + | 0.999801i | \(0.493653\pi\) | |||||||
\(504\) | 0.820758 | 0.0365595 | ||||||||
\(505\) | 16.0682 | 0.715025 | ||||||||
\(506\) | −4.68954 | −0.208475 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | −4.98016 | −0.220959 | ||||||||
\(509\) | −30.0244 | −1.33081 | −0.665404 | − | 0.746483i | \(-0.731741\pi\) | ||||
−0.665404 | + | 0.746483i | \(0.731741\pi\) | |||||||
\(510\) | −0.390768 | −0.0173035 | ||||||||
\(511\) | −78.1045 | −3.45514 | ||||||||
\(512\) | −31.5196 | −1.39298 | ||||||||
\(513\) | 3.04801 | 0.134573 | ||||||||
\(514\) | 23.1078 | 1.01924 | ||||||||
\(515\) | −2.16016 | −0.0951879 | ||||||||
\(516\) | 4.00009 | 0.176094 | ||||||||
\(517\) | 15.1800 | 0.667614 | ||||||||
\(518\) | −35.6275 | −1.56538 | ||||||||
\(519\) | −10.4525 | −0.458815 | ||||||||
\(520\) | 0.345839 | 0.0151661 | ||||||||
\(521\) | 11.5050 | 0.504042 | 0.252021 | − | 0.967722i | \(-0.418905\pi\) | ||||
0.252021 | + | 0.967722i | \(0.418905\pi\) | |||||||
\(522\) | 4.05655 | 0.177550 | ||||||||
\(523\) | 1.69772 | 0.0742362 | 0.0371181 | − | 0.999311i | \(-0.488182\pi\) | ||||
0.0371181 | + | 0.999311i | \(0.488182\pi\) | |||||||
\(524\) | 3.54611 | 0.154913 | ||||||||
\(525\) | 1.71086 | 0.0746680 | ||||||||
\(526\) | 25.7361 | 1.12215 | ||||||||
\(527\) | −0.926060 | −0.0403398 | ||||||||
\(528\) | 21.9536 | 0.955406 | ||||||||
\(529\) | −22.7990 | −0.991260 | ||||||||
\(530\) | −51.8482 | −2.25214 | ||||||||
\(531\) | −4.87431 | −0.211527 | ||||||||
\(532\) | −29.9879 | −1.30014 | ||||||||
\(533\) | −5.08046 | −0.220059 | ||||||||
\(534\) | 23.0241 | 0.996350 | ||||||||
\(535\) | −15.6996 | −0.678751 | ||||||||
\(536\) | −2.33442 | −0.100832 | ||||||||
\(537\) | −6.88247 | −0.297000 | ||||||||
\(538\) | 45.9466 | 1.98090 | ||||||||
\(539\) | 101.872 | 4.38795 | ||||||||
\(540\) | −4.14562 | −0.178399 | ||||||||
\(541\) | −35.3643 | −1.52043 | −0.760216 | − | 0.649671i | \(-0.774907\pi\) | ||||
−0.760216 | + | 0.649671i | \(0.774907\pi\) | |||||||
\(542\) | −24.9618 | −1.07220 | ||||||||
\(543\) | 22.4316 | 0.962633 | ||||||||
\(544\) | −0.722408 | −0.0309730 | ||||||||
\(545\) | −34.4352 | −1.47504 | ||||||||
\(546\) | 10.1489 | 0.434334 | ||||||||
\(547\) | −18.8060 | −0.804087 | −0.402044 | − | 0.915620i | \(-0.631700\pi\) | ||||
−0.402044 | + | 0.915620i | \(0.631700\pi\) | |||||||
\(548\) | 32.7341 | 1.39833 | ||||||||
\(549\) | 9.71819 | 0.414762 | ||||||||
\(550\) | 3.49056 | 0.148838 | ||||||||
\(551\) | 6.24566 | 0.266074 | ||||||||
\(552\) | −0.0717814 | −0.00305522 | ||||||||
\(553\) | −80.4991 | −3.42317 | ||||||||
\(554\) | −17.1964 | −0.730604 | ||||||||
\(555\) | −7.58315 | −0.321887 | ||||||||
\(556\) | −1.20008 | −0.0508947 | ||||||||
\(557\) | −27.2291 | −1.15373 | −0.576866 | − | 0.816839i | \(-0.695725\pi\) | ||||
−0.576866 | + | 0.816839i | \(0.695725\pi\) | |||||||
\(558\) | −20.0630 | −0.849334 | ||||||||
\(559\) | −2.08433 | −0.0881576 | ||||||||
\(560\) | −46.0154 | −1.94451 | ||||||||
\(561\) | 0.482782 | 0.0203831 | ||||||||
\(562\) | 33.4180 | 1.40965 | ||||||||
\(563\) | 17.2386 | 0.726518 | 0.363259 | − | 0.931688i | \(-0.381664\pi\) | ||||
0.363259 | + | 0.931688i | \(0.381664\pi\) | |||||||
\(564\) | −5.51394 | −0.232179 | ||||||||
\(565\) | 6.77442 | 0.285002 | ||||||||
\(566\) | −20.6207 | −0.866752 | ||||||||
\(567\) | 5.12656 | 0.215295 | ||||||||
\(568\) | 1.79516 | 0.0753232 | ||||||||
\(569\) | 8.24952 | 0.345838 | 0.172919 | − | 0.984936i | \(-0.444680\pi\) | ||||
0.172919 | + | 0.984936i | \(0.444680\pi\) | |||||||
\(570\) | −13.0346 | −0.545958 | ||||||||
\(571\) | 3.32708 | 0.139234 | 0.0696169 | − | 0.997574i | \(-0.477822\pi\) | ||||
0.0696169 | + | 0.997574i | \(0.477822\pi\) | |||||||
\(572\) | 10.1395 | 0.423954 | ||||||||
\(573\) | −3.33637 | −0.139379 | ||||||||
\(574\) | 51.5613 | 2.15213 | ||||||||
\(575\) | −0.149627 | −0.00623989 | ||||||||
\(576\) | −7.34048 | −0.305853 | ||||||||
\(577\) | 19.3393 | 0.805107 | 0.402553 | − | 0.915396i | \(-0.368123\pi\) | ||||
0.402553 | + | 0.915396i | \(0.368123\pi\) | |||||||
\(578\) | 33.6380 | 1.39916 | ||||||||
\(579\) | 4.05623 | 0.168571 | ||||||||
\(580\) | −8.49476 | −0.352726 | ||||||||
\(581\) | 17.8304 | 0.739731 | ||||||||
\(582\) | 11.2700 | 0.467156 | ||||||||
\(583\) | 64.0569 | 2.65297 | ||||||||
\(584\) | −2.43915 | −0.100933 | ||||||||
\(585\) | 2.16016 | 0.0893115 | ||||||||
\(586\) | 56.9277 | 2.35166 | ||||||||
\(587\) | −17.6941 | −0.730314 | −0.365157 | − | 0.930946i | \(-0.618985\pi\) | ||||
−0.365157 | + | 0.930946i | \(0.618985\pi\) | |||||||
\(588\) | −37.0039 | −1.52601 | ||||||||
\(589\) | −30.8900 | −1.27280 | ||||||||
\(590\) | 20.8446 | 0.858157 | ||||||||
\(591\) | −9.74945 | −0.401039 | ||||||||
\(592\) | −14.5867 | −0.599509 | ||||||||
\(593\) | 35.2011 | 1.44554 | 0.722769 | − | 0.691090i | \(-0.242869\pi\) | ||||
0.722769 | + | 0.691090i | \(0.242869\pi\) | |||||||
\(594\) | 10.4594 | 0.429155 | ||||||||
\(595\) | −1.01193 | −0.0414850 | ||||||||
\(596\) | 15.4403 | 0.632459 | ||||||||
\(597\) | −12.2267 | −0.500407 | ||||||||
\(598\) | −0.887600 | −0.0362967 | ||||||||
\(599\) | −38.6268 | −1.57825 | −0.789124 | − | 0.614234i | \(-0.789465\pi\) | ||||
−0.789124 | + | 0.614234i | \(0.789465\pi\) | |||||||
\(600\) | 0.0534291 | 0.00218123 | ||||||||
\(601\) | −42.2014 | −1.72143 | −0.860715 | − | 0.509088i | \(-0.829983\pi\) | ||||
−0.860715 | + | 0.509088i | \(0.829983\pi\) | |||||||
\(602\) | 21.1537 | 0.862160 | ||||||||
\(603\) | −14.5811 | −0.593789 | ||||||||
\(604\) | −14.3437 | −0.583636 | ||||||||
\(605\) | 36.5373 | 1.48545 | ||||||||
\(606\) | 14.7257 | 0.598192 | ||||||||
\(607\) | −6.59533 | −0.267696 | −0.133848 | − | 0.991002i | \(-0.542733\pi\) | ||||
−0.133848 | + | 0.991002i | \(0.542733\pi\) | |||||||
\(608\) | −24.0969 | −0.977257 | ||||||||
\(609\) | 10.5048 | 0.425676 | ||||||||
\(610\) | −41.5590 | −1.68268 | ||||||||
\(611\) | 2.87315 | 0.116235 | ||||||||
\(612\) | −0.175365 | −0.00708871 | ||||||||
\(613\) | 6.27206 | 0.253326 | 0.126663 | − | 0.991946i | \(-0.459573\pi\) | ||||
0.126663 | + | 0.991946i | \(0.459573\pi\) | |||||||
\(614\) | 51.5013 | 2.07842 | ||||||||
\(615\) | 10.9746 | 0.442538 | ||||||||
\(616\) | 4.33638 | 0.174718 | ||||||||
\(617\) | −26.8906 | −1.08257 | −0.541287 | − | 0.840838i | \(-0.682063\pi\) | ||||
−0.541287 | + | 0.840838i | \(0.682063\pi\) | |||||||
\(618\) | −1.97968 | −0.0796344 | ||||||||
\(619\) | −6.55026 | −0.263277 | −0.131639 | − | 0.991298i | \(-0.542024\pi\) | ||||
−0.131639 | + | 0.991298i | \(0.542024\pi\) | |||||||
\(620\) | 42.0136 | 1.68731 | ||||||||
\(621\) | −0.448356 | −0.0179919 | ||||||||
\(622\) | −54.6156 | −2.18989 | ||||||||
\(623\) | 59.6230 | 2.38874 | ||||||||
\(624\) | 4.15520 | 0.166341 | ||||||||
\(625\) | −23.2200 | −0.928800 | ||||||||
\(626\) | −4.07012 | −0.162675 | ||||||||
\(627\) | 16.1038 | 0.643125 | ||||||||
\(628\) | 23.3539 | 0.931923 | ||||||||
\(629\) | −0.320777 | −0.0127902 | ||||||||
\(630\) | −21.9233 | −0.873445 | ||||||||
\(631\) | 28.8500 | 1.14850 | 0.574251 | − | 0.818679i | \(-0.305293\pi\) | ||||
0.574251 | + | 0.818679i | \(0.305293\pi\) | |||||||
\(632\) | −2.51394 | −0.0999990 | ||||||||
\(633\) | 4.52040 | 0.179670 | ||||||||
\(634\) | −59.1567 | −2.34941 | ||||||||
\(635\) | −5.60563 | −0.222453 | ||||||||
\(636\) | −23.2679 | −0.922633 | ||||||||
\(637\) | 19.2816 | 0.763965 | ||||||||
\(638\) | 21.4323 | 0.848514 | ||||||||
\(639\) | 11.2128 | 0.443571 | ||||||||
\(640\) | −2.76445 | −0.109275 | ||||||||
\(641\) | 4.23827 | 0.167402 | 0.0837008 | − | 0.996491i | \(-0.473326\pi\) | ||||
0.0837008 | + | 0.996491i | \(0.473326\pi\) | |||||||
\(642\) | −14.3879 | −0.567845 | ||||||||
\(643\) | 30.9152 | 1.21918 | 0.609589 | − | 0.792718i | \(-0.291334\pi\) | ||||
0.609589 | + | 0.792718i | \(0.291334\pi\) | |||||||
\(644\) | 4.41116 | 0.173824 | ||||||||
\(645\) | 4.50247 | 0.177285 | ||||||||
\(646\) | −0.551379 | −0.0216937 | ||||||||
\(647\) | −34.6658 | −1.36285 | −0.681427 | − | 0.731886i | \(-0.738640\pi\) | ||||
−0.681427 | + | 0.731886i | \(0.738640\pi\) | |||||||
\(648\) | 0.160099 | 0.00628929 | ||||||||
\(649\) | −25.7529 | −1.01089 | ||||||||
\(650\) | 0.660668 | 0.0259135 | ||||||||
\(651\) | −51.9549 | −2.03627 | ||||||||
\(652\) | −24.3829 | −0.954908 | ||||||||
\(653\) | 26.2607 | 1.02766 | 0.513829 | − | 0.857892i | \(-0.328226\pi\) | ||||
0.513829 | + | 0.857892i | \(0.328226\pi\) | |||||||
\(654\) | −31.5582 | −1.23402 | ||||||||
\(655\) | 3.99148 | 0.155960 | ||||||||
\(656\) | 21.1103 | 0.824220 | ||||||||
\(657\) | −15.2353 | −0.594384 | ||||||||
\(658\) | −29.1594 | −1.13675 | ||||||||
\(659\) | −22.8862 | −0.891519 | −0.445760 | − | 0.895153i | \(-0.647066\pi\) | ||||
−0.445760 | + | 0.895153i | \(0.647066\pi\) | |||||||
\(660\) | −21.9029 | −0.852570 | ||||||||
\(661\) | −31.9954 | −1.24448 | −0.622238 | − | 0.782828i | \(-0.713776\pi\) | ||||
−0.622238 | + | 0.782828i | \(0.713776\pi\) | |||||||
\(662\) | 24.5627 | 0.954655 | ||||||||
\(663\) | 0.0913774 | 0.00354880 | ||||||||
\(664\) | 0.556833 | 0.0216093 | ||||||||
\(665\) | −33.7542 | −1.30893 | ||||||||
\(666\) | −6.94959 | −0.269291 | ||||||||
\(667\) | −0.918723 | −0.0355731 | ||||||||
\(668\) | −40.9294 | −1.58361 | ||||||||
\(669\) | −16.1875 | −0.625844 | ||||||||
\(670\) | 62.3549 | 2.40898 | ||||||||
\(671\) | 51.3450 | 1.98215 | ||||||||
\(672\) | −40.5294 | −1.56345 | ||||||||
\(673\) | 21.4647 | 0.827404 | 0.413702 | − | 0.910412i | \(-0.364236\pi\) | ||||
0.413702 | + | 0.910412i | \(0.364236\pi\) | |||||||
\(674\) | 55.6137 | 2.14216 | ||||||||
\(675\) | 0.333725 | 0.0128451 | ||||||||
\(676\) | 1.91913 | 0.0738126 | ||||||||
\(677\) | −3.70916 | −0.142555 | −0.0712773 | − | 0.997457i | \(-0.522708\pi\) | ||||
−0.0712773 | + | 0.997457i | \(0.522708\pi\) | |||||||
\(678\) | 6.20843 | 0.238433 | ||||||||
\(679\) | 29.1846 | 1.12000 | ||||||||
\(680\) | −0.0316019 | −0.00121188 | ||||||||
\(681\) | −21.7928 | −0.835103 | ||||||||
\(682\) | −106.001 | −4.05897 | ||||||||
\(683\) | 26.7177 | 1.02233 | 0.511163 | − | 0.859484i | \(-0.329215\pi\) | ||||
0.511163 | + | 0.859484i | \(0.329215\pi\) | |||||||
\(684\) | −5.84953 | −0.223662 | ||||||||
\(685\) | 36.8452 | 1.40778 | ||||||||
\(686\) | −124.645 | −4.75897 | ||||||||
\(687\) | 26.4450 | 1.00894 | ||||||||
\(688\) | 8.66080 | 0.330190 | ||||||||
\(689\) | 12.1242 | 0.461896 | ||||||||
\(690\) | 1.91736 | 0.0729925 | ||||||||
\(691\) | 8.67769 | 0.330115 | 0.165058 | − | 0.986284i | \(-0.447219\pi\) | ||||
0.165058 | + | 0.986284i | \(0.447219\pi\) | |||||||
\(692\) | 20.0597 | 0.762557 | ||||||||
\(693\) | 27.0856 | 1.02890 | ||||||||
\(694\) | −35.4067 | −1.34402 | ||||||||
\(695\) | −1.35080 | −0.0512388 | ||||||||
\(696\) | 0.328058 | 0.0124350 | ||||||||
\(697\) | 0.464239 | 0.0175843 | ||||||||
\(698\) | 45.9750 | 1.74018 | ||||||||
\(699\) | 15.3338 | 0.579976 | ||||||||
\(700\) | −3.28336 | −0.124099 | ||||||||
\(701\) | 29.4582 | 1.11262 | 0.556310 | − | 0.830975i | \(-0.312217\pi\) | ||||
0.556310 | + | 0.830975i | \(0.312217\pi\) | |||||||
\(702\) | 1.97968 | 0.0747182 | ||||||||
\(703\) | −10.6999 | −0.403556 | ||||||||
\(704\) | −38.7826 | −1.46167 | ||||||||
\(705\) | −6.20645 | −0.233749 | ||||||||
\(706\) | −14.7162 | −0.553850 | ||||||||
\(707\) | 38.1336 | 1.43416 | ||||||||
\(708\) | 9.35442 | 0.351561 | ||||||||
\(709\) | −20.4843 | −0.769302 | −0.384651 | − | 0.923062i | \(-0.625678\pi\) | ||||
−0.384651 | + | 0.923062i | \(0.625678\pi\) | |||||||
\(710\) | −47.9506 | −1.79955 | ||||||||
\(711\) | −15.7024 | −0.588885 | ||||||||
\(712\) | 1.86199 | 0.0697810 | ||||||||
\(713\) | 4.54384 | 0.170168 | ||||||||
\(714\) | −0.927383 | −0.0347064 | ||||||||
\(715\) | 11.4129 | 0.426820 | ||||||||
\(716\) | 13.2083 | 0.493619 | ||||||||
\(717\) | 9.50354 | 0.354916 | ||||||||
\(718\) | 41.3352 | 1.54261 | ||||||||
\(719\) | −12.5033 | −0.466293 | −0.233146 | − | 0.972442i | \(-0.574902\pi\) | ||||
−0.233146 | + | 0.972442i | \(0.574902\pi\) | |||||||
\(720\) | −8.97589 | −0.334512 | ||||||||
\(721\) | −5.12656 | −0.190923 | ||||||||
\(722\) | 19.2219 | 0.715366 | ||||||||
\(723\) | −8.61404 | −0.320360 | ||||||||
\(724\) | −43.0492 | −1.59991 | ||||||||
\(725\) | 0.683833 | 0.0253969 | ||||||||
\(726\) | 33.4847 | 1.24273 | ||||||||
\(727\) | 28.4805 | 1.05628 | 0.528141 | − | 0.849157i | \(-0.322889\pi\) | ||||
0.528141 | + | 0.849157i | \(0.322889\pi\) | |||||||
\(728\) | 0.820758 | 0.0304193 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 65.1523 | 2.41140 | ||||||||
\(731\) | 0.190460 | 0.00704443 | ||||||||
\(732\) | −18.6505 | −0.689341 | ||||||||
\(733\) | 19.6978 | 0.727556 | 0.363778 | − | 0.931486i | \(-0.381487\pi\) | ||||
0.363778 | + | 0.931486i | \(0.381487\pi\) | |||||||
\(734\) | 40.9166 | 1.51026 | ||||||||
\(735\) | −41.6513 | −1.53633 | ||||||||
\(736\) | 3.54460 | 0.130656 | ||||||||
\(737\) | −77.0377 | −2.83772 | ||||||||
\(738\) | 10.0577 | 0.370228 | ||||||||
\(739\) | −1.38039 | −0.0507784 | −0.0253892 | − | 0.999678i | \(-0.508083\pi\) | ||||
−0.0253892 | + | 0.999678i | \(0.508083\pi\) | |||||||
\(740\) | 14.5530 | 0.534981 | ||||||||
\(741\) | 3.04801 | 0.111972 | ||||||||
\(742\) | −123.048 | −4.51723 | ||||||||
\(743\) | 0.103395 | 0.00379320 | 0.00189660 | − | 0.999998i | \(-0.499396\pi\) | ||||
0.00189660 | + | 0.999998i | \(0.499396\pi\) | |||||||
\(744\) | −1.62252 | −0.0594844 | ||||||||
\(745\) | 17.3795 | 0.636735 | ||||||||
\(746\) | −4.39801 | −0.161023 | ||||||||
\(747\) | 3.47805 | 0.127255 | ||||||||
\(748\) | −0.926521 | −0.0338770 | ||||||||
\(749\) | −37.2587 | −1.36140 | ||||||||
\(750\) | −22.8092 | −0.832875 | ||||||||
\(751\) | 26.7414 | 0.975808 | 0.487904 | − | 0.872897i | \(-0.337762\pi\) | ||||
0.487904 | + | 0.872897i | \(0.337762\pi\) | |||||||
\(752\) | −11.9385 | −0.435353 | ||||||||
\(753\) | 6.34058 | 0.231064 | ||||||||
\(754\) | 4.05655 | 0.147731 | ||||||||
\(755\) | −16.1451 | −0.587581 | ||||||||
\(756\) | −9.83852 | −0.357824 | ||||||||
\(757\) | 37.8615 | 1.37610 | 0.688050 | − | 0.725663i | \(-0.258467\pi\) | ||||
0.688050 | + | 0.725663i | \(0.258467\pi\) | |||||||
\(758\) | −60.3397 | −2.19164 | ||||||||
\(759\) | −2.36884 | −0.0859834 | ||||||||
\(760\) | −1.05412 | −0.0382370 | ||||||||
\(761\) | 19.9429 | 0.722931 | 0.361465 | − | 0.932386i | \(-0.382277\pi\) | ||||
0.361465 | + | 0.932386i | \(0.382277\pi\) | |||||||
\(762\) | −5.13729 | −0.186104 | ||||||||
\(763\) | −81.7229 | −2.95857 | ||||||||
\(764\) | 6.40292 | 0.231650 | ||||||||
\(765\) | −0.197389 | −0.00713663 | ||||||||
\(766\) | −50.0438 | −1.80815 | ||||||||
\(767\) | −4.87431 | −0.176001 | ||||||||
\(768\) | −17.2144 | −0.621173 | ||||||||
\(769\) | 1.56420 | 0.0564066 | 0.0282033 | − | 0.999602i | \(-0.491021\pi\) | ||||
0.0282033 | + | 0.999602i | \(0.491021\pi\) | |||||||
\(770\) | −115.829 | −4.17420 | ||||||||
\(771\) | 11.6725 | 0.420375 | ||||||||
\(772\) | −7.78443 | −0.280168 | ||||||||
\(773\) | −45.2344 | −1.62697 | −0.813484 | − | 0.581588i | \(-0.802432\pi\) | ||||
−0.813484 | + | 0.581588i | \(0.802432\pi\) | |||||||
\(774\) | 4.12630 | 0.148317 | ||||||||
\(775\) | −3.38212 | −0.121489 | ||||||||
\(776\) | 0.911418 | 0.0327180 | ||||||||
\(777\) | −17.9966 | −0.645625 | ||||||||
\(778\) | 25.2383 | 0.904838 | ||||||||
\(779\) | 15.4853 | 0.554818 | ||||||||
\(780\) | −4.14562 | −0.148437 | ||||||||
\(781\) | 59.2416 | 2.11983 | ||||||||
\(782\) | 0.0811066 | 0.00290037 | ||||||||
\(783\) | 2.04909 | 0.0732287 | ||||||||
\(784\) | −80.1189 | −2.86139 | ||||||||
\(785\) | 26.2870 | 0.938223 | ||||||||
\(786\) | 3.65800 | 0.130476 | ||||||||
\(787\) | −26.0429 | −0.928329 | −0.464164 | − | 0.885749i | \(-0.653645\pi\) | ||||
−0.464164 | + | 0.885749i | \(0.653645\pi\) | |||||||
\(788\) | 18.7104 | 0.666532 | ||||||||
\(789\) | 13.0002 | 0.462818 | ||||||||
\(790\) | 67.1499 | 2.38908 | ||||||||
\(791\) | 16.0773 | 0.571642 | ||||||||
\(792\) | 0.845867 | 0.0300566 | ||||||||
\(793\) | 9.71819 | 0.345103 | ||||||||
\(794\) | 12.4732 | 0.442657 | ||||||||
\(795\) | −26.1902 | −0.928870 | ||||||||
\(796\) | 23.4647 | 0.831684 | ||||||||
\(797\) | −14.9595 | −0.529894 | −0.264947 | − | 0.964263i | \(-0.585355\pi\) | ||||
−0.264947 | + | 0.964263i | \(0.585355\pi\) | |||||||
\(798\) | −30.9341 | −1.09505 | ||||||||
\(799\) | −0.262541 | −0.00928803 | ||||||||
\(800\) | −2.63835 | −0.0932797 | ||||||||
\(801\) | 11.6302 | 0.410933 | ||||||||
\(802\) | 35.9024 | 1.26776 | ||||||||
\(803\) | −80.4938 | −2.84057 | ||||||||
\(804\) | 27.9830 | 0.986885 | ||||||||
\(805\) | 4.96517 | 0.174999 | ||||||||
\(806\) | −20.0630 | −0.706688 | ||||||||
\(807\) | 23.2091 | 0.817000 | ||||||||
\(808\) | 1.19089 | 0.0418953 | ||||||||
\(809\) | 23.5806 | 0.829049 | 0.414524 | − | 0.910038i | \(-0.363948\pi\) | ||||
0.414524 | + | 0.910038i | \(0.363948\pi\) | |||||||
\(810\) | −4.27642 | −0.150258 | ||||||||
\(811\) | 1.94285 | 0.0682228 | 0.0341114 | − | 0.999418i | \(-0.489140\pi\) | ||||
0.0341114 | + | 0.999418i | \(0.489140\pi\) | |||||||
\(812\) | −20.1601 | −0.707480 | ||||||||
\(813\) | −12.6090 | −0.442218 | ||||||||
\(814\) | −36.7174 | −1.28694 | ||||||||
\(815\) | −27.4452 | −0.961364 | ||||||||
\(816\) | −0.379691 | −0.0132919 | ||||||||
\(817\) | 6.35305 | 0.222265 | ||||||||
\(818\) | 27.5026 | 0.961607 | ||||||||
\(819\) | 5.12656 | 0.179136 | ||||||||
\(820\) | −21.0616 | −0.735504 | ||||||||
\(821\) | 8.00173 | 0.279262 | 0.139631 | − | 0.990204i | \(-0.455408\pi\) | ||||
0.139631 | + | 0.990204i | \(0.455408\pi\) | |||||||
\(822\) | 33.7669 | 1.17775 | ||||||||
\(823\) | 29.6081 | 1.03207 | 0.516037 | − | 0.856566i | \(-0.327407\pi\) | ||||
0.516037 | + | 0.856566i | \(0.327407\pi\) | |||||||
\(824\) | −0.160099 | −0.00557732 | ||||||||
\(825\) | 1.76320 | 0.0613866 | ||||||||
\(826\) | 49.4691 | 1.72125 | ||||||||
\(827\) | 13.0507 | 0.453817 | 0.226908 | − | 0.973916i | \(-0.427138\pi\) | ||||
0.226908 | + | 0.973916i | \(0.427138\pi\) | |||||||
\(828\) | 0.860452 | 0.0299028 | ||||||||
\(829\) | 7.05072 | 0.244882 | 0.122441 | − | 0.992476i | \(-0.460928\pi\) | ||||
0.122441 | + | 0.992476i | \(0.460928\pi\) | |||||||
\(830\) | −14.8736 | −0.516270 | ||||||||
\(831\) | −8.68645 | −0.301330 | ||||||||
\(832\) | −7.34048 | −0.254485 | ||||||||
\(833\) | −1.76190 | −0.0610463 | ||||||||
\(834\) | −1.23794 | −0.0428665 | ||||||||
\(835\) | −46.0699 | −1.59431 | ||||||||
\(836\) | −30.9053 | −1.06888 | ||||||||
\(837\) | −10.1345 | −0.350298 | ||||||||
\(838\) | −7.12119 | −0.245997 | ||||||||
\(839\) | −5.54693 | −0.191501 | −0.0957506 | − | 0.995405i | \(-0.530525\pi\) | ||||
−0.0957506 | + | 0.995405i | \(0.530525\pi\) | |||||||
\(840\) | −1.77297 | −0.0611731 | ||||||||
\(841\) | −24.8012 | −0.855214 | ||||||||
\(842\) | −21.5970 | −0.744283 | ||||||||
\(843\) | 16.8805 | 0.581396 | ||||||||
\(844\) | −8.67523 | −0.298614 | ||||||||
\(845\) | 2.16016 | 0.0743116 | ||||||||
\(846\) | −5.68791 | −0.195554 | ||||||||
\(847\) | 86.7116 | 2.97945 | ||||||||
\(848\) | −50.3785 | −1.73001 | ||||||||
\(849\) | −10.4162 | −0.357482 | ||||||||
\(850\) | −0.0603701 | −0.00207068 | ||||||||
\(851\) | 1.57394 | 0.0539539 | ||||||||
\(852\) | −21.5188 | −0.737222 | ||||||||
\(853\) | 43.2997 | 1.48255 | 0.741276 | − | 0.671200i | \(-0.234221\pi\) | ||||
0.741276 | + | 0.671200i | \(0.234221\pi\) | |||||||
\(854\) | −98.6294 | −3.37503 | ||||||||
\(855\) | −6.58418 | −0.225174 | ||||||||
\(856\) | −1.16357 | −0.0397699 | ||||||||
\(857\) | 0.534680 | 0.0182643 | 0.00913215 | − | 0.999958i | \(-0.497093\pi\) | ||||
0.00913215 | + | 0.999958i | \(0.497093\pi\) | |||||||
\(858\) | 10.4594 | 0.357079 | ||||||||
\(859\) | −34.5674 | −1.17942 | −0.589712 | − | 0.807613i | \(-0.700759\pi\) | ||||
−0.589712 | + | 0.807613i | \(0.700759\pi\) | |||||||
\(860\) | −8.64082 | −0.294650 | ||||||||
\(861\) | 26.0453 | 0.887620 | ||||||||
\(862\) | −18.8086 | −0.640622 | ||||||||
\(863\) | −15.4851 | −0.527118 | −0.263559 | − | 0.964643i | \(-0.584896\pi\) | ||||
−0.263559 | + | 0.964643i | \(0.584896\pi\) | |||||||
\(864\) | −7.90577 | −0.268960 | ||||||||
\(865\) | 22.5791 | 0.767712 | ||||||||
\(866\) | −70.1859 | −2.38501 | ||||||||
\(867\) | 16.9917 | 0.577067 | ||||||||
\(868\) | 99.7081 | 3.38431 | ||||||||
\(869\) | −82.9617 | −2.81428 | ||||||||
\(870\) | −8.76278 | −0.297086 | ||||||||
\(871\) | −14.5811 | −0.494062 | ||||||||
\(872\) | −2.55216 | −0.0864269 | ||||||||
\(873\) | 5.69283 | 0.192673 | ||||||||
\(874\) | 2.70542 | 0.0915121 | ||||||||
\(875\) | −59.0666 | −1.99681 | ||||||||
\(876\) | 29.2384 | 0.987875 | ||||||||
\(877\) | 24.3046 | 0.820708 | 0.410354 | − | 0.911926i | \(-0.365405\pi\) | ||||
0.410354 | + | 0.911926i | \(0.365405\pi\) | |||||||
\(878\) | −37.5681 | −1.26786 | ||||||||
\(879\) | 28.7560 | 0.969917 | ||||||||
\(880\) | −47.4231 | −1.59863 | ||||||||
\(881\) | 2.55899 | 0.0862145 | 0.0431073 | − | 0.999070i | \(-0.486274\pi\) | ||||
0.0431073 | + | 0.999070i | \(0.486274\pi\) | |||||||
\(882\) | −38.1714 | −1.28530 | ||||||||
\(883\) | −37.2802 | −1.25458 | −0.627290 | − | 0.778786i | \(-0.715836\pi\) | ||||
−0.627290 | + | 0.778786i | \(0.715836\pi\) | |||||||
\(884\) | −0.175365 | −0.00589816 | ||||||||
\(885\) | 10.5293 | 0.353937 | ||||||||
\(886\) | 25.8154 | 0.867286 | ||||||||
\(887\) | 49.8625 | 1.67422 | 0.837109 | − | 0.547036i | \(-0.184244\pi\) | ||||
0.837109 | + | 0.547036i | \(0.184244\pi\) | |||||||
\(888\) | −0.562023 | −0.0188602 | ||||||||
\(889\) | −13.3035 | −0.446184 | ||||||||
\(890\) | −49.7356 | −1.66714 | ||||||||
\(891\) | 5.28339 | 0.177000 | ||||||||
\(892\) | 31.0659 | 1.04016 | ||||||||
\(893\) | −8.75739 | −0.293055 | ||||||||
\(894\) | 15.9275 | 0.532694 | ||||||||
\(895\) | 14.8672 | 0.496956 | ||||||||
\(896\) | −6.56070 | −0.219177 | ||||||||
\(897\) | −0.448356 | −0.0149702 | ||||||||
\(898\) | −47.7613 | −1.59382 | ||||||||
\(899\) | −20.7665 | −0.692600 | ||||||||
\(900\) | −0.640461 | −0.0213487 | ||||||||
\(901\) | −1.10788 | −0.0369088 | ||||||||
\(902\) | 53.1386 | 1.76932 | ||||||||
\(903\) | 10.6854 | 0.355588 | ||||||||
\(904\) | 0.502084 | 0.0166991 | ||||||||
\(905\) | −48.4558 | −1.61073 | ||||||||
\(906\) | −14.7962 | −0.491572 | ||||||||
\(907\) | −3.29256 | −0.109328 | −0.0546638 | − | 0.998505i | \(-0.517409\pi\) | ||||
−0.0546638 | + | 0.998505i | \(0.517409\pi\) | |||||||
\(908\) | 41.8232 | 1.38795 | ||||||||
\(909\) | 7.43844 | 0.246718 | ||||||||
\(910\) | −21.9233 | −0.726750 | ||||||||
\(911\) | 13.2275 | 0.438246 | 0.219123 | − | 0.975697i | \(-0.429680\pi\) | ||||
0.219123 | + | 0.975697i | \(0.429680\pi\) | |||||||
\(912\) | −12.6651 | −0.419384 | ||||||||
\(913\) | 18.3759 | 0.608153 | ||||||||
\(914\) | 14.7576 | 0.488138 | ||||||||
\(915\) | −20.9928 | −0.694001 | ||||||||
\(916\) | −50.7514 | −1.67687 | ||||||||
\(917\) | 9.47271 | 0.312817 | ||||||||
\(918\) | −0.180898 | −0.00597052 | ||||||||
\(919\) | 26.2911 | 0.867262 | 0.433631 | − | 0.901090i | \(-0.357232\pi\) | ||||
0.433631 | + | 0.901090i | \(0.357232\pi\) | |||||||
\(920\) | 0.155059 | 0.00511214 | ||||||||
\(921\) | 26.0150 | 0.857223 | ||||||||
\(922\) | 63.0923 | 2.07783 | ||||||||
\(923\) | 11.2128 | 0.369074 | ||||||||
\(924\) | −51.9808 | −1.71004 | ||||||||
\(925\) | −1.17153 | −0.0385196 | ||||||||
\(926\) | −77.8471 | −2.55822 | ||||||||
\(927\) | −1.00000 | −0.0328443 | ||||||||
\(928\) | −16.1997 | −0.531780 | ||||||||
\(929\) | −35.0779 | −1.15087 | −0.575433 | − | 0.817849i | \(-0.695167\pi\) | ||||
−0.575433 | + | 0.817849i | \(0.695167\pi\) | |||||||
\(930\) | 43.3392 | 1.42115 | ||||||||
\(931\) | −58.7705 | −1.92613 | ||||||||
\(932\) | −29.4275 | −0.963929 | ||||||||
\(933\) | −27.5881 | −0.903194 | ||||||||
\(934\) | −41.4433 | −1.35607 | ||||||||
\(935\) | −1.04289 | −0.0341060 | ||||||||
\(936\) | 0.160099 | 0.00523301 | ||||||||
\(937\) | 15.9368 | 0.520631 | 0.260316 | − | 0.965524i | \(-0.416173\pi\) | ||||
0.260316 | + | 0.965524i | \(0.416173\pi\) | |||||||
\(938\) | 147.983 | 4.83181 | ||||||||
\(939\) | −2.05595 | −0.0670933 | ||||||||
\(940\) | 11.9110 | 0.388493 | ||||||||
\(941\) | 13.8647 | 0.451976 | 0.225988 | − | 0.974130i | \(-0.427439\pi\) | ||||
0.225988 | + | 0.974130i | \(0.427439\pi\) | |||||||
\(942\) | 24.0908 | 0.784919 | ||||||||
\(943\) | −2.27785 | −0.0741771 | ||||||||
\(944\) | 20.2537 | 0.659203 | ||||||||
\(945\) | −11.0742 | −0.360243 | ||||||||
\(946\) | 21.8008 | 0.708806 | ||||||||
\(947\) | 24.3912 | 0.792608 | 0.396304 | − | 0.918119i | \(-0.370293\pi\) | ||||
0.396304 | + | 0.918119i | \(0.370293\pi\) | |||||||
\(948\) | 30.1349 | 0.978735 | ||||||||
\(949\) | −15.2353 | −0.494558 | ||||||||
\(950\) | −2.01372 | −0.0653338 | ||||||||
\(951\) | −29.8820 | −0.968989 | ||||||||
\(952\) | −0.0749987 | −0.00243072 | ||||||||
\(953\) | 1.89900 | 0.0615147 | 0.0307573 | − | 0.999527i | \(-0.490208\pi\) | ||||
0.0307573 | + | 0.999527i | \(0.490208\pi\) | |||||||
\(954\) | −24.0020 | −0.777095 | ||||||||
\(955\) | 7.20708 | 0.233216 | ||||||||
\(956\) | −18.2385 | −0.589876 | ||||||||
\(957\) | 10.8262 | 0.349960 | ||||||||
\(958\) | 10.9276 | 0.353056 | ||||||||
\(959\) | 87.4424 | 2.82366 | ||||||||
\(960\) | 15.8566 | 0.511769 | ||||||||
\(961\) | 71.7073 | 2.31314 | ||||||||
\(962\) | −6.94959 | −0.224064 | ||||||||
\(963\) | −7.26779 | −0.234201 | ||||||||
\(964\) | 16.5315 | 0.532442 | ||||||||
\(965\) | −8.76209 | −0.282062 | ||||||||
\(966\) | 4.55033 | 0.146405 | ||||||||
\(967\) | −39.1038 | −1.25749 | −0.628746 | − | 0.777610i | \(-0.716432\pi\) | ||||
−0.628746 | + | 0.777610i | \(0.716432\pi\) | |||||||
\(968\) | 2.70795 | 0.0870368 | ||||||||
\(969\) | −0.278519 | −0.00894733 | ||||||||
\(970\) | −24.3449 | −0.781668 | ||||||||
\(971\) | −23.2225 | −0.745247 | −0.372623 | − | 0.927983i | \(-0.621542\pi\) | ||||
−0.372623 | + | 0.927983i | \(0.621542\pi\) | |||||||
\(972\) | −1.91913 | −0.0615561 | ||||||||
\(973\) | −3.20577 | −0.102772 | ||||||||
\(974\) | 45.3617 | 1.45348 | ||||||||
\(975\) | 0.333725 | 0.0106877 | ||||||||
\(976\) | −40.3811 | −1.29257 | ||||||||
\(977\) | −21.4840 | −0.687333 | −0.343667 | − | 0.939092i | \(-0.611669\pi\) | ||||
−0.343667 | + | 0.939092i | \(0.611669\pi\) | |||||||
\(978\) | −25.1522 | −0.804279 | ||||||||
\(979\) | 61.4469 | 1.96385 | ||||||||
\(980\) | 79.9341 | 2.55340 | ||||||||
\(981\) | −15.9411 | −0.508960 | ||||||||
\(982\) | −60.2014 | −1.92110 | ||||||||
\(983\) | −0.231936 | −0.00739761 | −0.00369880 | − | 0.999993i | \(-0.501177\pi\) | ||||
−0.00369880 | + | 0.999993i | \(0.501177\pi\) | |||||||
\(984\) | 0.813378 | 0.0259295 | ||||||||
\(985\) | 21.0603 | 0.671038 | ||||||||
\(986\) | −0.370677 | −0.0118048 | ||||||||
\(987\) | −14.7294 | −0.468841 | ||||||||
\(988\) | −5.84953 | −0.186098 | ||||||||
\(989\) | −0.934520 | −0.0297160 | ||||||||
\(990\) | −22.5940 | −0.718084 | ||||||||
\(991\) | −38.3917 | −1.21955 | −0.609776 | − | 0.792574i | \(-0.708741\pi\) | ||||
−0.609776 | + | 0.792574i | \(0.708741\pi\) | |||||||
\(992\) | 80.1207 | 2.54383 | ||||||||
\(993\) | 12.4074 | 0.393737 | ||||||||
\(994\) | −113.798 | −3.60945 | ||||||||
\(995\) | 26.4117 | 0.837306 | ||||||||
\(996\) | −6.67483 | −0.211500 | ||||||||
\(997\) | 0.364962 | 0.0115585 | 0.00577924 | − | 0.999983i | \(-0.498160\pi\) | ||||
0.00577924 | + | 0.999983i | \(0.498160\pi\) | |||||||
\(998\) | −51.5563 | −1.63198 | ||||||||
\(999\) | −3.51047 | −0.111066 |
(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 | 4017.2.a.j.1.4 | ✓ | 25 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4017.2.a.j.1.4 | ✓ | 25 | 1.1 | even | 1 | trivial |