Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8041,2,Mod(1,8041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8041, 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("8041.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8041 = 11 \cdot 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8041.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.2077082653\) |
Analytic rank: | \(0\) |
Dimension: | \(82\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 8041.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00119 | −1.41505 | −0.707526 | − | 0.706687i | \(-0.750189\pi\) | ||||
−0.707526 | + | 0.706687i | \(0.750189\pi\) | |||||||
\(3\) | −0.510214 | −0.294572 | −0.147286 | − | 0.989094i | \(-0.547054\pi\) | ||||
−0.147286 | + | 0.989094i | \(0.547054\pi\) | |||||||
\(4\) | 2.00475 | 1.00237 | ||||||||
\(5\) | 2.33538 | 1.04441 | 0.522207 | − | 0.852819i | \(-0.325109\pi\) | ||||
0.522207 | + | 0.852819i | \(0.325109\pi\) | |||||||
\(6\) | 1.02103 | 0.416835 | ||||||||
\(7\) | −3.93653 | −1.48787 | −0.743935 | − | 0.668252i | \(-0.767043\pi\) | ||||
−0.743935 | + | 0.668252i | \(0.767043\pi\) | |||||||
\(8\) | −0.00949577 | −0.00335726 | ||||||||
\(9\) | −2.73968 | −0.913227 | ||||||||
\(10\) | −4.67353 | −1.47790 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −1.02285 | −0.295271 | ||||||||
\(13\) | 5.23418 | 1.45170 | 0.725850 | − | 0.687853i | \(-0.241447\pi\) | ||||
0.725850 | + | 0.687853i | \(0.241447\pi\) | |||||||
\(14\) | 7.87773 | 2.10541 | ||||||||
\(15\) | −1.19154 | −0.307655 | ||||||||
\(16\) | −3.99049 | −0.997622 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 5.48261 | 1.29226 | ||||||||
\(19\) | −2.97160 | −0.681731 | −0.340865 | − | 0.940112i | \(-0.610720\pi\) | ||||
−0.340865 | + | 0.940112i | \(0.610720\pi\) | |||||||
\(20\) | 4.68184 | 1.04689 | ||||||||
\(21\) | 2.00847 | 0.438285 | ||||||||
\(22\) | −2.00119 | −0.426654 | ||||||||
\(23\) | 0.0593703 | 0.0123796 | 0.00618978 | − | 0.999981i | \(-0.498030\pi\) | ||||
0.00618978 | + | 0.999981i | \(0.498030\pi\) | |||||||
\(24\) | 0.00484488 | 0.000988957 0 | ||||||||
\(25\) | 0.453998 | 0.0907996 | ||||||||
\(26\) | −10.4746 | −2.05423 | ||||||||
\(27\) | 2.92847 | 0.563584 | ||||||||
\(28\) | −7.89174 | −1.49140 | ||||||||
\(29\) | −9.76766 | −1.81381 | −0.906904 | − | 0.421337i | \(-0.861561\pi\) | ||||
−0.906904 | + | 0.421337i | \(0.861561\pi\) | |||||||
\(30\) | 2.38450 | 0.435348 | ||||||||
\(31\) | −0.151436 | −0.0271988 | −0.0135994 | − | 0.999908i | \(-0.504329\pi\) | ||||
−0.0135994 | + | 0.999908i | \(0.504329\pi\) | |||||||
\(32\) | 8.00470 | 1.41504 | ||||||||
\(33\) | −0.510214 | −0.0888169 | ||||||||
\(34\) | −2.00119 | −0.343201 | ||||||||
\(35\) | −9.19330 | −1.55395 | ||||||||
\(36\) | −5.49236 | −0.915394 | ||||||||
\(37\) | −1.80139 | −0.296147 | −0.148073 | − | 0.988976i | \(-0.547307\pi\) | ||||
−0.148073 | + | 0.988976i | \(0.547307\pi\) | |||||||
\(38\) | 5.94671 | 0.964684 | ||||||||
\(39\) | −2.67055 | −0.427631 | ||||||||
\(40\) | −0.0221762 | −0.00350637 | ||||||||
\(41\) | 7.48468 | 1.16891 | 0.584456 | − | 0.811426i | \(-0.301308\pi\) | ||||
0.584456 | + | 0.811426i | \(0.301308\pi\) | |||||||
\(42\) | −4.01933 | −0.620196 | ||||||||
\(43\) | 1.00000 | 0.152499 | ||||||||
\(44\) | 2.00475 | 0.302227 | ||||||||
\(45\) | −6.39820 | −0.953787 | ||||||||
\(46\) | −0.118811 | −0.0175177 | ||||||||
\(47\) | −1.63126 | −0.237943 | −0.118972 | − | 0.992898i | \(-0.537960\pi\) | ||||
−0.118972 | + | 0.992898i | \(0.537960\pi\) | |||||||
\(48\) | 2.03600 | 0.293872 | ||||||||
\(49\) | 8.49628 | 1.21375 | ||||||||
\(50\) | −0.908534 | −0.128486 | ||||||||
\(51\) | −0.510214 | −0.0714443 | ||||||||
\(52\) | 10.4932 | 1.45514 | ||||||||
\(53\) | 2.27586 | 0.312613 | 0.156307 | − | 0.987709i | \(-0.450041\pi\) | ||||
0.156307 | + | 0.987709i | \(0.450041\pi\) | |||||||
\(54\) | −5.86041 | −0.797500 | ||||||||
\(55\) | 2.33538 | 0.314903 | ||||||||
\(56\) | 0.0373804 | 0.00499517 | ||||||||
\(57\) | 1.51615 | 0.200819 | ||||||||
\(58\) | 19.5469 | 2.56663 | ||||||||
\(59\) | 4.09795 | 0.533507 | 0.266754 | − | 0.963765i | \(-0.414049\pi\) | ||||
0.266754 | + | 0.963765i | \(0.414049\pi\) | |||||||
\(60\) | −2.38874 | −0.308385 | ||||||||
\(61\) | −7.28320 | −0.932518 | −0.466259 | − | 0.884648i | \(-0.654399\pi\) | ||||
−0.466259 | + | 0.884648i | \(0.654399\pi\) | |||||||
\(62\) | 0.303052 | 0.0384877 | ||||||||
\(63\) | 10.7848 | 1.35876 | ||||||||
\(64\) | −8.03792 | −1.00474 | ||||||||
\(65\) | 12.2238 | 1.51618 | ||||||||
\(66\) | 1.02103 | 0.125681 | ||||||||
\(67\) | 12.8220 | 1.56645 | 0.783227 | − | 0.621736i | \(-0.213572\pi\) | ||||
0.783227 | + | 0.621736i | \(0.213572\pi\) | |||||||
\(68\) | 2.00475 | 0.243111 | ||||||||
\(69\) | −0.0302916 | −0.00364668 | ||||||||
\(70\) | 18.3975 | 2.19892 | ||||||||
\(71\) | −9.00003 | −1.06811 | −0.534054 | − | 0.845451i | \(-0.679332\pi\) | ||||
−0.534054 | + | 0.845451i | \(0.679332\pi\) | |||||||
\(72\) | 0.0260154 | 0.00306594 | ||||||||
\(73\) | −15.6354 | −1.82999 | −0.914995 | − | 0.403466i | \(-0.867805\pi\) | ||||
−0.914995 | + | 0.403466i | \(0.867805\pi\) | |||||||
\(74\) | 3.60492 | 0.419063 | ||||||||
\(75\) | −0.231636 | −0.0267470 | ||||||||
\(76\) | −5.95729 | −0.683348 | ||||||||
\(77\) | −3.93653 | −0.448609 | ||||||||
\(78\) | 5.34427 | 0.605120 | ||||||||
\(79\) | 13.8794 | 1.56156 | 0.780778 | − | 0.624808i | \(-0.214823\pi\) | ||||
0.780778 | + | 0.624808i | \(0.214823\pi\) | |||||||
\(80\) | −9.31930 | −1.04193 | ||||||||
\(81\) | 6.72490 | 0.747211 | ||||||||
\(82\) | −14.9782 | −1.65407 | ||||||||
\(83\) | −5.94659 | −0.652723 | −0.326361 | − | 0.945245i | \(-0.605823\pi\) | ||||
−0.326361 | + | 0.945245i | \(0.605823\pi\) | |||||||
\(84\) | 4.02648 | 0.439325 | ||||||||
\(85\) | 2.33538 | 0.253307 | ||||||||
\(86\) | −2.00119 | −0.215793 | ||||||||
\(87\) | 4.98360 | 0.534298 | ||||||||
\(88\) | −0.00949577 | −0.00101225 | ||||||||
\(89\) | −9.06518 | −0.960907 | −0.480453 | − | 0.877020i | \(-0.659528\pi\) | ||||
−0.480453 | + | 0.877020i | \(0.659528\pi\) | |||||||
\(90\) | 12.8040 | 1.34966 | ||||||||
\(91\) | −20.6045 | −2.15994 | ||||||||
\(92\) | 0.119022 | 0.0124089 | ||||||||
\(93\) | 0.0772650 | 0.00801201 | ||||||||
\(94\) | 3.26444 | 0.336702 | ||||||||
\(95\) | −6.93980 | −0.712009 | ||||||||
\(96\) | −4.08411 | −0.416833 | ||||||||
\(97\) | 11.3857 | 1.15605 | 0.578023 | − | 0.816020i | \(-0.303824\pi\) | ||||
0.578023 | + | 0.816020i | \(0.303824\pi\) | |||||||
\(98\) | −17.0026 | −1.71753 | ||||||||
\(99\) | −2.73968 | −0.275348 | ||||||||
\(100\) | 0.910150 | 0.0910150 | ||||||||
\(101\) | −4.24687 | −0.422579 | −0.211290 | − | 0.977423i | \(-0.567766\pi\) | ||||
−0.211290 | + | 0.977423i | \(0.567766\pi\) | |||||||
\(102\) | 1.02103 | 0.101097 | ||||||||
\(103\) | 3.21297 | 0.316583 | 0.158292 | − | 0.987392i | \(-0.449401\pi\) | ||||
0.158292 | + | 0.987392i | \(0.449401\pi\) | |||||||
\(104\) | −0.0497026 | −0.00487374 | ||||||||
\(105\) | 4.69055 | 0.457751 | ||||||||
\(106\) | −4.55442 | −0.442364 | ||||||||
\(107\) | 15.6026 | 1.50836 | 0.754181 | − | 0.656666i | \(-0.228034\pi\) | ||||
0.754181 | + | 0.656666i | \(0.228034\pi\) | |||||||
\(108\) | 5.87083 | 0.564921 | ||||||||
\(109\) | −7.44771 | −0.713361 | −0.356680 | − | 0.934226i | \(-0.616091\pi\) | ||||
−0.356680 | + | 0.934226i | \(0.616091\pi\) | |||||||
\(110\) | −4.67353 | −0.445603 | ||||||||
\(111\) | 0.919096 | 0.0872367 | ||||||||
\(112\) | 15.7087 | 1.48433 | ||||||||
\(113\) | −13.7104 | −1.28977 | −0.644883 | − | 0.764282i | \(-0.723094\pi\) | ||||
−0.644883 | + | 0.764282i | \(0.723094\pi\) | |||||||
\(114\) | −3.03410 | −0.284169 | ||||||||
\(115\) | 0.138652 | 0.0129294 | ||||||||
\(116\) | −19.5817 | −1.81811 | ||||||||
\(117\) | −14.3400 | −1.32573 | ||||||||
\(118\) | −8.20075 | −0.754940 | ||||||||
\(119\) | −3.93653 | −0.360861 | ||||||||
\(120\) | 0.0113146 | 0.00103288 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 14.5750 | 1.31956 | ||||||||
\(123\) | −3.81879 | −0.344329 | ||||||||
\(124\) | −0.303591 | −0.0272633 | ||||||||
\(125\) | −10.6166 | −0.949581 | ||||||||
\(126\) | −21.5825 | −1.92272 | ||||||||
\(127\) | 9.22368 | 0.818469 | 0.409235 | − | 0.912429i | \(-0.365796\pi\) | ||||
0.409235 | + | 0.912429i | \(0.365796\pi\) | |||||||
\(128\) | 0.0759660 | 0.00671451 | ||||||||
\(129\) | −0.510214 | −0.0449219 | ||||||||
\(130\) | −24.4621 | −2.14547 | ||||||||
\(131\) | 6.83688 | 0.597341 | 0.298671 | − | 0.954356i | \(-0.403457\pi\) | ||||
0.298671 | + | 0.954356i | \(0.403457\pi\) | |||||||
\(132\) | −1.02285 | −0.0890276 | ||||||||
\(133\) | 11.6978 | 1.01433 | ||||||||
\(134\) | −25.6592 | −2.21661 | ||||||||
\(135\) | 6.83908 | 0.588615 | ||||||||
\(136\) | −0.00949577 | −0.000814256 0 | ||||||||
\(137\) | 16.5748 | 1.41608 | 0.708039 | − | 0.706173i | \(-0.249580\pi\) | ||||
0.708039 | + | 0.706173i | \(0.249580\pi\) | |||||||
\(138\) | 0.0606191 | 0.00516024 | ||||||||
\(139\) | −14.8185 | −1.25689 | −0.628446 | − | 0.777853i | \(-0.716309\pi\) | ||||
−0.628446 | + | 0.777853i | \(0.716309\pi\) | |||||||
\(140\) | −18.4302 | −1.55764 | ||||||||
\(141\) | 0.832290 | 0.0700914 | ||||||||
\(142\) | 18.0107 | 1.51143 | ||||||||
\(143\) | 5.23418 | 0.437704 | ||||||||
\(144\) | 10.9327 | 0.911055 | ||||||||
\(145\) | −22.8112 | −1.89437 | ||||||||
\(146\) | 31.2894 | 2.58953 | ||||||||
\(147\) | −4.33493 | −0.357539 | ||||||||
\(148\) | −3.61133 | −0.296850 | ||||||||
\(149\) | −2.86405 | −0.234632 | −0.117316 | − | 0.993095i | \(-0.537429\pi\) | ||||
−0.117316 | + | 0.993095i | \(0.537429\pi\) | |||||||
\(150\) | 0.463547 | 0.0378485 | ||||||||
\(151\) | −0.818528 | −0.0666109 | −0.0333054 | − | 0.999445i | \(-0.510603\pi\) | ||||
−0.0333054 | + | 0.999445i | \(0.510603\pi\) | |||||||
\(152\) | 0.0282176 | 0.00228875 | ||||||||
\(153\) | −2.73968 | −0.221490 | ||||||||
\(154\) | 7.87773 | 0.634806 | ||||||||
\(155\) | −0.353661 | −0.0284068 | ||||||||
\(156\) | −5.35378 | −0.428645 | ||||||||
\(157\) | 4.17895 | 0.333517 | 0.166758 | − | 0.985998i | \(-0.446670\pi\) | ||||
0.166758 | + | 0.985998i | \(0.446670\pi\) | |||||||
\(158\) | −27.7753 | −2.20968 | ||||||||
\(159\) | −1.16118 | −0.0920872 | ||||||||
\(160\) | 18.6940 | 1.47789 | ||||||||
\(161\) | −0.233713 | −0.0184192 | ||||||||
\(162\) | −13.4578 | −1.05734 | ||||||||
\(163\) | −1.56120 | −0.122283 | −0.0611413 | − | 0.998129i | \(-0.519474\pi\) | ||||
−0.0611413 | + | 0.998129i | \(0.519474\pi\) | |||||||
\(164\) | 15.0049 | 1.17168 | ||||||||
\(165\) | −1.19154 | −0.0927616 | ||||||||
\(166\) | 11.9002 | 0.923637 | ||||||||
\(167\) | 8.02859 | 0.621271 | 0.310636 | − | 0.950529i | \(-0.399458\pi\) | ||||
0.310636 | + | 0.950529i | \(0.399458\pi\) | |||||||
\(168\) | −0.0190720 | −0.00147144 | ||||||||
\(169\) | 14.3966 | 1.10743 | ||||||||
\(170\) | −4.67353 | −0.358443 | ||||||||
\(171\) | 8.14122 | 0.622575 | ||||||||
\(172\) | 2.00475 | 0.152860 | ||||||||
\(173\) | −23.0098 | −1.74941 | −0.874703 | − | 0.484659i | \(-0.838944\pi\) | ||||
−0.874703 | + | 0.484659i | \(0.838944\pi\) | |||||||
\(174\) | −9.97311 | −0.756059 | ||||||||
\(175\) | −1.78718 | −0.135098 | ||||||||
\(176\) | −3.99049 | −0.300794 | ||||||||
\(177\) | −2.09083 | −0.157156 | ||||||||
\(178\) | 18.1411 | 1.35973 | ||||||||
\(179\) | −14.1309 | −1.05619 | −0.528096 | − | 0.849185i | \(-0.677094\pi\) | ||||
−0.528096 | + | 0.849185i | \(0.677094\pi\) | |||||||
\(180\) | −12.8268 | −0.956050 | ||||||||
\(181\) | 14.2374 | 1.05826 | 0.529130 | − | 0.848541i | \(-0.322518\pi\) | ||||
0.529130 | + | 0.848541i | \(0.322518\pi\) | |||||||
\(182\) | 41.2335 | 3.05643 | ||||||||
\(183\) | 3.71599 | 0.274694 | ||||||||
\(184\) | −0.000563767 0 | −4.15614e−5 0 | ||||||||
\(185\) | −4.20693 | −0.309300 | ||||||||
\(186\) | −0.154622 | −0.0113374 | ||||||||
\(187\) | 1.00000 | 0.0731272 | ||||||||
\(188\) | −3.27025 | −0.238508 | ||||||||
\(189\) | −11.5280 | −0.838539 | ||||||||
\(190\) | 13.8878 | 1.00753 | ||||||||
\(191\) | 6.93198 | 0.501580 | 0.250790 | − | 0.968041i | \(-0.419310\pi\) | ||||
0.250790 | + | 0.968041i | \(0.419310\pi\) | |||||||
\(192\) | 4.10106 | 0.295968 | ||||||||
\(193\) | −0.666990 | −0.0480110 | −0.0240055 | − | 0.999712i | \(-0.507642\pi\) | ||||
−0.0240055 | + | 0.999712i | \(0.507642\pi\) | |||||||
\(194\) | −22.7850 | −1.63587 | ||||||||
\(195\) | −6.23676 | −0.446623 | ||||||||
\(196\) | 17.0329 | 1.21663 | ||||||||
\(197\) | 7.56580 | 0.539041 | 0.269520 | − | 0.962995i | \(-0.413135\pi\) | ||||
0.269520 | + | 0.962995i | \(0.413135\pi\) | |||||||
\(198\) | 5.48261 | 0.389632 | ||||||||
\(199\) | 18.7514 | 1.32925 | 0.664627 | − | 0.747176i | \(-0.268591\pi\) | ||||
0.664627 | + | 0.747176i | \(0.268591\pi\) | |||||||
\(200\) | −0.00431106 | −0.000304838 0 | ||||||||
\(201\) | −6.54195 | −0.461434 | ||||||||
\(202\) | 8.49877 | 0.597972 | ||||||||
\(203\) | 38.4507 | 2.69871 | ||||||||
\(204\) | −1.02285 | −0.0716138 | ||||||||
\(205\) | 17.4796 | 1.22083 | ||||||||
\(206\) | −6.42975 | −0.447982 | ||||||||
\(207\) | −0.162656 | −0.0113054 | ||||||||
\(208\) | −20.8869 | −1.44825 | ||||||||
\(209\) | −2.97160 | −0.205550 | ||||||||
\(210\) | −9.38666 | −0.647741 | ||||||||
\(211\) | 9.51422 | 0.654986 | 0.327493 | − | 0.944854i | \(-0.393796\pi\) | ||||
0.327493 | + | 0.944854i | \(0.393796\pi\) | |||||||
\(212\) | 4.56252 | 0.313355 | ||||||||
\(213\) | 4.59194 | 0.314635 | ||||||||
\(214\) | −31.2237 | −2.13441 | ||||||||
\(215\) | 2.33538 | 0.159272 | ||||||||
\(216\) | −0.0278081 | −0.00189210 | ||||||||
\(217\) | 0.596134 | 0.0404682 | ||||||||
\(218\) | 14.9042 | 1.00944 | ||||||||
\(219\) | 7.97742 | 0.539064 | ||||||||
\(220\) | 4.68184 | 0.315650 | ||||||||
\(221\) | 5.23418 | 0.352089 | ||||||||
\(222\) | −1.83928 | −0.123444 | ||||||||
\(223\) | 9.20959 | 0.616720 | 0.308360 | − | 0.951270i | \(-0.400220\pi\) | ||||
0.308360 | + | 0.951270i | \(0.400220\pi\) | |||||||
\(224\) | −31.5108 | −2.10540 | ||||||||
\(225\) | −1.24381 | −0.0829206 | ||||||||
\(226\) | 27.4370 | 1.82508 | ||||||||
\(227\) | 0.569489 | 0.0377983 | 0.0188992 | − | 0.999821i | \(-0.493984\pi\) | ||||
0.0188992 | + | 0.999821i | \(0.493984\pi\) | |||||||
\(228\) | 3.03949 | 0.201295 | ||||||||
\(229\) | 6.29506 | 0.415989 | 0.207995 | − | 0.978130i | \(-0.433306\pi\) | ||||
0.207995 | + | 0.978130i | \(0.433306\pi\) | |||||||
\(230\) | −0.277469 | −0.0182957 | ||||||||
\(231\) | 2.00847 | 0.132148 | ||||||||
\(232\) | 0.0927514 | 0.00608943 | ||||||||
\(233\) | −15.0067 | −0.983119 | −0.491559 | − | 0.870844i | \(-0.663573\pi\) | ||||
−0.491559 | + | 0.870844i | \(0.663573\pi\) | |||||||
\(234\) | 28.6970 | 1.87598 | ||||||||
\(235\) | −3.80960 | −0.248511 | ||||||||
\(236\) | 8.21534 | 0.534773 | ||||||||
\(237\) | −7.08148 | −0.459991 | ||||||||
\(238\) | 7.87773 | 0.510638 | ||||||||
\(239\) | 23.2725 | 1.50537 | 0.752687 | − | 0.658379i | \(-0.228757\pi\) | ||||
0.752687 | + | 0.658379i | \(0.228757\pi\) | |||||||
\(240\) | 4.75484 | 0.306924 | ||||||||
\(241\) | 5.92917 | 0.381931 | 0.190966 | − | 0.981597i | \(-0.438838\pi\) | ||||
0.190966 | + | 0.981597i | \(0.438838\pi\) | |||||||
\(242\) | −2.00119 | −0.128641 | ||||||||
\(243\) | −12.2165 | −0.783691 | ||||||||
\(244\) | −14.6010 | −0.934731 | ||||||||
\(245\) | 19.8421 | 1.26766 | ||||||||
\(246\) | 7.64211 | 0.487243 | ||||||||
\(247\) | −15.5539 | −0.989669 | ||||||||
\(248\) | 0.00143800 | 9.13134e−5 0 | ||||||||
\(249\) | 3.03403 | 0.192274 | ||||||||
\(250\) | 21.2459 | 1.34371 | ||||||||
\(251\) | 5.75160 | 0.363038 | 0.181519 | − | 0.983387i | \(-0.441899\pi\) | ||||
0.181519 | + | 0.983387i | \(0.441899\pi\) | |||||||
\(252\) | 21.6209 | 1.36199 | ||||||||
\(253\) | 0.0593703 | 0.00373258 | ||||||||
\(254\) | −18.4583 | −1.15818 | ||||||||
\(255\) | −1.19154 | −0.0746174 | ||||||||
\(256\) | 15.9238 | 0.995238 | ||||||||
\(257\) | 3.40258 | 0.212247 | 0.106123 | − | 0.994353i | \(-0.466156\pi\) | ||||
0.106123 | + | 0.994353i | \(0.466156\pi\) | |||||||
\(258\) | 1.02103 | 0.0635668 | ||||||||
\(259\) | 7.09124 | 0.440628 | ||||||||
\(260\) | 24.5056 | 1.51977 | ||||||||
\(261\) | 26.7603 | 1.65642 | ||||||||
\(262\) | −13.6819 | −0.845269 | ||||||||
\(263\) | 12.9937 | 0.801227 | 0.400613 | − | 0.916247i | \(-0.368797\pi\) | ||||
0.400613 | + | 0.916247i | \(0.368797\pi\) | |||||||
\(264\) | 0.00484488 | 0.000298182 0 | ||||||||
\(265\) | 5.31499 | 0.326497 | ||||||||
\(266\) | −23.4094 | −1.43532 | ||||||||
\(267\) | 4.62518 | 0.283057 | ||||||||
\(268\) | 25.7048 | 1.57017 | ||||||||
\(269\) | −28.8142 | −1.75683 | −0.878416 | − | 0.477897i | \(-0.841399\pi\) | ||||
−0.878416 | + | 0.477897i | \(0.841399\pi\) | |||||||
\(270\) | −13.6863 | −0.832920 | ||||||||
\(271\) | 21.0282 | 1.27737 | 0.638685 | − | 0.769468i | \(-0.279479\pi\) | ||||
0.638685 | + | 0.769468i | \(0.279479\pi\) | |||||||
\(272\) | −3.99049 | −0.241959 | ||||||||
\(273\) | 10.5127 | 0.636259 | ||||||||
\(274\) | −33.1692 | −2.00383 | ||||||||
\(275\) | 0.453998 | 0.0273771 | ||||||||
\(276\) | −0.0607269 | −0.00365533 | ||||||||
\(277\) | −15.5587 | −0.934830 | −0.467415 | − | 0.884038i | \(-0.654815\pi\) | ||||
−0.467415 | + | 0.884038i | \(0.654815\pi\) | |||||||
\(278\) | 29.6546 | 1.77857 | ||||||||
\(279\) | 0.414887 | 0.0248387 | ||||||||
\(280\) | 0.0872974 | 0.00521702 | ||||||||
\(281\) | −4.25632 | −0.253911 | −0.126955 | − | 0.991908i | \(-0.540520\pi\) | ||||
−0.126955 | + | 0.991908i | \(0.540520\pi\) | |||||||
\(282\) | −1.66557 | −0.0991830 | ||||||||
\(283\) | −27.4760 | −1.63328 | −0.816639 | − | 0.577148i | \(-0.804165\pi\) | ||||
−0.816639 | + | 0.577148i | \(0.804165\pi\) | |||||||
\(284\) | −18.0428 | −1.07064 | ||||||||
\(285\) | 3.54079 | 0.209738 | ||||||||
\(286\) | −10.4746 | −0.619374 | ||||||||
\(287\) | −29.4637 | −1.73919 | ||||||||
\(288\) | −21.9303 | −1.29226 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 45.6494 | 2.68063 | ||||||||
\(291\) | −5.80916 | −0.340539 | ||||||||
\(292\) | −31.3451 | −1.83433 | ||||||||
\(293\) | −22.3199 | −1.30394 | −0.651972 | − | 0.758243i | \(-0.726058\pi\) | ||||
−0.651972 | + | 0.758243i | \(0.726058\pi\) | |||||||
\(294\) | 8.67499 | 0.505936 | ||||||||
\(295\) | 9.57026 | 0.557202 | ||||||||
\(296\) | 0.0171056 | 0.000994243 0 | ||||||||
\(297\) | 2.92847 | 0.169927 | ||||||||
\(298\) | 5.73150 | 0.332017 | ||||||||
\(299\) | 0.310755 | 0.0179714 | ||||||||
\(300\) | −0.464371 | −0.0268105 | ||||||||
\(301\) | −3.93653 | −0.226898 | ||||||||
\(302\) | 1.63803 | 0.0942579 | ||||||||
\(303\) | 2.16681 | 0.124480 | ||||||||
\(304\) | 11.8581 | 0.680109 | ||||||||
\(305\) | −17.0090 | −0.973935 | ||||||||
\(306\) | 5.48261 | 0.313420 | ||||||||
\(307\) | −20.3931 | −1.16390 | −0.581949 | − | 0.813225i | \(-0.697710\pi\) | ||||
−0.581949 | + | 0.813225i | \(0.697710\pi\) | |||||||
\(308\) | −7.89174 | −0.449674 | ||||||||
\(309\) | −1.63930 | −0.0932566 | ||||||||
\(310\) | 0.707742 | 0.0401971 | ||||||||
\(311\) | 11.5468 | 0.654757 | 0.327379 | − | 0.944893i | \(-0.393835\pi\) | ||||
0.327379 | + | 0.944893i | \(0.393835\pi\) | |||||||
\(312\) | 0.0253590 | 0.00143567 | ||||||||
\(313\) | 4.96935 | 0.280884 | 0.140442 | − | 0.990089i | \(-0.455148\pi\) | ||||
0.140442 | + | 0.990089i | \(0.455148\pi\) | |||||||
\(314\) | −8.36286 | −0.471943 | ||||||||
\(315\) | 25.1867 | 1.41911 | ||||||||
\(316\) | 27.8247 | 1.56526 | ||||||||
\(317\) | −16.5534 | −0.929730 | −0.464865 | − | 0.885381i | \(-0.653897\pi\) | ||||
−0.464865 | + | 0.885381i | \(0.653897\pi\) | |||||||
\(318\) | 2.32373 | 0.130308 | ||||||||
\(319\) | −9.76766 | −0.546884 | ||||||||
\(320\) | −18.7716 | −1.04936 | ||||||||
\(321\) | −7.96068 | −0.444322 | ||||||||
\(322\) | 0.467703 | 0.0260641 | ||||||||
\(323\) | −2.97160 | −0.165344 | ||||||||
\(324\) | 13.4817 | 0.748984 | ||||||||
\(325\) | 2.37631 | 0.131814 | ||||||||
\(326\) | 3.12425 | 0.173036 | ||||||||
\(327\) | 3.79993 | 0.210136 | ||||||||
\(328\) | −0.0710728 | −0.00392434 | ||||||||
\(329\) | 6.42149 | 0.354028 | ||||||||
\(330\) | 2.38450 | 0.131262 | ||||||||
\(331\) | 8.22636 | 0.452162 | 0.226081 | − | 0.974109i | \(-0.427409\pi\) | ||||
0.226081 | + | 0.974109i | \(0.427409\pi\) | |||||||
\(332\) | −11.9214 | −0.654271 | ||||||||
\(333\) | 4.93524 | 0.270449 | ||||||||
\(334\) | −16.0667 | −0.879131 | ||||||||
\(335\) | 29.9442 | 1.63602 | ||||||||
\(336\) | −8.01479 | −0.437243 | ||||||||
\(337\) | −5.61124 | −0.305664 | −0.152832 | − | 0.988252i | \(-0.548839\pi\) | ||||
−0.152832 | + | 0.988252i | \(0.548839\pi\) | |||||||
\(338\) | −28.8104 | −1.56708 | ||||||||
\(339\) | 6.99524 | 0.379929 | ||||||||
\(340\) | 4.68184 | 0.253908 | ||||||||
\(341\) | −0.151436 | −0.00820074 | ||||||||
\(342\) | −16.2921 | −0.880976 | ||||||||
\(343\) | −5.89017 | −0.318039 | ||||||||
\(344\) | −0.00949577 | −0.000511978 0 | ||||||||
\(345\) | −0.0707423 | −0.00380864 | ||||||||
\(346\) | 46.0470 | 2.47550 | ||||||||
\(347\) | 29.3420 | 1.57516 | 0.787580 | − | 0.616213i | \(-0.211334\pi\) | ||||
0.787580 | + | 0.616213i | \(0.211334\pi\) | |||||||
\(348\) | 9.99084 | 0.535565 | ||||||||
\(349\) | −18.4204 | −0.986024 | −0.493012 | − | 0.870023i | \(-0.664104\pi\) | ||||
−0.493012 | + | 0.870023i | \(0.664104\pi\) | |||||||
\(350\) | 3.57647 | 0.191171 | ||||||||
\(351\) | 15.3281 | 0.818155 | ||||||||
\(352\) | 8.00470 | 0.426652 | ||||||||
\(353\) | 24.7243 | 1.31594 | 0.657970 | − | 0.753044i | \(-0.271415\pi\) | ||||
0.657970 | + | 0.753044i | \(0.271415\pi\) | |||||||
\(354\) | 4.18414 | 0.222385 | ||||||||
\(355\) | −21.0185 | −1.11555 | ||||||||
\(356\) | −18.1734 | −0.963187 | ||||||||
\(357\) | 2.00847 | 0.106300 | ||||||||
\(358\) | 28.2785 | 1.49457 | ||||||||
\(359\) | 8.36752 | 0.441621 | 0.220810 | − | 0.975317i | \(-0.429130\pi\) | ||||
0.220810 | + | 0.975317i | \(0.429130\pi\) | |||||||
\(360\) | 0.0607558 | 0.00320211 | ||||||||
\(361\) | −10.1696 | −0.535243 | ||||||||
\(362\) | −28.4918 | −1.49749 | ||||||||
\(363\) | −0.510214 | −0.0267793 | ||||||||
\(364\) | −41.3068 | −2.16507 | ||||||||
\(365\) | −36.5147 | −1.91127 | ||||||||
\(366\) | −7.43639 | −0.388707 | ||||||||
\(367\) | 1.01560 | 0.0530137 | 0.0265068 | − | 0.999649i | \(-0.491562\pi\) | ||||
0.0265068 | + | 0.999649i | \(0.491562\pi\) | |||||||
\(368\) | −0.236916 | −0.0123501 | ||||||||
\(369\) | −20.5057 | −1.06748 | ||||||||
\(370\) | 8.41885 | 0.437675 | ||||||||
\(371\) | −8.95899 | −0.465128 | ||||||||
\(372\) | 0.154897 | 0.00803101 | ||||||||
\(373\) | 19.5396 | 1.01172 | 0.505861 | − | 0.862615i | \(-0.331175\pi\) | ||||
0.505861 | + | 0.862615i | \(0.331175\pi\) | |||||||
\(374\) | −2.00119 | −0.103479 | ||||||||
\(375\) | 5.41676 | 0.279720 | ||||||||
\(376\) | 0.0154900 | 0.000798837 0 | ||||||||
\(377\) | −51.1257 | −2.63311 | ||||||||
\(378\) | 23.0697 | 1.18658 | ||||||||
\(379\) | −9.99246 | −0.513278 | −0.256639 | − | 0.966507i | \(-0.582615\pi\) | ||||
−0.256639 | + | 0.966507i | \(0.582615\pi\) | |||||||
\(380\) | −13.9125 | −0.713698 | ||||||||
\(381\) | −4.70605 | −0.241098 | ||||||||
\(382\) | −13.8722 | −0.709762 | ||||||||
\(383\) | −6.99998 | −0.357682 | −0.178841 | − | 0.983878i | \(-0.557235\pi\) | ||||
−0.178841 | + | 0.983878i | \(0.557235\pi\) | |||||||
\(384\) | −0.0387589 | −0.00197791 | ||||||||
\(385\) | −9.19330 | −0.468534 | ||||||||
\(386\) | 1.33477 | 0.0679381 | ||||||||
\(387\) | −2.73968 | −0.139266 | ||||||||
\(388\) | 22.8255 | 1.15879 | ||||||||
\(389\) | 22.8231 | 1.15718 | 0.578588 | − | 0.815620i | \(-0.303604\pi\) | ||||
0.578588 | + | 0.815620i | \(0.303604\pi\) | |||||||
\(390\) | 12.4809 | 0.631995 | ||||||||
\(391\) | 0.0593703 | 0.00300248 | ||||||||
\(392\) | −0.0806788 | −0.00407489 | ||||||||
\(393\) | −3.48827 | −0.175960 | ||||||||
\(394\) | −15.1406 | −0.762771 | ||||||||
\(395\) | 32.4137 | 1.63091 | ||||||||
\(396\) | −5.49236 | −0.276002 | ||||||||
\(397\) | 7.72213 | 0.387563 | 0.193781 | − | 0.981045i | \(-0.437925\pi\) | ||||
0.193781 | + | 0.981045i | \(0.437925\pi\) | |||||||
\(398\) | −37.5251 | −1.88096 | ||||||||
\(399\) | −5.96837 | −0.298792 | ||||||||
\(400\) | −1.81167 | −0.0905836 | ||||||||
\(401\) | 38.6727 | 1.93122 | 0.965612 | − | 0.259987i | \(-0.0837184\pi\) | ||||
0.965612 | + | 0.259987i | \(0.0837184\pi\) | |||||||
\(402\) | 13.0917 | 0.652953 | ||||||||
\(403\) | −0.792645 | −0.0394845 | ||||||||
\(404\) | −8.51389 | −0.423582 | ||||||||
\(405\) | 15.7052 | 0.780397 | ||||||||
\(406\) | −76.9470 | −3.81882 | ||||||||
\(407\) | −1.80139 | −0.0892917 | ||||||||
\(408\) | 0.00484488 | 0.000239857 0 | ||||||||
\(409\) | −0.587094 | −0.0290299 | −0.0145150 | − | 0.999895i | \(-0.504620\pi\) | ||||
−0.0145150 | + | 0.999895i | \(0.504620\pi\) | |||||||
\(410\) | −34.9799 | −1.72753 | ||||||||
\(411\) | −8.45669 | −0.417138 | ||||||||
\(412\) | 6.44118 | 0.317334 | ||||||||
\(413\) | −16.1317 | −0.793789 | ||||||||
\(414\) | 0.325504 | 0.0159977 | ||||||||
\(415\) | −13.8875 | −0.681713 | ||||||||
\(416\) | 41.8980 | 2.05422 | ||||||||
\(417\) | 7.56063 | 0.370246 | ||||||||
\(418\) | 5.94671 | 0.290863 | ||||||||
\(419\) | 3.61037 | 0.176378 | 0.0881890 | − | 0.996104i | \(-0.471892\pi\) | ||||
0.0881890 | + | 0.996104i | \(0.471892\pi\) | |||||||
\(420\) | 9.40336 | 0.458837 | ||||||||
\(421\) | 36.9882 | 1.80269 | 0.901346 | − | 0.433099i | \(-0.142580\pi\) | ||||
0.901346 | + | 0.433099i | \(0.142580\pi\) | |||||||
\(422\) | −19.0397 | −0.926839 | ||||||||
\(423\) | 4.46912 | 0.217296 | ||||||||
\(424\) | −0.0216110 | −0.00104952 | ||||||||
\(425\) | 0.453998 | 0.0220221 | ||||||||
\(426\) | −9.18933 | −0.445225 | ||||||||
\(427\) | 28.6706 | 1.38747 | ||||||||
\(428\) | 31.2793 | 1.51194 | ||||||||
\(429\) | −2.67055 | −0.128936 | ||||||||
\(430\) | −4.67353 | −0.225378 | ||||||||
\(431\) | 3.29861 | 0.158888 | 0.0794442 | − | 0.996839i | \(-0.474685\pi\) | ||||
0.0794442 | + | 0.996839i | \(0.474685\pi\) | |||||||
\(432\) | −11.6860 | −0.562243 | ||||||||
\(433\) | 13.4354 | 0.645666 | 0.322833 | − | 0.946456i | \(-0.395365\pi\) | ||||
0.322833 | + | 0.946456i | \(0.395365\pi\) | |||||||
\(434\) | −1.19298 | −0.0572646 | ||||||||
\(435\) | 11.6386 | 0.558028 | ||||||||
\(436\) | −14.9308 | −0.715053 | ||||||||
\(437\) | −0.176424 | −0.00843953 | ||||||||
\(438\) | −15.9643 | −0.762804 | ||||||||
\(439\) | 0.441484 | 0.0210709 | 0.0105354 | − | 0.999945i | \(-0.496646\pi\) | ||||
0.0105354 | + | 0.999945i | \(0.496646\pi\) | |||||||
\(440\) | −0.0221762 | −0.00105721 | ||||||||
\(441\) | −23.2771 | −1.10843 | ||||||||
\(442\) | −10.4746 | −0.498224 | ||||||||
\(443\) | −1.34419 | −0.0638643 | −0.0319321 | − | 0.999490i | \(-0.510166\pi\) | ||||
−0.0319321 | + | 0.999490i | \(0.510166\pi\) | |||||||
\(444\) | 1.84255 | 0.0874437 | ||||||||
\(445\) | −21.1706 | −1.00358 | ||||||||
\(446\) | −18.4301 | −0.872691 | ||||||||
\(447\) | 1.46128 | 0.0691162 | ||||||||
\(448\) | 31.6415 | 1.49492 | ||||||||
\(449\) | 23.9721 | 1.13131 | 0.565657 | − | 0.824641i | \(-0.308623\pi\) | ||||
0.565657 | + | 0.824641i | \(0.308623\pi\) | |||||||
\(450\) | 2.48909 | 0.117337 | ||||||||
\(451\) | 7.48468 | 0.352440 | ||||||||
\(452\) | −27.4858 | −1.29283 | ||||||||
\(453\) | 0.417625 | 0.0196217 | ||||||||
\(454\) | −1.13965 | −0.0534866 | ||||||||
\(455\) | −48.1194 | −2.25587 | ||||||||
\(456\) | −0.0143970 | −0.000674202 0 | ||||||||
\(457\) | −15.3473 | −0.717917 | −0.358959 | − | 0.933353i | \(-0.616868\pi\) | ||||
−0.358959 | + | 0.933353i | \(0.616868\pi\) | |||||||
\(458\) | −12.5976 | −0.588647 | ||||||||
\(459\) | 2.92847 | 0.136689 | ||||||||
\(460\) | 0.277962 | 0.0129601 | ||||||||
\(461\) | −40.5155 | −1.88700 | −0.943498 | − | 0.331379i | \(-0.892486\pi\) | ||||
−0.943498 | + | 0.331379i | \(0.892486\pi\) | |||||||
\(462\) | −4.01933 | −0.186996 | ||||||||
\(463\) | 24.2300 | 1.12606 | 0.563031 | − | 0.826436i | \(-0.309635\pi\) | ||||
0.563031 | + | 0.826436i | \(0.309635\pi\) | |||||||
\(464\) | 38.9777 | 1.80949 | ||||||||
\(465\) | 0.180443 | 0.00836785 | ||||||||
\(466\) | 30.0311 | 1.39116 | ||||||||
\(467\) | −21.9439 | −1.01544 | −0.507721 | − | 0.861521i | \(-0.669512\pi\) | ||||
−0.507721 | + | 0.861521i | \(0.669512\pi\) | |||||||
\(468\) | −28.7480 | −1.32888 | ||||||||
\(469\) | −50.4741 | −2.33068 | ||||||||
\(470\) | 7.62372 | 0.351656 | ||||||||
\(471\) | −2.13216 | −0.0982448 | ||||||||
\(472\) | −0.0389132 | −0.00179112 | ||||||||
\(473\) | 1.00000 | 0.0459800 | ||||||||
\(474\) | 14.1714 | 0.650912 | ||||||||
\(475\) | −1.34910 | −0.0619008 | ||||||||
\(476\) | −7.89174 | −0.361717 | ||||||||
\(477\) | −6.23513 | −0.285487 | ||||||||
\(478\) | −46.5726 | −2.13018 | ||||||||
\(479\) | 3.16129 | 0.144443 | 0.0722216 | − | 0.997389i | \(-0.476991\pi\) | ||||
0.0722216 | + | 0.997389i | \(0.476991\pi\) | |||||||
\(480\) | −9.53795 | −0.435346 | ||||||||
\(481\) | −9.42881 | −0.429917 | ||||||||
\(482\) | −11.8654 | −0.540453 | ||||||||
\(483\) | 0.119244 | 0.00542578 | ||||||||
\(484\) | 2.00475 | 0.0911248 | ||||||||
\(485\) | 26.5900 | 1.20739 | ||||||||
\(486\) | 24.4476 | 1.10896 | ||||||||
\(487\) | −14.6023 | −0.661694 | −0.330847 | − | 0.943684i | \(-0.607334\pi\) | ||||
−0.330847 | + | 0.943684i | \(0.607334\pi\) | |||||||
\(488\) | 0.0691596 | 0.00313071 | ||||||||
\(489\) | 0.796546 | 0.0360210 | ||||||||
\(490\) | −39.7076 | −1.79381 | ||||||||
\(491\) | −23.5476 | −1.06269 | −0.531344 | − | 0.847156i | \(-0.678313\pi\) | ||||
−0.531344 | + | 0.847156i | \(0.678313\pi\) | |||||||
\(492\) | −7.65571 | −0.345146 | ||||||||
\(493\) | −9.76766 | −0.439913 | ||||||||
\(494\) | 31.1262 | 1.40043 | ||||||||
\(495\) | −6.39820 | −0.287578 | ||||||||
\(496\) | 0.604305 | 0.0271341 | ||||||||
\(497\) | 35.4289 | 1.58920 | ||||||||
\(498\) | −6.07167 | −0.272078 | ||||||||
\(499\) | −39.9410 | −1.78800 | −0.894002 | − | 0.448063i | \(-0.852114\pi\) | ||||
−0.894002 | + | 0.448063i | \(0.852114\pi\) | |||||||
\(500\) | −21.2837 | −0.951834 | ||||||||
\(501\) | −4.09630 | −0.183009 | ||||||||
\(502\) | −11.5100 | −0.513717 | ||||||||
\(503\) | 19.9446 | 0.889287 | 0.444644 | − | 0.895708i | \(-0.353330\pi\) | ||||
0.444644 | + | 0.895708i | \(0.353330\pi\) | |||||||
\(504\) | −0.102410 | −0.00456172 | ||||||||
\(505\) | −9.91805 | −0.441347 | ||||||||
\(506\) | −0.118811 | −0.00528179 | ||||||||
\(507\) | −7.34537 | −0.326220 | ||||||||
\(508\) | 18.4911 | 0.820411 | ||||||||
\(509\) | −24.6342 | −1.09189 | −0.545946 | − | 0.837820i | \(-0.683830\pi\) | ||||
−0.545946 | + | 0.837820i | \(0.683830\pi\) | |||||||
\(510\) | 2.38450 | 0.105587 | ||||||||
\(511\) | 61.5494 | 2.72278 | ||||||||
\(512\) | −32.0184 | −1.41503 | ||||||||
\(513\) | −8.70222 | −0.384212 | ||||||||
\(514\) | −6.80919 | −0.300340 | ||||||||
\(515\) | 7.50350 | 0.330644 | ||||||||
\(516\) | −1.02285 | −0.0450284 | ||||||||
\(517\) | −1.63126 | −0.0717425 | ||||||||
\(518\) | −14.1909 | −0.623511 | ||||||||
\(519\) | 11.7400 | 0.515327 | ||||||||
\(520\) | −0.116074 | −0.00509020 | ||||||||
\(521\) | 14.4156 | 0.631560 | 0.315780 | − | 0.948832i | \(-0.397734\pi\) | ||||
0.315780 | + | 0.948832i | \(0.397734\pi\) | |||||||
\(522\) | −53.5523 | −2.34392 | ||||||||
\(523\) | −37.9966 | −1.66148 | −0.830739 | − | 0.556663i | \(-0.812082\pi\) | ||||
−0.830739 | + | 0.556663i | \(0.812082\pi\) | |||||||
\(524\) | 13.7062 | 0.598758 | ||||||||
\(525\) | 0.911843 | 0.0397961 | ||||||||
\(526\) | −26.0028 | −1.13378 | ||||||||
\(527\) | −0.151436 | −0.00659667 | ||||||||
\(528\) | 2.03600 | 0.0886057 | ||||||||
\(529\) | −22.9965 | −0.999847 | ||||||||
\(530\) | −10.6363 | −0.462011 | ||||||||
\(531\) | −11.2271 | −0.487213 | ||||||||
\(532\) | 23.4511 | 1.01673 | ||||||||
\(533\) | 39.1762 | 1.69691 | ||||||||
\(534\) | −9.25585 | −0.400540 | ||||||||
\(535\) | 36.4380 | 1.57535 | ||||||||
\(536\) | −0.121755 | −0.00525899 | ||||||||
\(537\) | 7.20977 | 0.311125 | ||||||||
\(538\) | 57.6625 | 2.48601 | ||||||||
\(539\) | 8.49628 | 0.365961 | ||||||||
\(540\) | 13.7106 | 0.590011 | ||||||||
\(541\) | −2.41675 | −0.103904 | −0.0519521 | − | 0.998650i | \(-0.516544\pi\) | ||||
−0.0519521 | + | 0.998650i | \(0.516544\pi\) | |||||||
\(542\) | −42.0813 | −1.80755 | ||||||||
\(543\) | −7.26414 | −0.311734 | ||||||||
\(544\) | 8.00470 | 0.343199 | ||||||||
\(545\) | −17.3932 | −0.745044 | ||||||||
\(546\) | −21.0379 | −0.900339 | ||||||||
\(547\) | 4.93835 | 0.211148 | 0.105574 | − | 0.994411i | \(-0.466332\pi\) | ||||
0.105574 | + | 0.994411i | \(0.466332\pi\) | |||||||
\(548\) | 33.2282 | 1.41944 | ||||||||
\(549\) | 19.9537 | 0.851601 | ||||||||
\(550\) | −0.908534 | −0.0387400 | ||||||||
\(551\) | 29.0255 | 1.23653 | ||||||||
\(552\) | 0.000287642 0 | 1.22428e−5 0 | ||||||||
\(553\) | −54.6368 | −2.32339 | ||||||||
\(554\) | 31.1358 | 1.32283 | ||||||||
\(555\) | 2.14644 | 0.0911112 | ||||||||
\(556\) | −29.7074 | −1.25987 | ||||||||
\(557\) | 38.2611 | 1.62117 | 0.810587 | − | 0.585619i | \(-0.199148\pi\) | ||||
0.810587 | + | 0.585619i | \(0.199148\pi\) | |||||||
\(558\) | −0.830267 | −0.0351480 | ||||||||
\(559\) | 5.23418 | 0.221382 | ||||||||
\(560\) | 36.6857 | 1.55026 | ||||||||
\(561\) | −0.510214 | −0.0215413 | ||||||||
\(562\) | 8.51768 | 0.359297 | ||||||||
\(563\) | −3.87484 | −0.163305 | −0.0816526 | − | 0.996661i | \(-0.526020\pi\) | ||||
−0.0816526 | + | 0.996661i | \(0.526020\pi\) | |||||||
\(564\) | 1.66853 | 0.0702577 | ||||||||
\(565\) | −32.0190 | −1.34705 | ||||||||
\(566\) | 54.9846 | 2.31117 | ||||||||
\(567\) | −26.4728 | −1.11175 | ||||||||
\(568\) | 0.0854622 | 0.00358592 | ||||||||
\(569\) | −20.1346 | −0.844087 | −0.422043 | − | 0.906576i | \(-0.638687\pi\) | ||||
−0.422043 | + | 0.906576i | \(0.638687\pi\) | |||||||
\(570\) | −7.08577 | −0.296790 | ||||||||
\(571\) | 40.9352 | 1.71308 | 0.856542 | − | 0.516077i | \(-0.172608\pi\) | ||||
0.856542 | + | 0.516077i | \(0.172608\pi\) | |||||||
\(572\) | 10.4932 | 0.438743 | ||||||||
\(573\) | −3.53679 | −0.147752 | ||||||||
\(574\) | 58.9623 | 2.46104 | ||||||||
\(575\) | 0.0269540 | 0.00112406 | ||||||||
\(576\) | 22.0213 | 0.917555 | ||||||||
\(577\) | 30.3027 | 1.26152 | 0.630759 | − | 0.775979i | \(-0.282744\pi\) | ||||
0.630759 | + | 0.775979i | \(0.282744\pi\) | |||||||
\(578\) | −2.00119 | −0.0832384 | ||||||||
\(579\) | 0.340308 | 0.0141427 | ||||||||
\(580\) | −45.7306 | −1.89886 | ||||||||
\(581\) | 23.4089 | 0.971166 | ||||||||
\(582\) | 11.6252 | 0.481881 | ||||||||
\(583\) | 2.27586 | 0.0942564 | ||||||||
\(584\) | 0.148471 | 0.00614375 | ||||||||
\(585\) | −33.4893 | −1.38461 | ||||||||
\(586\) | 44.6663 | 1.84515 | ||||||||
\(587\) | 10.5504 | 0.435461 | 0.217731 | − | 0.976009i | \(-0.430135\pi\) | ||||
0.217731 | + | 0.976009i | \(0.430135\pi\) | |||||||
\(588\) | −8.69042 | −0.358387 | ||||||||
\(589\) | 0.450008 | 0.0185422 | ||||||||
\(590\) | −19.1519 | −0.788470 | ||||||||
\(591\) | −3.86018 | −0.158786 | ||||||||
\(592\) | 7.18843 | 0.295443 | ||||||||
\(593\) | 5.41032 | 0.222175 | 0.111088 | − | 0.993811i | \(-0.464567\pi\) | ||||
0.111088 | + | 0.993811i | \(0.464567\pi\) | |||||||
\(594\) | −5.86041 | −0.240455 | ||||||||
\(595\) | −9.19330 | −0.376888 | ||||||||
\(596\) | −5.74169 | −0.235189 | ||||||||
\(597\) | −9.56724 | −0.391561 | ||||||||
\(598\) | −0.621878 | −0.0254305 | ||||||||
\(599\) | 40.3259 | 1.64767 | 0.823835 | − | 0.566829i | \(-0.191830\pi\) | ||||
0.823835 | + | 0.566829i | \(0.191830\pi\) | |||||||
\(600\) | 0.00219956 | 8.97968e−5 0 | ||||||||
\(601\) | 12.5929 | 0.513675 | 0.256837 | − | 0.966455i | \(-0.417320\pi\) | ||||
0.256837 | + | 0.966455i | \(0.417320\pi\) | |||||||
\(602\) | 7.87773 | 0.321072 | ||||||||
\(603\) | −35.1281 | −1.43053 | ||||||||
\(604\) | −1.64094 | −0.0667689 | ||||||||
\(605\) | 2.33538 | 0.0949467 | ||||||||
\(606\) | −4.33620 | −0.176146 | ||||||||
\(607\) | −33.9938 | −1.37976 | −0.689882 | − | 0.723922i | \(-0.742338\pi\) | ||||
−0.689882 | + | 0.723922i | \(0.742338\pi\) | |||||||
\(608\) | −23.7867 | −0.964679 | ||||||||
\(609\) | −19.6181 | −0.794965 | ||||||||
\(610\) | 34.0383 | 1.37817 | ||||||||
\(611\) | −8.53828 | −0.345422 | ||||||||
\(612\) | −5.49236 | −0.222016 | ||||||||
\(613\) | −3.43514 | −0.138744 | −0.0693720 | − | 0.997591i | \(-0.522100\pi\) | ||||
−0.0693720 | + | 0.997591i | \(0.522100\pi\) | |||||||
\(614\) | 40.8105 | 1.64698 | ||||||||
\(615\) | −8.91833 | −0.359622 | ||||||||
\(616\) | 0.0373804 | 0.00150610 | ||||||||
\(617\) | −6.32568 | −0.254662 | −0.127331 | − | 0.991860i | \(-0.540641\pi\) | ||||
−0.127331 | + | 0.991860i | \(0.540641\pi\) | |||||||
\(618\) | 3.28055 | 0.131963 | ||||||||
\(619\) | 13.9742 | 0.561673 | 0.280836 | − | 0.959756i | \(-0.409388\pi\) | ||||
0.280836 | + | 0.959756i | \(0.409388\pi\) | |||||||
\(620\) | −0.709001 | −0.0284742 | ||||||||
\(621\) | 0.173864 | 0.00697692 | ||||||||
\(622\) | −23.1072 | −0.926515 | ||||||||
\(623\) | 35.6854 | 1.42970 | ||||||||
\(624\) | 10.6568 | 0.426614 | ||||||||
\(625\) | −27.0639 | −1.08255 | ||||||||
\(626\) | −9.94460 | −0.397466 | ||||||||
\(627\) | 1.51615 | 0.0605492 | ||||||||
\(628\) | 8.37773 | 0.334308 | ||||||||
\(629\) | −1.80139 | −0.0718262 | ||||||||
\(630\) | −50.4033 | −2.00811 | ||||||||
\(631\) | −6.84549 | −0.272514 | −0.136257 | − | 0.990673i | \(-0.543507\pi\) | ||||
−0.136257 | + | 0.990673i | \(0.543507\pi\) | |||||||
\(632\) | −0.131796 | −0.00524256 | ||||||||
\(633\) | −4.85429 | −0.192941 | ||||||||
\(634\) | 33.1264 | 1.31562 | ||||||||
\(635\) | 21.5408 | 0.854820 | ||||||||
\(636\) | −2.32786 | −0.0923057 | ||||||||
\(637\) | 44.4711 | 1.76201 | ||||||||
\(638\) | 19.5469 | 0.773869 | ||||||||
\(639\) | 24.6572 | 0.975425 | ||||||||
\(640\) | 0.177409 | 0.00701272 | ||||||||
\(641\) | 22.7772 | 0.899646 | 0.449823 | − | 0.893118i | \(-0.351487\pi\) | ||||
0.449823 | + | 0.893118i | \(0.351487\pi\) | |||||||
\(642\) | 15.9308 | 0.628739 | ||||||||
\(643\) | 25.5687 | 1.00833 | 0.504166 | − | 0.863607i | \(-0.331800\pi\) | ||||
0.504166 | + | 0.863607i | \(0.331800\pi\) | |||||||
\(644\) | −0.468535 | −0.0184629 | ||||||||
\(645\) | −1.19154 | −0.0469170 | ||||||||
\(646\) | 5.94671 | 0.233970 | ||||||||
\(647\) | 24.0035 | 0.943673 | 0.471837 | − | 0.881686i | \(-0.343591\pi\) | ||||
0.471837 | + | 0.881686i | \(0.343591\pi\) | |||||||
\(648\) | −0.0638581 | −0.00250858 | ||||||||
\(649\) | 4.09795 | 0.160858 | ||||||||
\(650\) | −4.75543 | −0.186523 | ||||||||
\(651\) | −0.304156 | −0.0119208 | ||||||||
\(652\) | −3.12980 | −0.122573 | ||||||||
\(653\) | −39.5512 | −1.54776 | −0.773878 | − | 0.633334i | \(-0.781686\pi\) | ||||
−0.773878 | + | 0.633334i | \(0.781686\pi\) | |||||||
\(654\) | −7.60436 | −0.297354 | ||||||||
\(655\) | 15.9667 | 0.623871 | ||||||||
\(656\) | −29.8675 | −1.16613 | ||||||||
\(657\) | 42.8361 | 1.67120 | ||||||||
\(658\) | −12.8506 | −0.500968 | ||||||||
\(659\) | 12.4586 | 0.485316 | 0.242658 | − | 0.970112i | \(-0.421981\pi\) | ||||
0.242658 | + | 0.970112i | \(0.421981\pi\) | |||||||
\(660\) | −2.38874 | −0.0929816 | ||||||||
\(661\) | −6.31587 | −0.245659 | −0.122829 | − | 0.992428i | \(-0.539197\pi\) | ||||
−0.122829 | + | 0.992428i | \(0.539197\pi\) | |||||||
\(662\) | −16.4625 | −0.639833 | ||||||||
\(663\) | −2.67055 | −0.103716 | ||||||||
\(664\) | 0.0564674 | 0.00219136 | ||||||||
\(665\) | 27.3188 | 1.05938 | ||||||||
\(666\) | −9.87633 | −0.382700 | ||||||||
\(667\) | −0.579909 | −0.0224542 | ||||||||
\(668\) | 16.0953 | 0.622745 | ||||||||
\(669\) | −4.69887 | −0.181669 | ||||||||
\(670\) | −59.9239 | −2.31506 | ||||||||
\(671\) | −7.28320 | −0.281165 | ||||||||
\(672\) | 16.0772 | 0.620193 | ||||||||
\(673\) | 21.1714 | 0.816096 | 0.408048 | − | 0.912960i | \(-0.366210\pi\) | ||||
0.408048 | + | 0.912960i | \(0.366210\pi\) | |||||||
\(674\) | 11.2291 | 0.432530 | ||||||||
\(675\) | 1.32952 | 0.0511732 | ||||||||
\(676\) | 28.8616 | 1.11006 | ||||||||
\(677\) | 31.2475 | 1.20094 | 0.600469 | − | 0.799648i | \(-0.294980\pi\) | ||||
0.600469 | + | 0.799648i | \(0.294980\pi\) | |||||||
\(678\) | −13.9988 | −0.537619 | ||||||||
\(679\) | −44.8203 | −1.72005 | ||||||||
\(680\) | −0.0221762 | −0.000850420 0 | ||||||||
\(681\) | −0.290561 | −0.0111343 | ||||||||
\(682\) | 0.303052 | 0.0116045 | ||||||||
\(683\) | 39.9494 | 1.52862 | 0.764311 | − | 0.644848i | \(-0.223079\pi\) | ||||
0.764311 | + | 0.644848i | \(0.223079\pi\) | |||||||
\(684\) | 16.3211 | 0.624052 | ||||||||
\(685\) | 38.7084 | 1.47897 | ||||||||
\(686\) | 11.7873 | 0.450042 | ||||||||
\(687\) | −3.21183 | −0.122539 | ||||||||
\(688\) | −3.99049 | −0.152136 | ||||||||
\(689\) | 11.9123 | 0.453821 | ||||||||
\(690\) | 0.141568 | 0.00538942 | ||||||||
\(691\) | 5.13326 | 0.195278 | 0.0976392 | − | 0.995222i | \(-0.468871\pi\) | ||||
0.0976392 | + | 0.995222i | \(0.468871\pi\) | |||||||
\(692\) | −46.1289 | −1.75356 | ||||||||
\(693\) | 10.7848 | 0.409682 | ||||||||
\(694\) | −58.7187 | −2.22893 | ||||||||
\(695\) | −34.6069 | −1.31271 | ||||||||
\(696\) | −0.0473231 | −0.00179378 | ||||||||
\(697\) | 7.48468 | 0.283503 | ||||||||
\(698\) | 36.8627 | 1.39527 | ||||||||
\(699\) | 7.65661 | 0.289600 | ||||||||
\(700\) | −3.58283 | −0.135418 | ||||||||
\(701\) | 48.2753 | 1.82333 | 0.911666 | − | 0.410933i | \(-0.134797\pi\) | ||||
0.911666 | + | 0.410933i | \(0.134797\pi\) | |||||||
\(702\) | −30.6744 | −1.15773 | ||||||||
\(703\) | 5.35301 | 0.201892 | ||||||||
\(704\) | −8.03792 | −0.302940 | ||||||||
\(705\) | 1.94371 | 0.0732044 | ||||||||
\(706\) | −49.4779 | −1.86212 | ||||||||
\(707\) | 16.7179 | 0.628743 | ||||||||
\(708\) | −4.19158 | −0.157529 | ||||||||
\(709\) | −1.05698 | −0.0396958 | −0.0198479 | − | 0.999803i | \(-0.506318\pi\) | ||||
−0.0198479 | + | 0.999803i | \(0.506318\pi\) | |||||||
\(710\) | 42.0619 | 1.57856 | ||||||||
\(711\) | −38.0252 | −1.42606 | ||||||||
\(712\) | 0.0860809 | 0.00322602 | ||||||||
\(713\) | −0.00899082 | −0.000336709 0 | ||||||||
\(714\) | −4.01933 | −0.150420 | ||||||||
\(715\) | 12.2238 | 0.457144 | ||||||||
\(716\) | −28.3288 | −1.05870 | ||||||||
\(717\) | −11.8740 | −0.443441 | ||||||||
\(718\) | −16.7450 | −0.624917 | ||||||||
\(719\) | 20.2170 | 0.753966 | 0.376983 | − | 0.926220i | \(-0.376961\pi\) | ||||
0.376983 | + | 0.926220i | \(0.376961\pi\) | |||||||
\(720\) | 25.5319 | 0.951518 | ||||||||
\(721\) | −12.6480 | −0.471034 | ||||||||
\(722\) | 20.3513 | 0.757397 | ||||||||
\(723\) | −3.02515 | −0.112506 | ||||||||
\(724\) | 28.5424 | 1.06077 | ||||||||
\(725\) | −4.43449 | −0.164693 | ||||||||
\(726\) | 1.02103 | 0.0378941 | ||||||||
\(727\) | 49.4689 | 1.83470 | 0.917350 | − | 0.398081i | \(-0.130324\pi\) | ||||
0.917350 | + | 0.398081i | \(0.130324\pi\) | |||||||
\(728\) | 0.195656 | 0.00725149 | ||||||||
\(729\) | −13.9416 | −0.516357 | ||||||||
\(730\) | 73.0727 | 2.70454 | ||||||||
\(731\) | 1.00000 | 0.0369863 | ||||||||
\(732\) | 7.44962 | 0.275346 | ||||||||
\(733\) | 21.0044 | 0.775815 | 0.387908 | − | 0.921698i | \(-0.373198\pi\) | ||||
0.387908 | + | 0.921698i | \(0.373198\pi\) | |||||||
\(734\) | −2.03240 | −0.0750171 | ||||||||
\(735\) | −10.1237 | −0.373418 | ||||||||
\(736\) | 0.475241 | 0.0175176 | ||||||||
\(737\) | 12.8220 | 0.472303 | ||||||||
\(738\) | 41.0356 | 1.51054 | ||||||||
\(739\) | 41.0547 | 1.51022 | 0.755110 | − | 0.655598i | \(-0.227583\pi\) | ||||
0.755110 | + | 0.655598i | \(0.227583\pi\) | |||||||
\(740\) | −8.43383 | −0.310034 | ||||||||
\(741\) | 7.93580 | 0.291529 | ||||||||
\(742\) | 17.9286 | 0.658180 | ||||||||
\(743\) | 37.7544 | 1.38507 | 0.692537 | − | 0.721382i | \(-0.256493\pi\) | ||||
0.692537 | + | 0.721382i | \(0.256493\pi\) | |||||||
\(744\) | −0.000733691 0 | −2.68984e−5 0 | ||||||||
\(745\) | −6.68865 | −0.245053 | ||||||||
\(746\) | −39.1024 | −1.43164 | ||||||||
\(747\) | 16.2918 | 0.596084 | ||||||||
\(748\) | 2.00475 | 0.0733007 | ||||||||
\(749\) | −61.4202 | −2.24425 | ||||||||
\(750\) | −10.8399 | −0.395819 | ||||||||
\(751\) | 51.1162 | 1.86526 | 0.932629 | − | 0.360837i | \(-0.117509\pi\) | ||||
0.932629 | + | 0.360837i | \(0.117509\pi\) | |||||||
\(752\) | 6.50950 | 0.237377 | ||||||||
\(753\) | −2.93455 | −0.106941 | ||||||||
\(754\) | 102.312 | 3.72598 | ||||||||
\(755\) | −1.91157 | −0.0695693 | ||||||||
\(756\) | −23.1107 | −0.840528 | ||||||||
\(757\) | 18.0813 | 0.657176 | 0.328588 | − | 0.944473i | \(-0.393427\pi\) | ||||
0.328588 | + | 0.944473i | \(0.393427\pi\) | |||||||
\(758\) | 19.9968 | 0.726316 | ||||||||
\(759\) | −0.0302916 | −0.00109951 | ||||||||
\(760\) | 0.0658988 | 0.00239040 | ||||||||
\(761\) | 12.5547 | 0.455109 | 0.227554 | − | 0.973765i | \(-0.426927\pi\) | ||||
0.227554 | + | 0.973765i | \(0.426927\pi\) | |||||||
\(762\) | 9.41769 | 0.341167 | ||||||||
\(763\) | 29.3181 | 1.06139 | ||||||||
\(764\) | 13.8968 | 0.502770 | ||||||||
\(765\) | −6.39820 | −0.231327 | ||||||||
\(766\) | 14.0083 | 0.506139 | ||||||||
\(767\) | 21.4494 | 0.774492 | ||||||||
\(768\) | −8.12455 | −0.293170 | ||||||||
\(769\) | −21.6407 | −0.780385 | −0.390193 | − | 0.920733i | \(-0.627592\pi\) | ||||
−0.390193 | + | 0.920733i | \(0.627592\pi\) | |||||||
\(770\) | 18.3975 | 0.663000 | ||||||||
\(771\) | −1.73604 | −0.0625220 | ||||||||
\(772\) | −1.33715 | −0.0481249 | ||||||||
\(773\) | −4.75588 | −0.171057 | −0.0855285 | − | 0.996336i | \(-0.527258\pi\) | ||||
−0.0855285 | + | 0.996336i | \(0.527258\pi\) | |||||||
\(774\) | 5.48261 | 0.197068 | ||||||||
\(775\) | −0.0687518 | −0.00246964 | ||||||||
\(776\) | −0.108116 | −0.00388115 | ||||||||
\(777\) | −3.61805 | −0.129797 | ||||||||
\(778\) | −45.6732 | −1.63746 | ||||||||
\(779\) | −22.2415 | −0.796883 | ||||||||
\(780\) | −12.5031 | −0.447683 | ||||||||
\(781\) | −9.00003 | −0.322046 | ||||||||
\(782\) | −0.118811 | −0.00424867 | ||||||||
\(783\) | −28.6043 | −1.02223 | ||||||||
\(784\) | −33.9043 | −1.21087 | ||||||||
\(785\) | 9.75944 | 0.348329 | ||||||||
\(786\) | 6.98068 | 0.248993 | ||||||||
\(787\) | −39.0420 | −1.39170 | −0.695849 | − | 0.718189i | \(-0.744972\pi\) | ||||
−0.695849 | + | 0.718189i | \(0.744972\pi\) | |||||||
\(788\) | 15.1675 | 0.540320 | ||||||||
\(789\) | −6.62958 | −0.236019 | ||||||||
\(790\) | −64.8659 | −2.30782 | ||||||||
\(791\) | 53.9714 | 1.91900 | ||||||||
\(792\) | 0.0260154 | 0.000924417 0 | ||||||||
\(793\) | −38.1216 | −1.35374 | ||||||||
\(794\) | −15.4534 | −0.548421 | ||||||||
\(795\) | −2.71178 | −0.0961771 | ||||||||
\(796\) | 37.5918 | 1.33241 | ||||||||
\(797\) | 39.6294 | 1.40375 | 0.701873 | − | 0.712302i | \(-0.252347\pi\) | ||||
0.701873 | + | 0.712302i | \(0.252347\pi\) | |||||||
\(798\) | 11.9438 | 0.422807 | ||||||||
\(799\) | −1.63126 | −0.0577097 | ||||||||
\(800\) | 3.63412 | 0.128485 | ||||||||
\(801\) | 24.8357 | 0.877526 | ||||||||
\(802\) | −77.3913 | −2.73278 | ||||||||
\(803\) | −15.6354 | −0.551763 | ||||||||
\(804\) | −13.1149 | −0.462529 | ||||||||
\(805\) | −0.545809 | −0.0192372 | ||||||||
\(806\) | 1.58623 | 0.0558726 | ||||||||
\(807\) | 14.7014 | 0.517514 | ||||||||
\(808\) | 0.0403273 | 0.00141871 | ||||||||
\(809\) | 49.7006 | 1.74738 | 0.873689 | − | 0.486484i | \(-0.161721\pi\) | ||||
0.873689 | + | 0.486484i | \(0.161721\pi\) | |||||||
\(810\) | −31.4290 | −1.10430 | ||||||||
\(811\) | −30.6224 | −1.07530 | −0.537648 | − | 0.843169i | \(-0.680687\pi\) | ||||
−0.537648 | + | 0.843169i | \(0.680687\pi\) | |||||||
\(812\) | 77.0838 | 2.70511 | ||||||||
\(813\) | −10.7289 | −0.376278 | ||||||||
\(814\) | 3.60492 | 0.126352 | ||||||||
\(815\) | −3.64599 | −0.127713 | ||||||||
\(816\) | 2.03600 | 0.0712744 | ||||||||
\(817\) | −2.97160 | −0.103963 | ||||||||
\(818\) | 1.17488 | 0.0410789 | ||||||||
\(819\) | 56.4498 | 1.97252 | ||||||||
\(820\) | 35.0421 | 1.22372 | ||||||||
\(821\) | 32.6707 | 1.14021 | 0.570107 | − | 0.821570i | \(-0.306902\pi\) | ||||
0.570107 | + | 0.821570i | \(0.306902\pi\) | |||||||
\(822\) | 16.9234 | 0.590272 | ||||||||
\(823\) | 50.9251 | 1.77514 | 0.887568 | − | 0.460676i | \(-0.152393\pi\) | ||||
0.887568 | + | 0.460676i | \(0.152393\pi\) | |||||||
\(824\) | −0.0305096 | −0.00106285 | ||||||||
\(825\) | −0.231636 | −0.00806453 | ||||||||
\(826\) | 32.2825 | 1.12325 | ||||||||
\(827\) | 43.7759 | 1.52224 | 0.761119 | − | 0.648612i | \(-0.224650\pi\) | ||||
0.761119 | + | 0.648612i | \(0.224650\pi\) | |||||||
\(828\) | −0.326083 | −0.0113322 | ||||||||
\(829\) | 42.0428 | 1.46021 | 0.730104 | − | 0.683337i | \(-0.239472\pi\) | ||||
0.730104 | + | 0.683337i | \(0.239472\pi\) | |||||||
\(830\) | 27.7916 | 0.964659 | ||||||||
\(831\) | 7.93826 | 0.275375 | ||||||||
\(832\) | −42.0719 | −1.45858 | ||||||||
\(833\) | 8.49628 | 0.294379 | ||||||||
\(834\) | −15.1302 | −0.523917 | ||||||||
\(835\) | 18.7498 | 0.648864 | ||||||||
\(836\) | −5.95729 | −0.206037 | ||||||||
\(837\) | −0.443476 | −0.0153288 | ||||||||
\(838\) | −7.22502 | −0.249584 | ||||||||
\(839\) | −1.03105 | −0.0355957 | −0.0177979 | − | 0.999842i | \(-0.505666\pi\) | ||||
−0.0177979 | + | 0.999842i | \(0.505666\pi\) | |||||||
\(840\) | −0.0445404 | −0.00153679 | ||||||||
\(841\) | 66.4071 | 2.28990 | ||||||||
\(842\) | −74.0202 | −2.55090 | ||||||||
\(843\) | 2.17163 | 0.0747951 | ||||||||
\(844\) | 19.0736 | 0.656540 | ||||||||
\(845\) | 33.6216 | 1.15662 | ||||||||
\(846\) | −8.94354 | −0.307485 | ||||||||
\(847\) | −3.93653 | −0.135261 | ||||||||
\(848\) | −9.08178 | −0.311870 | ||||||||
\(849\) | 14.0186 | 0.481119 | ||||||||
\(850\) | −0.908534 | −0.0311625 | ||||||||
\(851\) | −0.106949 | −0.00366617 | ||||||||
\(852\) | 9.20568 | 0.315381 | ||||||||
\(853\) | −14.1009 | −0.482806 | −0.241403 | − | 0.970425i | \(-0.577608\pi\) | ||||
−0.241403 | + | 0.970425i | \(0.577608\pi\) | |||||||
\(854\) | −57.3751 | −1.96334 | ||||||||
\(855\) | 19.0128 | 0.650226 | ||||||||
\(856\) | −0.148159 | −0.00506397 | ||||||||
\(857\) | −46.9479 | −1.60371 | −0.801855 | − | 0.597518i | \(-0.796154\pi\) | ||||
−0.801855 | + | 0.597518i | \(0.796154\pi\) | |||||||
\(858\) | 5.34427 | 0.182451 | ||||||||
\(859\) | −27.4488 | −0.936541 | −0.468271 | − | 0.883585i | \(-0.655123\pi\) | ||||
−0.468271 | + | 0.883585i | \(0.655123\pi\) | |||||||
\(860\) | 4.68184 | 0.159649 | ||||||||
\(861\) | 15.0328 | 0.512316 | ||||||||
\(862\) | −6.60113 | −0.224835 | ||||||||
\(863\) | 20.6359 | 0.702456 | 0.351228 | − | 0.936290i | \(-0.385764\pi\) | ||||
0.351228 | + | 0.936290i | \(0.385764\pi\) | |||||||
\(864\) | 23.4415 | 0.797496 | ||||||||
\(865\) | −53.7367 | −1.82710 | ||||||||
\(866\) | −26.8868 | −0.913651 | ||||||||
\(867\) | −0.510214 | −0.0173278 | ||||||||
\(868\) | 1.19510 | 0.0405642 | ||||||||
\(869\) | 13.8794 | 0.470827 | ||||||||
\(870\) | −23.2910 | −0.789638 | ||||||||
\(871\) | 67.1125 | 2.27402 | ||||||||
\(872\) | 0.0707217 | 0.00239494 | ||||||||
\(873\) | −31.1933 | −1.05573 | ||||||||
\(874\) | 0.353058 | 0.0119424 | ||||||||
\(875\) | 41.7927 | 1.41285 | ||||||||
\(876\) | 15.9927 | 0.540343 | ||||||||
\(877\) | −16.5448 | −0.558679 | −0.279340 | − | 0.960192i | \(-0.590116\pi\) | ||||
−0.279340 | + | 0.960192i | \(0.590116\pi\) | |||||||
\(878\) | −0.883491 | −0.0298164 | ||||||||
\(879\) | 11.3879 | 0.384106 | ||||||||
\(880\) | −9.31930 | −0.314154 | ||||||||
\(881\) | −8.49121 | −0.286076 | −0.143038 | − | 0.989717i | \(-0.545687\pi\) | ||||
−0.143038 | + | 0.989717i | \(0.545687\pi\) | |||||||
\(882\) | 46.5818 | 1.56849 | ||||||||
\(883\) | 34.8691 | 1.17344 | 0.586719 | − | 0.809790i | \(-0.300419\pi\) | ||||
0.586719 | + | 0.809790i | \(0.300419\pi\) | |||||||
\(884\) | 10.4932 | 0.352924 | ||||||||
\(885\) | −4.88288 | −0.164136 | ||||||||
\(886\) | 2.68997 | 0.0903713 | ||||||||
\(887\) | −31.7678 | −1.06666 | −0.533330 | − | 0.845907i | \(-0.679060\pi\) | ||||
−0.533330 | + | 0.845907i | \(0.679060\pi\) | |||||||
\(888\) | −0.00872752 | −0.000292876 0 | ||||||||
\(889\) | −36.3093 | −1.21778 | ||||||||
\(890\) | 42.3664 | 1.42012 | ||||||||
\(891\) | 6.72490 | 0.225293 | ||||||||
\(892\) | 18.4629 | 0.618183 | ||||||||
\(893\) | 4.84743 | 0.162213 | ||||||||
\(894\) | −2.92429 | −0.0978030 | ||||||||
\(895\) | −33.0010 | −1.10310 | ||||||||
\(896\) | −0.299042 | −0.00999031 | ||||||||
\(897\) | −0.158552 | −0.00529388 | ||||||||
\(898\) | −47.9726 | −1.60087 | ||||||||
\(899\) | 1.47918 | 0.0493334 | ||||||||
\(900\) | −2.49352 | −0.0831173 | ||||||||
\(901\) | 2.27586 | 0.0758198 | ||||||||
\(902\) | −14.9782 | −0.498721 | ||||||||
\(903\) | 2.00847 | 0.0668379 | ||||||||
\(904\) | 0.130191 | 0.00433008 | ||||||||
\(905\) | 33.2498 | 1.10526 | ||||||||
\(906\) | −0.835745 | −0.0277658 | ||||||||
\(907\) | 9.02766 | 0.299759 | 0.149879 | − | 0.988704i | \(-0.452111\pi\) | ||||
0.149879 | + | 0.988704i | \(0.452111\pi\) | |||||||
\(908\) | 1.14168 | 0.0378880 | ||||||||
\(909\) | 11.6351 | 0.385911 | ||||||||
\(910\) | 96.2958 | 3.19218 | ||||||||
\(911\) | −20.2933 | −0.672346 | −0.336173 | − | 0.941800i | \(-0.609133\pi\) | ||||
−0.336173 | + | 0.941800i | \(0.609133\pi\) | |||||||
\(912\) | −6.05018 | −0.200341 | ||||||||
\(913\) | −5.94659 | −0.196803 | ||||||||
\(914\) | 30.7128 | 1.01589 | ||||||||
\(915\) | 8.67826 | 0.286894 | ||||||||
\(916\) | 12.6200 | 0.416976 | ||||||||
\(917\) | −26.9136 | −0.888765 | ||||||||
\(918\) | −5.86041 | −0.193422 | ||||||||
\(919\) | −13.2130 | −0.435858 | −0.217929 | − | 0.975965i | \(-0.569930\pi\) | ||||
−0.217929 | + | 0.975965i | \(0.569930\pi\) | |||||||
\(920\) | −0.00131661 | −4.34073e−5 0 | ||||||||
\(921\) | 10.4049 | 0.342852 | ||||||||
\(922\) | 81.0791 | 2.67020 | ||||||||
\(923\) | −47.1078 | −1.55057 | ||||||||
\(924\) | 4.02648 | 0.132461 | ||||||||
\(925\) | −0.817828 | −0.0268900 | ||||||||
\(926\) | −48.4887 | −1.59344 | ||||||||
\(927\) | −8.80251 | −0.289112 | ||||||||
\(928\) | −78.1872 | −2.56662 | ||||||||
\(929\) | 51.9918 | 1.70580 | 0.852898 | − | 0.522078i | \(-0.174843\pi\) | ||||
0.852898 | + | 0.522078i | \(0.174843\pi\) | |||||||
\(930\) | −0.361100 | −0.0118409 | ||||||||
\(931\) | −25.2475 | −0.827454 | ||||||||
\(932\) | −30.0845 | −0.985451 | ||||||||
\(933\) | −5.89132 | −0.192873 | ||||||||
\(934\) | 43.9138 | 1.43690 | ||||||||
\(935\) | 2.33538 | 0.0763751 | ||||||||
\(936\) | 0.136169 | 0.00445083 | ||||||||
\(937\) | 42.4970 | 1.38832 | 0.694158 | − | 0.719823i | \(-0.255777\pi\) | ||||
0.694158 | + | 0.719823i | \(0.255777\pi\) | |||||||
\(938\) | 101.008 | 3.29803 | ||||||||
\(939\) | −2.53543 | −0.0827408 | ||||||||
\(940\) | −7.63728 | −0.249100 | ||||||||
\(941\) | 57.6190 | 1.87833 | 0.939163 | − | 0.343471i | \(-0.111603\pi\) | ||||
0.939163 | + | 0.343471i | \(0.111603\pi\) | |||||||
\(942\) | 4.26685 | 0.139021 | ||||||||
\(943\) | 0.444368 | 0.0144706 | ||||||||
\(944\) | −16.3528 | −0.532238 | ||||||||
\(945\) | −26.9223 | −0.875781 | ||||||||
\(946\) | −2.00119 | −0.0650642 | ||||||||
\(947\) | 60.6058 | 1.96942 | 0.984712 | − | 0.174189i | \(-0.0557305\pi\) | ||||
0.984712 | + | 0.174189i | \(0.0557305\pi\) | |||||||
\(948\) | −14.1966 | −0.461083 | ||||||||
\(949\) | −81.8387 | −2.65660 | ||||||||
\(950\) | 2.69980 | 0.0875929 | ||||||||
\(951\) | 8.44577 | 0.273873 | ||||||||
\(952\) | 0.0373804 | 0.00121151 | ||||||||
\(953\) | −47.1823 | −1.52839 | −0.764193 | − | 0.644988i | \(-0.776862\pi\) | ||||
−0.764193 | + | 0.644988i | \(0.776862\pi\) | |||||||
\(954\) | 12.4776 | 0.403979 | ||||||||
\(955\) | 16.1888 | 0.523857 | ||||||||
\(956\) | 46.6555 | 1.50895 | ||||||||
\(957\) | 4.98360 | 0.161097 | ||||||||
\(958\) | −6.32634 | −0.204395 | ||||||||
\(959\) | −65.2471 | −2.10694 | ||||||||
\(960\) | 9.57753 | 0.309113 | ||||||||
\(961\) | −30.9771 | −0.999260 | ||||||||
\(962\) | 18.8688 | 0.608354 | ||||||||
\(963\) | −42.7462 | −1.37748 | ||||||||
\(964\) | 11.8865 | 0.382838 | ||||||||
\(965\) | −1.55768 | −0.0501434 | ||||||||
\(966\) | −0.238629 | −0.00767776 | ||||||||
\(967\) | −24.6420 | −0.792432 | −0.396216 | − | 0.918157i | \(-0.629677\pi\) | ||||
−0.396216 | + | 0.918157i | \(0.629677\pi\) | |||||||
\(968\) | −0.00949577 | −0.000305206 0 | ||||||||
\(969\) | 1.51615 | 0.0487058 | ||||||||
\(970\) | −53.2116 | −1.70852 | ||||||||
\(971\) | 11.2730 | 0.361768 | 0.180884 | − | 0.983504i | \(-0.442104\pi\) | ||||
0.180884 | + | 0.983504i | \(0.442104\pi\) | |||||||
\(972\) | −24.4910 | −0.785551 | ||||||||
\(973\) | 58.3336 | 1.87009 | ||||||||
\(974\) | 29.2220 | 0.936332 | ||||||||
\(975\) | −1.21243 | −0.0388287 | ||||||||
\(976\) | 29.0635 | 0.930301 | ||||||||
\(977\) | 13.8289 | 0.442425 | 0.221212 | − | 0.975226i | \(-0.428999\pi\) | ||||
0.221212 | + | 0.975226i | \(0.428999\pi\) | |||||||
\(978\) | −1.59404 | −0.0509717 | ||||||||
\(979\) | −9.06518 | −0.289724 | ||||||||
\(980\) | 39.7783 | 1.27067 | ||||||||
\(981\) | 20.4043 | 0.651460 | ||||||||
\(982\) | 47.1231 | 1.50376 | ||||||||
\(983\) | −32.5424 | −1.03794 | −0.518970 | − | 0.854792i | \(-0.673684\pi\) | ||||
−0.518970 | + | 0.854792i | \(0.673684\pi\) | |||||||
\(984\) | 0.0362624 | 0.00115600 | ||||||||
\(985\) | 17.6690 | 0.562981 | ||||||||
\(986\) | 19.5469 | 0.622500 | ||||||||
\(987\) | −3.27633 | −0.104287 | ||||||||
\(988\) | −31.1815 | −0.992017 | ||||||||
\(989\) | 0.0593703 | 0.00188787 | ||||||||
\(990\) | 12.8040 | 0.406937 | ||||||||
\(991\) | 20.3540 | 0.646565 | 0.323283 | − | 0.946302i | \(-0.395214\pi\) | ||||
0.323283 | + | 0.946302i | \(0.395214\pi\) | |||||||
\(992\) | −1.21220 | −0.0384875 | ||||||||
\(993\) | −4.19721 | −0.133194 | ||||||||
\(994\) | −70.8998 | −2.24881 | ||||||||
\(995\) | 43.7917 | 1.38829 | ||||||||
\(996\) | 6.08246 | 0.192730 | ||||||||
\(997\) | −25.2795 | −0.800610 | −0.400305 | − | 0.916382i | \(-0.631096\pi\) | ||||
−0.400305 | + | 0.916382i | \(0.631096\pi\) | |||||||
\(998\) | 79.9294 | 2.53012 | ||||||||
\(999\) | −5.27532 | −0.166904 |
(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 | 8041.2.a.j.1.14 | ✓ | 82 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8041.2.a.j.1.14 | ✓ | 82 | 1.1 | even | 1 | trivial |