Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1681,2,Mod(1,1681)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1681, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1681.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1681 = 41^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1681.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: | \(13.4228525798\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 41) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 1681.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.47960 | 1.04623 | 0.523117 | − | 0.852261i | \(-0.324769\pi\) | ||||
0.523117 | + | 0.852261i | \(0.324769\pi\) | |||||||
\(3\) | 2.68766 | 1.55172 | 0.775859 | − | 0.630906i | \(-0.217317\pi\) | ||||
0.775859 | + | 0.630906i | \(0.217317\pi\) | |||||||
\(4\) | 0.189211 | 0.0946056 | ||||||||
\(5\) | −0.774365 | −0.346307 | −0.173153 | − | 0.984895i | \(-0.555396\pi\) | ||||
−0.173153 | + | 0.984895i | \(0.555396\pi\) | |||||||
\(6\) | 3.97665 | 1.62346 | ||||||||
\(7\) | 4.67709 | 1.76777 | 0.883887 | − | 0.467700i | \(-0.154917\pi\) | ||||
0.883887 | + | 0.467700i | \(0.154917\pi\) | |||||||
\(8\) | −2.67924 | −0.947254 | ||||||||
\(9\) | 4.22349 | 1.40783 | ||||||||
\(10\) | −1.14575 | −0.362318 | ||||||||
\(11\) | 0.545050 | 0.164339 | 0.0821694 | − | 0.996618i | \(-0.473815\pi\) | ||||
0.0821694 | + | 0.996618i | \(0.473815\pi\) | |||||||
\(12\) | 0.508535 | 0.146801 | ||||||||
\(13\) | 0.907468 | 0.251686 | 0.125843 | − | 0.992050i | \(-0.459836\pi\) | ||||
0.125843 | + | 0.992050i | \(0.459836\pi\) | |||||||
\(14\) | 6.92022 | 1.84951 | ||||||||
\(15\) | −2.08123 | −0.537371 | ||||||||
\(16\) | −4.34262 | −1.08566 | ||||||||
\(17\) | 5.99197 | 1.45327 | 0.726633 | − | 0.687026i | \(-0.241084\pi\) | ||||
0.726633 | + | 0.687026i | \(0.241084\pi\) | |||||||
\(18\) | 6.24907 | 1.47292 | ||||||||
\(19\) | −4.38157 | −1.00520 | −0.502601 | − | 0.864519i | \(-0.667623\pi\) | ||||
−0.502601 | + | 0.864519i | \(0.667623\pi\) | |||||||
\(20\) | −0.146519 | −0.0327626 | ||||||||
\(21\) | 12.5704 | 2.74309 | ||||||||
\(22\) | 0.806456 | 0.171937 | ||||||||
\(23\) | 1.04686 | 0.218286 | 0.109143 | − | 0.994026i | \(-0.465189\pi\) | ||||
0.109143 | + | 0.994026i | \(0.465189\pi\) | |||||||
\(24\) | −7.20087 | −1.46987 | ||||||||
\(25\) | −4.40036 | −0.880072 | ||||||||
\(26\) | 1.34269 | 0.263323 | ||||||||
\(27\) | 3.28832 | 0.632838 | ||||||||
\(28\) | 0.884959 | 0.167241 | ||||||||
\(29\) | 1.23385 | 0.229120 | 0.114560 | − | 0.993416i | \(-0.463454\pi\) | ||||
0.114560 | + | 0.993416i | \(0.463454\pi\) | |||||||
\(30\) | −3.07938 | −0.562215 | ||||||||
\(31\) | 1.52019 | 0.273035 | 0.136517 | − | 0.990638i | \(-0.456409\pi\) | ||||
0.136517 | + | 0.990638i | \(0.456409\pi\) | |||||||
\(32\) | −1.06686 | −0.188595 | ||||||||
\(33\) | 1.46491 | 0.255008 | ||||||||
\(34\) | 8.86571 | 1.52046 | ||||||||
\(35\) | −3.62178 | −0.612192 | ||||||||
\(36\) | 0.799132 | 0.133189 | ||||||||
\(37\) | −7.25720 | −1.19308 | −0.596539 | − | 0.802584i | \(-0.703458\pi\) | ||||
−0.596539 | + | 0.802584i | \(0.703458\pi\) | |||||||
\(38\) | −6.48297 | −1.05168 | ||||||||
\(39\) | 2.43896 | 0.390546 | ||||||||
\(40\) | 2.07471 | 0.328041 | ||||||||
\(41\) | 0 | 0 | ||||||||
\(42\) | 18.5992 | 2.86991 | ||||||||
\(43\) | 6.22101 | 0.948696 | 0.474348 | − | 0.880338i | \(-0.342684\pi\) | ||||
0.474348 | + | 0.880338i | \(0.342684\pi\) | |||||||
\(44\) | 0.103130 | 0.0155474 | ||||||||
\(45\) | −3.27052 | −0.487541 | ||||||||
\(46\) | 1.54893 | 0.228378 | ||||||||
\(47\) | −3.97043 | −0.579146 | −0.289573 | − | 0.957156i | \(-0.593513\pi\) | ||||
−0.289573 | + | 0.957156i | \(0.593513\pi\) | |||||||
\(48\) | −11.6715 | −1.68463 | ||||||||
\(49\) | 14.8752 | 2.12503 | ||||||||
\(50\) | −6.51076 | −0.920761 | ||||||||
\(51\) | 16.1043 | 2.25506 | ||||||||
\(52\) | 0.171703 | 0.0238109 | ||||||||
\(53\) | −5.35331 | −0.735334 | −0.367667 | − | 0.929957i | \(-0.619843\pi\) | ||||
−0.367667 | + | 0.929957i | \(0.619843\pi\) | |||||||
\(54\) | 4.86540 | 0.662096 | ||||||||
\(55\) | −0.422068 | −0.0569117 | ||||||||
\(56\) | −12.5311 | −1.67453 | ||||||||
\(57\) | −11.7762 | −1.55979 | ||||||||
\(58\) | 1.82560 | 0.239713 | ||||||||
\(59\) | 8.87496 | 1.15542 | 0.577711 | − | 0.816242i | \(-0.303946\pi\) | ||||
0.577711 | + | 0.816242i | \(0.303946\pi\) | |||||||
\(60\) | −0.393792 | −0.0508383 | ||||||||
\(61\) | 1.38786 | 0.177698 | 0.0888489 | − | 0.996045i | \(-0.471681\pi\) | ||||
0.0888489 | + | 0.996045i | \(0.471681\pi\) | |||||||
\(62\) | 2.24927 | 0.285658 | ||||||||
\(63\) | 19.7537 | 2.48873 | ||||||||
\(64\) | 7.10673 | 0.888341 | ||||||||
\(65\) | −0.702711 | −0.0871606 | ||||||||
\(66\) | 2.16747 | 0.266798 | ||||||||
\(67\) | −5.63556 | −0.688493 | −0.344247 | − | 0.938879i | \(-0.611866\pi\) | ||||
−0.344247 | + | 0.938879i | \(0.611866\pi\) | |||||||
\(68\) | 1.13375 | 0.137487 | ||||||||
\(69\) | 2.81360 | 0.338718 | ||||||||
\(70\) | −5.35878 | −0.640496 | ||||||||
\(71\) | −1.08971 | −0.129325 | −0.0646623 | − | 0.997907i | \(-0.520597\pi\) | ||||
−0.0646623 | + | 0.997907i | \(0.520597\pi\) | |||||||
\(72\) | −11.3157 | −1.33357 | ||||||||
\(73\) | −5.61291 | −0.656941 | −0.328471 | − | 0.944514i | \(-0.606533\pi\) | ||||
−0.328471 | + | 0.944514i | \(0.606533\pi\) | |||||||
\(74\) | −10.7377 | −1.24824 | ||||||||
\(75\) | −11.8266 | −1.36562 | ||||||||
\(76\) | −0.829043 | −0.0950977 | ||||||||
\(77\) | 2.54925 | 0.290514 | ||||||||
\(78\) | 3.60868 | 0.408603 | ||||||||
\(79\) | 12.1959 | 1.37214 | 0.686072 | − | 0.727534i | \(-0.259334\pi\) | ||||
0.686072 | + | 0.727534i | \(0.259334\pi\) | |||||||
\(80\) | 3.36278 | 0.375970 | ||||||||
\(81\) | −3.83260 | −0.425844 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −13.1576 | −1.44423 | −0.722116 | − | 0.691772i | \(-0.756830\pi\) | ||||
−0.722116 | + | 0.691772i | \(0.756830\pi\) | |||||||
\(84\) | 2.37846 | 0.259512 | ||||||||
\(85\) | −4.63997 | −0.503276 | ||||||||
\(86\) | 9.20460 | 0.992558 | ||||||||
\(87\) | 3.31616 | 0.355530 | ||||||||
\(88\) | −1.46032 | −0.155671 | ||||||||
\(89\) | −1.95076 | −0.206781 | −0.103390 | − | 0.994641i | \(-0.532969\pi\) | ||||
−0.103390 | + | 0.994641i | \(0.532969\pi\) | |||||||
\(90\) | −4.83906 | −0.510082 | ||||||||
\(91\) | 4.24431 | 0.444925 | ||||||||
\(92\) | 0.198078 | 0.0206510 | ||||||||
\(93\) | 4.08575 | 0.423673 | ||||||||
\(94\) | −5.87464 | −0.605922 | ||||||||
\(95\) | 3.39294 | 0.348108 | ||||||||
\(96\) | −2.86734 | −0.292647 | ||||||||
\(97\) | 1.94271 | 0.197252 | 0.0986262 | − | 0.995125i | \(-0.468555\pi\) | ||||
0.0986262 | + | 0.995125i | \(0.468555\pi\) | |||||||
\(98\) | 22.0093 | 2.22328 | ||||||||
\(99\) | 2.30202 | 0.231361 | ||||||||
\(100\) | −0.832597 | −0.0832597 | ||||||||
\(101\) | −8.41293 | −0.837117 | −0.418559 | − | 0.908190i | \(-0.637465\pi\) | ||||
−0.418559 | + | 0.908190i | \(0.637465\pi\) | |||||||
\(102\) | 23.8280 | 2.35932 | ||||||||
\(103\) | −4.29663 | −0.423359 | −0.211680 | − | 0.977339i | \(-0.567893\pi\) | ||||
−0.211680 | + | 0.977339i | \(0.567893\pi\) | |||||||
\(104\) | −2.43132 | −0.238411 | ||||||||
\(105\) | −9.73409 | −0.949950 | ||||||||
\(106\) | −7.92076 | −0.769332 | ||||||||
\(107\) | −12.3843 | −1.19723 | −0.598617 | − | 0.801035i | \(-0.704283\pi\) | ||||
−0.598617 | + | 0.801035i | \(0.704283\pi\) | |||||||
\(108\) | 0.622188 | 0.0598700 | ||||||||
\(109\) | 1.73022 | 0.165725 | 0.0828624 | − | 0.996561i | \(-0.473594\pi\) | ||||
0.0828624 | + | 0.996561i | \(0.473594\pi\) | |||||||
\(110\) | −0.624491 | −0.0595429 | ||||||||
\(111\) | −19.5049 | −1.85132 | ||||||||
\(112\) | −20.3108 | −1.91919 | ||||||||
\(113\) | 1.16784 | 0.109861 | 0.0549305 | − | 0.998490i | \(-0.482506\pi\) | ||||
0.0549305 | + | 0.998490i | \(0.482506\pi\) | |||||||
\(114\) | −17.4240 | −1.63191 | ||||||||
\(115\) | −0.810653 | −0.0755937 | ||||||||
\(116\) | 0.233458 | 0.0216761 | ||||||||
\(117\) | 3.83268 | 0.354331 | ||||||||
\(118\) | 13.1314 | 1.20884 | ||||||||
\(119\) | 28.0250 | 2.56905 | ||||||||
\(120\) | 5.57611 | 0.509027 | ||||||||
\(121\) | −10.7029 | −0.972993 | ||||||||
\(122\) | 2.05348 | 0.185913 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.287638 | 0.0258306 | ||||||||
\(125\) | 7.27931 | 0.651081 | ||||||||
\(126\) | 29.2275 | 2.60379 | ||||||||
\(127\) | 9.99403 | 0.886827 | 0.443413 | − | 0.896317i | \(-0.353767\pi\) | ||||
0.443413 | + | 0.896317i | \(0.353767\pi\) | |||||||
\(128\) | 12.6488 | 1.11801 | ||||||||
\(129\) | 16.7199 | 1.47211 | ||||||||
\(130\) | −1.03973 | −0.0911904 | ||||||||
\(131\) | 0.814910 | 0.0711990 | 0.0355995 | − | 0.999366i | \(-0.488666\pi\) | ||||
0.0355995 | + | 0.999366i | \(0.488666\pi\) | |||||||
\(132\) | 0.277177 | 0.0241252 | ||||||||
\(133\) | −20.4930 | −1.77697 | ||||||||
\(134\) | −8.33836 | −0.720325 | ||||||||
\(135\) | −2.54636 | −0.219156 | ||||||||
\(136\) | −16.0539 | −1.37661 | ||||||||
\(137\) | 4.30393 | 0.367710 | 0.183855 | − | 0.982953i | \(-0.441142\pi\) | ||||
0.183855 | + | 0.982953i | \(0.441142\pi\) | |||||||
\(138\) | 4.16300 | 0.354378 | ||||||||
\(139\) | 5.02414 | 0.426142 | 0.213071 | − | 0.977037i | \(-0.431653\pi\) | ||||
0.213071 | + | 0.977037i | \(0.431653\pi\) | |||||||
\(140\) | −0.685281 | −0.0579168 | ||||||||
\(141\) | −10.6711 | −0.898672 | ||||||||
\(142\) | −1.61233 | −0.135304 | ||||||||
\(143\) | 0.494616 | 0.0413618 | ||||||||
\(144\) | −18.3410 | −1.52842 | ||||||||
\(145\) | −0.955451 | −0.0793459 | ||||||||
\(146\) | −8.30485 | −0.687314 | ||||||||
\(147\) | 39.9794 | 3.29745 | ||||||||
\(148\) | −1.37315 | −0.112872 | ||||||||
\(149\) | 7.92556 | 0.649287 | 0.324644 | − | 0.945836i | \(-0.394756\pi\) | ||||
0.324644 | + | 0.945836i | \(0.394756\pi\) | |||||||
\(150\) | −17.4987 | −1.42876 | ||||||||
\(151\) | −20.6732 | −1.68236 | −0.841182 | − | 0.540752i | \(-0.818140\pi\) | ||||
−0.841182 | + | 0.540752i | \(0.818140\pi\) | |||||||
\(152\) | 11.7393 | 0.952182 | ||||||||
\(153\) | 25.3070 | 2.04595 | ||||||||
\(154\) | 3.77187 | 0.303946 | ||||||||
\(155\) | −1.17718 | −0.0945537 | ||||||||
\(156\) | 0.461479 | 0.0369479 | ||||||||
\(157\) | −12.0702 | −0.963309 | −0.481654 | − | 0.876361i | \(-0.659964\pi\) | ||||
−0.481654 | + | 0.876361i | \(0.659964\pi\) | |||||||
\(158\) | 18.0450 | 1.43558 | ||||||||
\(159\) | −14.3879 | −1.14103 | ||||||||
\(160\) | 0.826136 | 0.0653118 | ||||||||
\(161\) | 4.89626 | 0.385880 | ||||||||
\(162\) | −5.67070 | −0.445533 | ||||||||
\(163\) | 2.00089 | 0.156722 | 0.0783609 | − | 0.996925i | \(-0.475031\pi\) | ||||
0.0783609 | + | 0.996925i | \(0.475031\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.13437 | −0.0883109 | ||||||||
\(166\) | −19.4679 | −1.51100 | ||||||||
\(167\) | −19.1232 | −1.47980 | −0.739899 | − | 0.672718i | \(-0.765127\pi\) | ||||
−0.739899 | + | 0.672718i | \(0.765127\pi\) | |||||||
\(168\) | −33.6792 | −2.59840 | ||||||||
\(169\) | −12.1765 | −0.936654 | ||||||||
\(170\) | −6.86530 | −0.526544 | ||||||||
\(171\) | −18.5055 | −1.41515 | ||||||||
\(172\) | 1.17709 | 0.0897520 | ||||||||
\(173\) | −6.00388 | −0.456467 | −0.228233 | − | 0.973606i | \(-0.573295\pi\) | ||||
−0.228233 | + | 0.973606i | \(0.573295\pi\) | |||||||
\(174\) | 4.90659 | 0.371968 | ||||||||
\(175\) | −20.5809 | −1.55577 | ||||||||
\(176\) | −2.36695 | −0.178415 | ||||||||
\(177\) | 23.8528 | 1.79289 | ||||||||
\(178\) | −2.88635 | −0.216341 | ||||||||
\(179\) | 9.15427 | 0.684222 | 0.342111 | − | 0.939660i | \(-0.388858\pi\) | ||||
0.342111 | + | 0.939660i | \(0.388858\pi\) | |||||||
\(180\) | −0.618820 | −0.0461241 | ||||||||
\(181\) | 19.0537 | 1.41625 | 0.708125 | − | 0.706087i | \(-0.249541\pi\) | ||||
0.708125 | + | 0.706087i | \(0.249541\pi\) | |||||||
\(182\) | 6.27987 | 0.465495 | ||||||||
\(183\) | 3.73010 | 0.275737 | ||||||||
\(184\) | −2.80479 | −0.206772 | ||||||||
\(185\) | 5.61973 | 0.413171 | ||||||||
\(186\) | 6.04527 | 0.443261 | ||||||||
\(187\) | 3.26593 | 0.238828 | ||||||||
\(188\) | −0.751250 | −0.0547905 | ||||||||
\(189\) | 15.3798 | 1.11871 | ||||||||
\(190\) | 5.02019 | 0.364203 | ||||||||
\(191\) | 11.2658 | 0.815166 | 0.407583 | − | 0.913168i | \(-0.366372\pi\) | ||||
0.407583 | + | 0.913168i | \(0.366372\pi\) | |||||||
\(192\) | 19.1004 | 1.37845 | ||||||||
\(193\) | −11.6925 | −0.841647 | −0.420823 | − | 0.907143i | \(-0.638259\pi\) | ||||
−0.420823 | + | 0.907143i | \(0.638259\pi\) | |||||||
\(194\) | 2.87443 | 0.206372 | ||||||||
\(195\) | −1.88865 | −0.135249 | ||||||||
\(196\) | 2.81456 | 0.201040 | ||||||||
\(197\) | −10.1058 | −0.720008 | −0.360004 | − | 0.932951i | \(-0.617225\pi\) | ||||
−0.360004 | + | 0.932951i | \(0.617225\pi\) | |||||||
\(198\) | 3.40606 | 0.242058 | ||||||||
\(199\) | −8.41556 | −0.596563 | −0.298281 | − | 0.954478i | \(-0.596413\pi\) | ||||
−0.298281 | + | 0.954478i | \(0.596413\pi\) | |||||||
\(200\) | 11.7896 | 0.833652 | ||||||||
\(201\) | −15.1464 | −1.06835 | ||||||||
\(202\) | −12.4478 | −0.875821 | ||||||||
\(203\) | 5.77083 | 0.405033 | ||||||||
\(204\) | 3.04712 | 0.213341 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −6.35728 | −0.442933 | ||||||||
\(207\) | 4.42141 | 0.307309 | ||||||||
\(208\) | −3.94079 | −0.273245 | ||||||||
\(209\) | −2.38818 | −0.165194 | ||||||||
\(210\) | −14.4025 | −0.993870 | ||||||||
\(211\) | −12.9839 | −0.893851 | −0.446925 | − | 0.894571i | \(-0.647481\pi\) | ||||
−0.446925 | + | 0.894571i | \(0.647481\pi\) | |||||||
\(212\) | −1.01291 | −0.0695668 | ||||||||
\(213\) | −2.92876 | −0.200675 | ||||||||
\(214\) | −18.3238 | −1.25259 | ||||||||
\(215\) | −4.81734 | −0.328540 | ||||||||
\(216\) | −8.81020 | −0.599458 | ||||||||
\(217\) | 7.11008 | 0.482664 | ||||||||
\(218\) | 2.56003 | 0.173387 | ||||||||
\(219\) | −15.0856 | −1.01939 | ||||||||
\(220\) | −0.0798601 | −0.00538416 | ||||||||
\(221\) | 5.43752 | 0.365767 | ||||||||
\(222\) | −28.8594 | −1.93691 | ||||||||
\(223\) | −17.4981 | −1.17176 | −0.585881 | − | 0.810397i | \(-0.699251\pi\) | ||||
−0.585881 | + | 0.810397i | \(0.699251\pi\) | |||||||
\(224\) | −4.98978 | −0.333394 | ||||||||
\(225\) | −18.5849 | −1.23899 | ||||||||
\(226\) | 1.72793 | 0.114940 | ||||||||
\(227\) | −27.2403 | −1.80800 | −0.904002 | − | 0.427529i | \(-0.859384\pi\) | ||||
−0.904002 | + | 0.427529i | \(0.859384\pi\) | |||||||
\(228\) | −2.22818 | −0.147565 | ||||||||
\(229\) | −22.6347 | −1.49574 | −0.747870 | − | 0.663845i | \(-0.768923\pi\) | ||||
−0.747870 | + | 0.663845i | \(0.768923\pi\) | |||||||
\(230\) | −1.19944 | −0.0790888 | ||||||||
\(231\) | 6.85151 | 0.450796 | ||||||||
\(232\) | −3.30578 | −0.217035 | ||||||||
\(233\) | 24.2104 | 1.58607 | 0.793036 | − | 0.609174i | \(-0.208499\pi\) | ||||
0.793036 | + | 0.609174i | \(0.208499\pi\) | |||||||
\(234\) | 5.67083 | 0.370714 | ||||||||
\(235\) | 3.07456 | 0.200562 | ||||||||
\(236\) | 1.67924 | 0.109309 | ||||||||
\(237\) | 32.7783 | 2.12918 | ||||||||
\(238\) | 41.4657 | 2.68782 | ||||||||
\(239\) | 22.2811 | 1.44125 | 0.720623 | − | 0.693327i | \(-0.243856\pi\) | ||||
0.720623 | + | 0.693327i | \(0.243856\pi\) | |||||||
\(240\) | 9.03798 | 0.583399 | ||||||||
\(241\) | 12.0839 | 0.778394 | 0.389197 | − | 0.921155i | \(-0.372753\pi\) | ||||
0.389197 | + | 0.921155i | \(0.372753\pi\) | |||||||
\(242\) | −15.8360 | −1.01798 | ||||||||
\(243\) | −20.1657 | −1.29363 | ||||||||
\(244\) | 0.262599 | 0.0168112 | ||||||||
\(245\) | −11.5188 | −0.735911 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.97613 | −0.252995 | ||||||||
\(248\) | −4.07296 | −0.258633 | ||||||||
\(249\) | −35.3630 | −2.24104 | ||||||||
\(250\) | 10.7705 | 0.681184 | ||||||||
\(251\) | 7.94589 | 0.501540 | 0.250770 | − | 0.968047i | \(-0.419316\pi\) | ||||
0.250770 | + | 0.968047i | \(0.419316\pi\) | |||||||
\(252\) | 3.73762 | 0.235448 | ||||||||
\(253\) | 0.570592 | 0.0358728 | ||||||||
\(254\) | 14.7872 | 0.927828 | ||||||||
\(255\) | −12.4706 | −0.780942 | ||||||||
\(256\) | 4.50171 | 0.281357 | ||||||||
\(257\) | 23.5058 | 1.46625 | 0.733125 | − | 0.680094i | \(-0.238061\pi\) | ||||
0.733125 | + | 0.680094i | \(0.238061\pi\) | |||||||
\(258\) | 24.7388 | 1.54017 | ||||||||
\(259\) | −33.9426 | −2.10909 | ||||||||
\(260\) | −0.132961 | −0.00824589 | ||||||||
\(261\) | 5.21115 | 0.322562 | ||||||||
\(262\) | 1.20574 | 0.0744909 | ||||||||
\(263\) | −21.3787 | −1.31827 | −0.659134 | − | 0.752026i | \(-0.729077\pi\) | ||||
−0.659134 | + | 0.752026i | \(0.729077\pi\) | |||||||
\(264\) | −3.92484 | −0.241557 | ||||||||
\(265\) | 4.14542 | 0.254651 | ||||||||
\(266\) | −30.3214 | −1.85913 | ||||||||
\(267\) | −5.24298 | −0.320865 | ||||||||
\(268\) | −1.06631 | −0.0651353 | ||||||||
\(269\) | 27.0347 | 1.64834 | 0.824169 | − | 0.566344i | \(-0.191643\pi\) | ||||
0.824169 | + | 0.566344i | \(0.191643\pi\) | |||||||
\(270\) | −3.76759 | −0.229288 | ||||||||
\(271\) | 11.9376 | 0.725158 | 0.362579 | − | 0.931953i | \(-0.381896\pi\) | ||||
0.362579 | + | 0.931953i | \(0.381896\pi\) | |||||||
\(272\) | −26.0209 | −1.57775 | ||||||||
\(273\) | 11.4072 | 0.690398 | ||||||||
\(274\) | 6.36809 | 0.384710 | ||||||||
\(275\) | −2.39842 | −0.144630 | ||||||||
\(276\) | 0.532365 | 0.0320446 | ||||||||
\(277\) | −14.6668 | −0.881242 | −0.440621 | − | 0.897693i | \(-0.645242\pi\) | ||||
−0.440621 | + | 0.897693i | \(0.645242\pi\) | |||||||
\(278\) | 7.43371 | 0.445844 | ||||||||
\(279\) | 6.42052 | 0.384386 | ||||||||
\(280\) | 9.70361 | 0.579902 | ||||||||
\(281\) | −10.6965 | −0.638098 | −0.319049 | − | 0.947738i | \(-0.603364\pi\) | ||||
−0.319049 | + | 0.947738i | \(0.603364\pi\) | |||||||
\(282\) | −15.7890 | −0.940221 | ||||||||
\(283\) | −19.0733 | −1.13379 | −0.566894 | − | 0.823791i | \(-0.691855\pi\) | ||||
−0.566894 | + | 0.823791i | \(0.691855\pi\) | |||||||
\(284\) | −0.206185 | −0.0122348 | ||||||||
\(285\) | 9.11905 | 0.540166 | ||||||||
\(286\) | 0.731832 | 0.0432742 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −4.50586 | −0.265510 | ||||||||
\(289\) | 18.9037 | 1.11198 | ||||||||
\(290\) | −1.41368 | −0.0830143 | ||||||||
\(291\) | 5.22134 | 0.306080 | ||||||||
\(292\) | −1.06203 | −0.0621504 | ||||||||
\(293\) | 25.9387 | 1.51535 | 0.757677 | − | 0.652629i | \(-0.226334\pi\) | ||||
0.757677 | + | 0.652629i | \(0.226334\pi\) | |||||||
\(294\) | 59.1535 | 3.44990 | ||||||||
\(295\) | −6.87246 | −0.400130 | ||||||||
\(296\) | 19.4438 | 1.13015 | ||||||||
\(297\) | 1.79230 | 0.104000 | ||||||||
\(298\) | 11.7266 | 0.679306 | ||||||||
\(299\) | 0.949992 | 0.0549395 | ||||||||
\(300\) | −2.23773 | −0.129196 | ||||||||
\(301\) | 29.0963 | 1.67708 | ||||||||
\(302\) | −30.5881 | −1.76015 | ||||||||
\(303\) | −22.6110 | −1.29897 | ||||||||
\(304\) | 19.0275 | 1.09130 | ||||||||
\(305\) | −1.07471 | −0.0615379 | ||||||||
\(306\) | 37.4442 | 2.14054 | ||||||||
\(307\) | −8.65704 | −0.494084 | −0.247042 | − | 0.969005i | \(-0.579459\pi\) | ||||
−0.247042 | + | 0.969005i | \(0.579459\pi\) | |||||||
\(308\) | 0.482347 | 0.0274843 | ||||||||
\(309\) | −11.5479 | −0.656935 | ||||||||
\(310\) | −1.74176 | −0.0989253 | ||||||||
\(311\) | −8.07904 | −0.458120 | −0.229060 | − | 0.973412i | \(-0.573565\pi\) | ||||
−0.229060 | + | 0.973412i | \(0.573565\pi\) | |||||||
\(312\) | −6.53456 | −0.369947 | ||||||||
\(313\) | −3.45127 | −0.195077 | −0.0975387 | − | 0.995232i | \(-0.531097\pi\) | ||||
−0.0975387 | + | 0.995232i | \(0.531097\pi\) | |||||||
\(314\) | −17.8591 | −1.00785 | ||||||||
\(315\) | −15.2965 | −0.861863 | ||||||||
\(316\) | 2.30760 | 0.129813 | ||||||||
\(317\) | 27.9163 | 1.56794 | 0.783968 | − | 0.620801i | \(-0.213193\pi\) | ||||
0.783968 | + | 0.620801i | \(0.213193\pi\) | |||||||
\(318\) | −21.2883 | −1.19379 | ||||||||
\(319\) | 0.672510 | 0.0376534 | ||||||||
\(320\) | −5.50320 | −0.307638 | ||||||||
\(321\) | −33.2847 | −1.85777 | ||||||||
\(322\) | 7.24451 | 0.403720 | ||||||||
\(323\) | −26.2542 | −1.46083 | ||||||||
\(324\) | −0.725171 | −0.0402873 | ||||||||
\(325\) | −3.99318 | −0.221502 | ||||||||
\(326\) | 2.96051 | 0.163968 | ||||||||
\(327\) | 4.65023 | 0.257158 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −18.5701 | −1.02380 | ||||||||
\(330\) | −1.67842 | −0.0923938 | ||||||||
\(331\) | 22.5781 | 1.24100 | 0.620501 | − | 0.784205i | \(-0.286929\pi\) | ||||
0.620501 | + | 0.784205i | \(0.286929\pi\) | |||||||
\(332\) | −2.48956 | −0.136632 | ||||||||
\(333\) | −30.6507 | −1.67965 | ||||||||
\(334\) | −28.2947 | −1.54822 | ||||||||
\(335\) | 4.36398 | 0.238430 | ||||||||
\(336\) | −54.5885 | −2.97805 | ||||||||
\(337\) | 24.7909 | 1.35045 | 0.675223 | − | 0.737614i | \(-0.264048\pi\) | ||||
0.675223 | + | 0.737614i | \(0.264048\pi\) | |||||||
\(338\) | −18.0163 | −0.979959 | ||||||||
\(339\) | 3.13875 | 0.170473 | ||||||||
\(340\) | −0.877935 | −0.0476127 | ||||||||
\(341\) | 0.828581 | 0.0448702 | ||||||||
\(342\) | −27.3808 | −1.48058 | ||||||||
\(343\) | 36.8330 | 1.98880 | ||||||||
\(344\) | −16.6676 | −0.898656 | ||||||||
\(345\) | −2.17875 | −0.117300 | ||||||||
\(346\) | −8.88334 | −0.477571 | ||||||||
\(347\) | 3.59498 | 0.192989 | 0.0964943 | − | 0.995334i | \(-0.469237\pi\) | ||||
0.0964943 | + | 0.995334i | \(0.469237\pi\) | |||||||
\(348\) | 0.627456 | 0.0336351 | ||||||||
\(349\) | 0.286874 | 0.0153560 | 0.00767800 | − | 0.999971i | \(-0.497556\pi\) | ||||
0.00767800 | + | 0.999971i | \(0.497556\pi\) | |||||||
\(350\) | −30.4514 | −1.62770 | ||||||||
\(351\) | 2.98405 | 0.159277 | ||||||||
\(352\) | −0.581490 | −0.0309935 | ||||||||
\(353\) | 23.5120 | 1.25142 | 0.625708 | − | 0.780057i | \(-0.284810\pi\) | ||||
0.625708 | + | 0.780057i | \(0.284810\pi\) | |||||||
\(354\) | 35.2926 | 1.87578 | ||||||||
\(355\) | 0.843832 | 0.0447860 | ||||||||
\(356\) | −0.369107 | −0.0195626 | ||||||||
\(357\) | 75.3215 | 3.98644 | ||||||||
\(358\) | 13.5446 | 0.715857 | ||||||||
\(359\) | 34.3543 | 1.81315 | 0.906575 | − | 0.422045i | \(-0.138687\pi\) | ||||
0.906575 | + | 0.422045i | \(0.138687\pi\) | |||||||
\(360\) | 8.76252 | 0.461825 | ||||||||
\(361\) | 0.198176 | 0.0104303 | ||||||||
\(362\) | 28.1918 | 1.48173 | ||||||||
\(363\) | −28.7658 | −1.50981 | ||||||||
\(364\) | 0.803071 | 0.0420924 | ||||||||
\(365\) | 4.34644 | 0.227503 | ||||||||
\(366\) | 5.51905 | 0.288485 | ||||||||
\(367\) | 26.0833 | 1.36154 | 0.680769 | − | 0.732498i | \(-0.261646\pi\) | ||||
0.680769 | + | 0.732498i | \(0.261646\pi\) | |||||||
\(368\) | −4.54612 | −0.236983 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 8.31494 | 0.432273 | ||||||||
\(371\) | −25.0380 | −1.29991 | ||||||||
\(372\) | 0.773070 | 0.0400818 | ||||||||
\(373\) | 10.0988 | 0.522894 | 0.261447 | − | 0.965218i | \(-0.415800\pi\) | ||||
0.261447 | + | 0.965218i | \(0.415800\pi\) | |||||||
\(374\) | 4.83226 | 0.249870 | ||||||||
\(375\) | 19.5643 | 1.01030 | ||||||||
\(376\) | 10.6377 | 0.548599 | ||||||||
\(377\) | 1.11968 | 0.0576664 | ||||||||
\(378\) | 22.7559 | 1.17044 | ||||||||
\(379\) | −13.2339 | −0.679778 | −0.339889 | − | 0.940466i | \(-0.610389\pi\) | ||||
−0.339889 | + | 0.940466i | \(0.610389\pi\) | |||||||
\(380\) | 0.641982 | 0.0329330 | ||||||||
\(381\) | 26.8605 | 1.37611 | ||||||||
\(382\) | 16.6689 | 0.852855 | ||||||||
\(383\) | −6.87869 | −0.351485 | −0.175742 | − | 0.984436i | \(-0.556233\pi\) | ||||
−0.175742 | + | 0.984436i | \(0.556233\pi\) | |||||||
\(384\) | 33.9956 | 1.73483 | ||||||||
\(385\) | −1.97405 | −0.100607 | ||||||||
\(386\) | −17.3002 | −0.880559 | ||||||||
\(387\) | 26.2744 | 1.33560 | ||||||||
\(388\) | 0.367583 | 0.0186612 | ||||||||
\(389\) | 30.5169 | 1.54727 | 0.773633 | − | 0.633634i | \(-0.218437\pi\) | ||||
0.773633 | + | 0.633634i | \(0.218437\pi\) | |||||||
\(390\) | −2.79444 | −0.141502 | ||||||||
\(391\) | 6.27276 | 0.317227 | ||||||||
\(392\) | −39.8542 | −2.01294 | ||||||||
\(393\) | 2.19020 | 0.110481 | ||||||||
\(394\) | −14.9525 | −0.753296 | ||||||||
\(395\) | −9.44406 | −0.475182 | ||||||||
\(396\) | 0.435567 | 0.0218881 | ||||||||
\(397\) | −24.0343 | −1.20625 | −0.603124 | − | 0.797647i | \(-0.706078\pi\) | ||||
−0.603124 | + | 0.797647i | \(0.706078\pi\) | |||||||
\(398\) | −12.4516 | −0.624145 | ||||||||
\(399\) | −55.0782 | −2.75736 | ||||||||
\(400\) | 19.1091 | 0.955455 | ||||||||
\(401\) | −4.76630 | −0.238018 | −0.119009 | − | 0.992893i | \(-0.537972\pi\) | ||||
−0.119009 | + | 0.992893i | \(0.537972\pi\) | |||||||
\(402\) | −22.4106 | −1.11774 | ||||||||
\(403\) | 1.37953 | 0.0687190 | ||||||||
\(404\) | −1.59182 | −0.0791960 | ||||||||
\(405\) | 2.96783 | 0.147473 | ||||||||
\(406\) | 8.53851 | 0.423759 | ||||||||
\(407\) | −3.95554 | −0.196069 | ||||||||
\(408\) | −43.1474 | −2.13612 | ||||||||
\(409\) | 37.1120 | 1.83507 | 0.917534 | − | 0.397657i | \(-0.130176\pi\) | ||||
0.917534 | + | 0.397657i | \(0.130176\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.5675 | 0.570582 | ||||||||
\(412\) | −0.812971 | −0.0400522 | ||||||||
\(413\) | 41.5090 | 2.04252 | ||||||||
\(414\) | 6.54191 | 0.321517 | ||||||||
\(415\) | 10.1888 | 0.500147 | ||||||||
\(416\) | −0.968137 | −0.0474668 | ||||||||
\(417\) | 13.5031 | 0.661252 | ||||||||
\(418\) | −3.53354 | −0.172831 | ||||||||
\(419\) | 11.2273 | 0.548491 | 0.274246 | − | 0.961660i | \(-0.411572\pi\) | ||||
0.274246 | + | 0.961660i | \(0.411572\pi\) | |||||||
\(420\) | −1.84180 | −0.0898706 | ||||||||
\(421\) | 16.9472 | 0.825956 | 0.412978 | − | 0.910741i | \(-0.364489\pi\) | ||||
0.412978 | + | 0.910741i | \(0.364489\pi\) | |||||||
\(422\) | −19.2110 | −0.935177 | ||||||||
\(423\) | −16.7691 | −0.815340 | ||||||||
\(424\) | 14.3428 | 0.696549 | ||||||||
\(425\) | −26.3668 | −1.27898 | ||||||||
\(426\) | −4.33339 | −0.209953 | ||||||||
\(427\) | 6.49117 | 0.314130 | ||||||||
\(428\) | −2.34325 | −0.113265 | ||||||||
\(429\) | 1.32936 | 0.0641819 | ||||||||
\(430\) | −7.12772 | −0.343729 | ||||||||
\(431\) | 20.3505 | 0.980248 | 0.490124 | − | 0.871653i | \(-0.336952\pi\) | ||||
0.490124 | + | 0.871653i | \(0.336952\pi\) | |||||||
\(432\) | −14.2799 | −0.687044 | ||||||||
\(433\) | −21.1989 | −1.01875 | −0.509377 | − | 0.860543i | \(-0.670124\pi\) | ||||
−0.509377 | + | 0.860543i | \(0.670124\pi\) | |||||||
\(434\) | 10.5201 | 0.504979 | ||||||||
\(435\) | −2.56792 | −0.123122 | ||||||||
\(436\) | 0.327377 | 0.0156785 | ||||||||
\(437\) | −4.58690 | −0.219421 | ||||||||
\(438\) | −22.3206 | −1.06652 | ||||||||
\(439\) | 20.6673 | 0.986397 | 0.493198 | − | 0.869917i | \(-0.335828\pi\) | ||||
0.493198 | + | 0.869917i | \(0.335828\pi\) | |||||||
\(440\) | 1.13082 | 0.0539098 | ||||||||
\(441\) | 62.8253 | 2.99168 | ||||||||
\(442\) | 8.04534 | 0.382678 | ||||||||
\(443\) | 21.7029 | 1.03114 | 0.515568 | − | 0.856849i | \(-0.327581\pi\) | ||||
0.515568 | + | 0.856849i | \(0.327581\pi\) | |||||||
\(444\) | −3.69054 | −0.175145 | ||||||||
\(445\) | 1.51060 | 0.0716095 | ||||||||
\(446\) | −25.8902 | −1.22594 | ||||||||
\(447\) | 21.3012 | 1.00751 | ||||||||
\(448\) | 33.2388 | 1.57039 | ||||||||
\(449\) | −5.55296 | −0.262061 | −0.131030 | − | 0.991378i | \(-0.541829\pi\) | ||||
−0.131030 | + | 0.991378i | \(0.541829\pi\) | |||||||
\(450\) | −27.4981 | −1.29628 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0.220968 | 0.0103935 | ||||||||
\(453\) | −55.5625 | −2.61055 | ||||||||
\(454\) | −40.3047 | −1.89159 | ||||||||
\(455\) | −3.28665 | −0.154080 | ||||||||
\(456\) | 31.5511 | 1.47752 | ||||||||
\(457\) | −38.7172 | −1.81111 | −0.905557 | − | 0.424224i | \(-0.860547\pi\) | ||||
−0.905557 | + | 0.424224i | \(0.860547\pi\) | |||||||
\(458\) | −33.4902 | −1.56489 | ||||||||
\(459\) | 19.7035 | 0.919682 | ||||||||
\(460\) | −0.153385 | −0.00715160 | ||||||||
\(461\) | 5.09040 | 0.237084 | 0.118542 | − | 0.992949i | \(-0.462178\pi\) | ||||
0.118542 | + | 0.992949i | \(0.462178\pi\) | |||||||
\(462\) | 10.1375 | 0.471638 | ||||||||
\(463\) | 2.88369 | 0.134017 | 0.0670083 | − | 0.997752i | \(-0.478655\pi\) | ||||
0.0670083 | + | 0.997752i | \(0.478655\pi\) | |||||||
\(464\) | −5.35814 | −0.248746 | ||||||||
\(465\) | −3.16387 | −0.146721 | ||||||||
\(466\) | 35.8216 | 1.65940 | ||||||||
\(467\) | 36.8563 | 1.70551 | 0.852753 | − | 0.522315i | \(-0.174931\pi\) | ||||
0.852753 | + | 0.522315i | \(0.174931\pi\) | |||||||
\(468\) | 0.725186 | 0.0335218 | ||||||||
\(469\) | −26.3580 | −1.21710 | ||||||||
\(470\) | 4.54911 | 0.209835 | ||||||||
\(471\) | −32.4406 | −1.49478 | ||||||||
\(472\) | −23.7781 | −1.09448 | ||||||||
\(473\) | 3.39077 | 0.155908 | ||||||||
\(474\) | 48.4987 | 2.22762 | ||||||||
\(475\) | 19.2805 | 0.884649 | ||||||||
\(476\) | 5.30265 | 0.243046 | ||||||||
\(477\) | −22.6097 | −1.03523 | ||||||||
\(478\) | 32.9671 | 1.50788 | ||||||||
\(479\) | −31.9019 | −1.45763 | −0.728817 | − | 0.684708i | \(-0.759930\pi\) | ||||
−0.728817 | + | 0.684708i | \(0.759930\pi\) | |||||||
\(480\) | 2.22037 | 0.101346 | ||||||||
\(481\) | −6.58568 | −0.300281 | ||||||||
\(482\) | 17.8793 | 0.814382 | ||||||||
\(483\) | 13.1595 | 0.598777 | ||||||||
\(484\) | −2.02511 | −0.0920506 | ||||||||
\(485\) | −1.50437 | −0.0683099 | ||||||||
\(486\) | −29.8371 | −1.35344 | ||||||||
\(487\) | −17.9320 | −0.812578 | −0.406289 | − | 0.913745i | \(-0.633177\pi\) | ||||
−0.406289 | + | 0.913745i | \(0.633177\pi\) | |||||||
\(488\) | −3.71842 | −0.168325 | ||||||||
\(489\) | 5.37770 | 0.243188 | ||||||||
\(490\) | −17.0433 | −0.769936 | ||||||||
\(491\) | −25.0172 | −1.12901 | −0.564505 | − | 0.825430i | \(-0.690933\pi\) | ||||
−0.564505 | + | 0.825430i | \(0.690933\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.39319 | 0.332973 | ||||||||
\(494\) | −5.88308 | −0.264692 | ||||||||
\(495\) | −1.78260 | −0.0801219 | ||||||||
\(496\) | −6.60162 | −0.296421 | ||||||||
\(497\) | −5.09667 | −0.228617 | ||||||||
\(498\) | −52.3231 | −2.34465 | ||||||||
\(499\) | 25.8218 | 1.15594 | 0.577970 | − | 0.816058i | \(-0.303845\pi\) | ||||
0.577970 | + | 0.816058i | \(0.303845\pi\) | |||||||
\(500\) | 1.37733 | 0.0615960 | ||||||||
\(501\) | −51.3966 | −2.29623 | ||||||||
\(502\) | 11.7567 | 0.524728 | ||||||||
\(503\) | 18.4128 | 0.820985 | 0.410493 | − | 0.911864i | \(-0.365357\pi\) | ||||
0.410493 | + | 0.911864i | \(0.365357\pi\) | |||||||
\(504\) | −52.9248 | −2.35746 | ||||||||
\(505\) | 6.51468 | 0.289899 | ||||||||
\(506\) | 0.844247 | 0.0375313 | ||||||||
\(507\) | −32.7262 | −1.45342 | ||||||||
\(508\) | 1.89098 | 0.0838988 | ||||||||
\(509\) | −18.5528 | −0.822338 | −0.411169 | − | 0.911559i | \(-0.634879\pi\) | ||||
−0.411169 | + | 0.911559i | \(0.634879\pi\) | |||||||
\(510\) | −18.4516 | −0.817048 | ||||||||
\(511\) | −26.2521 | −1.16132 | ||||||||
\(512\) | −18.6369 | −0.823642 | ||||||||
\(513\) | −14.4080 | −0.636130 | ||||||||
\(514\) | 34.7791 | 1.53404 | ||||||||
\(515\) | 3.32716 | 0.146612 | ||||||||
\(516\) | 3.16360 | 0.139270 | ||||||||
\(517\) | −2.16408 | −0.0951762 | ||||||||
\(518\) | −50.2214 | −2.20660 | ||||||||
\(519\) | −16.1364 | −0.708308 | ||||||||
\(520\) | 1.88273 | 0.0825633 | ||||||||
\(521\) | −8.23340 | −0.360712 | −0.180356 | − | 0.983601i | \(-0.557725\pi\) | ||||
−0.180356 | + | 0.983601i | \(0.557725\pi\) | |||||||
\(522\) | 7.71041 | 0.337476 | ||||||||
\(523\) | −34.2863 | −1.49924 | −0.749618 | − | 0.661870i | \(-0.769763\pi\) | ||||
−0.749618 | + | 0.661870i | \(0.769763\pi\) | |||||||
\(524\) | 0.154190 | 0.00673583 | ||||||||
\(525\) | −55.3143 | −2.41411 | ||||||||
\(526\) | −31.6319 | −1.37922 | ||||||||
\(527\) | 9.10894 | 0.396792 | ||||||||
\(528\) | −6.36154 | −0.276850 | ||||||||
\(529\) | −21.9041 | −0.952351 | ||||||||
\(530\) | 6.13356 | 0.266425 | ||||||||
\(531\) | 37.4833 | 1.62664 | ||||||||
\(532\) | −3.87751 | −0.168111 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −7.75751 | −0.335700 | ||||||||
\(535\) | 9.58996 | 0.414610 | ||||||||
\(536\) | 15.0990 | 0.652178 | ||||||||
\(537\) | 24.6035 | 1.06172 | ||||||||
\(538\) | 40.0006 | 1.72455 | ||||||||
\(539\) | 8.10773 | 0.349225 | ||||||||
\(540\) | −0.481800 | −0.0207334 | ||||||||
\(541\) | −0.834839 | −0.0358925 | −0.0179463 | − | 0.999839i | \(-0.505713\pi\) | ||||
−0.0179463 | + | 0.999839i | \(0.505713\pi\) | |||||||
\(542\) | 17.6629 | 0.758685 | ||||||||
\(543\) | 51.2097 | 2.19762 | ||||||||
\(544\) | −6.39257 | −0.274079 | ||||||||
\(545\) | −1.33982 | −0.0573916 | ||||||||
\(546\) | 16.8781 | 0.722318 | ||||||||
\(547\) | −31.9375 | −1.36555 | −0.682775 | − | 0.730629i | \(-0.739227\pi\) | ||||
−0.682775 | + | 0.730629i | \(0.739227\pi\) | |||||||
\(548\) | 0.814353 | 0.0347874 | ||||||||
\(549\) | 5.86163 | 0.250168 | ||||||||
\(550\) | −3.54869 | −0.151317 | ||||||||
\(551\) | −5.40620 | −0.230312 | ||||||||
\(552\) | −7.53831 | −0.320852 | ||||||||
\(553\) | 57.0412 | 2.42564 | ||||||||
\(554\) | −21.7010 | −0.921985 | ||||||||
\(555\) | 15.1039 | 0.641124 | ||||||||
\(556\) | 0.950624 | 0.0403154 | ||||||||
\(557\) | −27.8329 | −1.17932 | −0.589660 | − | 0.807652i | \(-0.700738\pi\) | ||||
−0.589660 | + | 0.807652i | \(0.700738\pi\) | |||||||
\(558\) | 9.49979 | 0.402158 | ||||||||
\(559\) | 5.64537 | 0.238774 | ||||||||
\(560\) | 15.7280 | 0.664630 | ||||||||
\(561\) | 8.77768 | 0.370594 | ||||||||
\(562\) | −15.8265 | −0.667600 | ||||||||
\(563\) | −29.5266 | −1.24440 | −0.622200 | − | 0.782859i | \(-0.713761\pi\) | ||||
−0.622200 | + | 0.782859i | \(0.713761\pi\) | |||||||
\(564\) | −2.01910 | −0.0850194 | ||||||||
\(565\) | −0.904334 | −0.0380456 | ||||||||
\(566\) | −28.2208 | −1.18621 | ||||||||
\(567\) | −17.9254 | −0.752797 | ||||||||
\(568\) | 2.91959 | 0.122503 | ||||||||
\(569\) | 28.7842 | 1.20670 | 0.603348 | − | 0.797478i | \(-0.293833\pi\) | ||||
0.603348 | + | 0.797478i | \(0.293833\pi\) | |||||||
\(570\) | 13.4925 | 0.565140 | ||||||||
\(571\) | −27.3640 | −1.14515 | −0.572574 | − | 0.819853i | \(-0.694055\pi\) | ||||
−0.572574 | + | 0.819853i | \(0.694055\pi\) | |||||||
\(572\) | 0.0935868 | 0.00391306 | ||||||||
\(573\) | 30.2786 | 1.26491 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.60656 | −0.192107 | ||||||||
\(576\) | 30.0152 | 1.25063 | ||||||||
\(577\) | −9.05413 | −0.376929 | −0.188464 | − | 0.982080i | \(-0.560351\pi\) | ||||
−0.188464 | + | 0.982080i | \(0.560351\pi\) | |||||||
\(578\) | 27.9699 | 1.16339 | ||||||||
\(579\) | −31.4255 | −1.30600 | ||||||||
\(580\) | −0.180782 | −0.00750657 | ||||||||
\(581\) | −61.5392 | −2.55308 | ||||||||
\(582\) | 7.72548 | 0.320232 | ||||||||
\(583\) | −2.91783 | −0.120844 | ||||||||
\(584\) | 15.0383 | 0.622291 | ||||||||
\(585\) | −2.96790 | −0.122707 | ||||||||
\(586\) | 38.3788 | 1.58542 | ||||||||
\(587\) | 5.18703 | 0.214091 | 0.107046 | − | 0.994254i | \(-0.465861\pi\) | ||||
0.107046 | + | 0.994254i | \(0.465861\pi\) | |||||||
\(588\) | 7.56455 | 0.311957 | ||||||||
\(589\) | −6.66083 | −0.274455 | ||||||||
\(590\) | −10.1685 | −0.418630 | ||||||||
\(591\) | −27.1609 | −1.11725 | ||||||||
\(592\) | 31.5153 | 1.29527 | ||||||||
\(593\) | 23.4369 | 0.962437 | 0.481219 | − | 0.876601i | \(-0.340194\pi\) | ||||
0.481219 | + | 0.876601i | \(0.340194\pi\) | |||||||
\(594\) | 2.65189 | 0.108808 | ||||||||
\(595\) | −21.7016 | −0.889678 | ||||||||
\(596\) | 1.49961 | 0.0614262 | ||||||||
\(597\) | −22.6181 | −0.925698 | ||||||||
\(598\) | 1.40561 | 0.0574795 | ||||||||
\(599\) | 30.6974 | 1.25426 | 0.627130 | − | 0.778914i | \(-0.284229\pi\) | ||||
0.627130 | + | 0.778914i | \(0.284229\pi\) | |||||||
\(600\) | 31.6864 | 1.29359 | ||||||||
\(601\) | 7.38136 | 0.301092 | 0.150546 | − | 0.988603i | \(-0.451897\pi\) | ||||
0.150546 | + | 0.988603i | \(0.451897\pi\) | |||||||
\(602\) | 43.0508 | 1.75462 | ||||||||
\(603\) | −23.8017 | −0.969281 | ||||||||
\(604\) | −3.91161 | −0.159161 | ||||||||
\(605\) | 8.28797 | 0.336954 | ||||||||
\(606\) | −33.4553 | −1.35903 | ||||||||
\(607\) | 31.3718 | 1.27334 | 0.636671 | − | 0.771136i | \(-0.280311\pi\) | ||||
0.636671 | + | 0.771136i | \(0.280311\pi\) | |||||||
\(608\) | 4.67451 | 0.189576 | ||||||||
\(609\) | 15.5100 | 0.628497 | ||||||||
\(610\) | −1.59014 | −0.0643831 | ||||||||
\(611\) | −3.60303 | −0.145763 | ||||||||
\(612\) | 4.78838 | 0.193559 | ||||||||
\(613\) | 17.6297 | 0.712059 | 0.356029 | − | 0.934475i | \(-0.384130\pi\) | ||||
0.356029 | + | 0.934475i | \(0.384130\pi\) | |||||||
\(614\) | −12.8089 | −0.516927 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −6.83006 | −0.275191 | ||||||||
\(617\) | 8.04598 | 0.323919 | 0.161959 | − | 0.986797i | \(-0.448219\pi\) | ||||
0.161959 | + | 0.986797i | \(0.448219\pi\) | |||||||
\(618\) | −17.0862 | −0.687307 | ||||||||
\(619\) | −6.35587 | −0.255464 | −0.127732 | − | 0.991809i | \(-0.540770\pi\) | ||||
−0.127732 | + | 0.991809i | \(0.540770\pi\) | |||||||
\(620\) | −0.222737 | −0.00894531 | ||||||||
\(621\) | 3.44241 | 0.138139 | ||||||||
\(622\) | −11.9537 | −0.479301 | ||||||||
\(623\) | −9.12391 | −0.365542 | ||||||||
\(624\) | −10.5915 | −0.423999 | ||||||||
\(625\) | 16.3649 | 0.654598 | ||||||||
\(626\) | −5.10649 | −0.204097 | ||||||||
\(627\) | −6.41860 | −0.256334 | ||||||||
\(628\) | −2.28382 | −0.0911345 | ||||||||
\(629\) | −43.4849 | −1.73386 | ||||||||
\(630\) | −22.6327 | −0.901710 | ||||||||
\(631\) | 4.18327 | 0.166533 | 0.0832667 | − | 0.996527i | \(-0.473465\pi\) | ||||
0.0832667 | + | 0.996527i | \(0.473465\pi\) | |||||||
\(632\) | −32.6757 | −1.29977 | ||||||||
\(633\) | −34.8963 | −1.38700 | ||||||||
\(634\) | 41.3049 | 1.64043 | ||||||||
\(635\) | −7.73903 | −0.307114 | ||||||||
\(636\) | −2.72235 | −0.107948 | ||||||||
\(637\) | 13.4988 | 0.534840 | ||||||||
\(638\) | 0.995045 | 0.0393942 | ||||||||
\(639\) | −4.60237 | −0.182067 | ||||||||
\(640\) | −9.79480 | −0.387173 | ||||||||
\(641\) | 19.6147 | 0.774734 | 0.387367 | − | 0.921926i | \(-0.373385\pi\) | ||||
0.387367 | + | 0.921926i | \(0.373385\pi\) | |||||||
\(642\) | −49.2480 | −1.94366 | ||||||||
\(643\) | −11.1171 | −0.438416 | −0.219208 | − | 0.975678i | \(-0.570347\pi\) | ||||
−0.219208 | + | 0.975678i | \(0.570347\pi\) | |||||||
\(644\) | 0.926429 | 0.0365064 | ||||||||
\(645\) | −12.9473 | −0.509801 | ||||||||
\(646\) | −38.8457 | −1.52837 | ||||||||
\(647\) | 10.4368 | 0.410313 | 0.205157 | − | 0.978729i | \(-0.434230\pi\) | ||||
0.205157 | + | 0.978729i | \(0.434230\pi\) | |||||||
\(648\) | 10.2684 | 0.403383 | ||||||||
\(649\) | 4.83730 | 0.189881 | ||||||||
\(650\) | −5.90831 | −0.231743 | ||||||||
\(651\) | 19.1094 | 0.748958 | ||||||||
\(652\) | 0.378591 | 0.0148268 | ||||||||
\(653\) | 26.9884 | 1.05614 | 0.528069 | − | 0.849202i | \(-0.322916\pi\) | ||||
0.528069 | + | 0.849202i | \(0.322916\pi\) | |||||||
\(654\) | 6.88047 | 0.269048 | ||||||||
\(655\) | −0.631038 | −0.0246567 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −23.7061 | −0.924862 | ||||||||
\(658\) | −27.4762 | −1.07113 | ||||||||
\(659\) | 15.3561 | 0.598190 | 0.299095 | − | 0.954223i | \(-0.403315\pi\) | ||||
0.299095 | + | 0.954223i | \(0.403315\pi\) | |||||||
\(660\) | −0.214636 | −0.00835471 | ||||||||
\(661\) | 0.339382 | 0.0132004 | 0.00660021 | − | 0.999978i | \(-0.497899\pi\) | ||||
0.00660021 | + | 0.999978i | \(0.497899\pi\) | |||||||
\(662\) | 33.4065 | 1.29838 | ||||||||
\(663\) | 14.6142 | 0.567567 | ||||||||
\(664\) | 35.2523 | 1.36806 | ||||||||
\(665\) | 15.8691 | 0.615377 | ||||||||
\(666\) | −45.3508 | −1.75731 | ||||||||
\(667\) | 1.29167 | 0.0500136 | ||||||||
\(668\) | −3.61833 | −0.139997 | ||||||||
\(669\) | −47.0290 | −1.81824 | ||||||||
\(670\) | 6.45694 | 0.249453 | ||||||||
\(671\) | 0.756456 | 0.0292026 | ||||||||
\(672\) | −13.4108 | −0.517334 | ||||||||
\(673\) | 12.5261 | 0.482847 | 0.241424 | − | 0.970420i | \(-0.422386\pi\) | ||||
0.241424 | + | 0.970420i | \(0.422386\pi\) | |||||||
\(674\) | 36.6805 | 1.41288 | ||||||||
\(675\) | −14.4698 | −0.556943 | ||||||||
\(676\) | −2.30393 | −0.0886128 | ||||||||
\(677\) | 29.2489 | 1.12413 | 0.562063 | − | 0.827094i | \(-0.310008\pi\) | ||||
0.562063 | + | 0.827094i | \(0.310008\pi\) | |||||||
\(678\) | 4.64409 | 0.178355 | ||||||||
\(679\) | 9.08624 | 0.348698 | ||||||||
\(680\) | 12.4316 | 0.476730 | ||||||||
\(681\) | −73.2126 | −2.80551 | ||||||||
\(682\) | 1.22597 | 0.0469447 | ||||||||
\(683\) | 23.6545 | 0.905115 | 0.452558 | − | 0.891735i | \(-0.350512\pi\) | ||||
0.452558 | + | 0.891735i | \(0.350512\pi\) | |||||||
\(684\) | −3.50146 | −0.133881 | ||||||||
\(685\) | −3.33282 | −0.127340 | ||||||||
\(686\) | 54.4981 | 2.08075 | ||||||||
\(687\) | −60.8342 | −2.32097 | ||||||||
\(688\) | −27.0155 | −1.02996 | ||||||||
\(689\) | −4.85796 | −0.185074 | ||||||||
\(690\) | −3.22368 | −0.122723 | ||||||||
\(691\) | 16.7116 | 0.635739 | 0.317870 | − | 0.948134i | \(-0.397033\pi\) | ||||
0.317870 | + | 0.948134i | \(0.397033\pi\) | |||||||
\(692\) | −1.13600 | −0.0431843 | ||||||||
\(693\) | 10.7667 | 0.408995 | ||||||||
\(694\) | 5.31912 | 0.201911 | ||||||||
\(695\) | −3.89052 | −0.147576 | ||||||||
\(696\) | −8.88480 | −0.336777 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0.424458 | 0.0160660 | ||||||||
\(699\) | 65.0691 | 2.46114 | ||||||||
\(700\) | −3.89414 | −0.147184 | ||||||||
\(701\) | −35.8707 | −1.35482 | −0.677409 | − | 0.735607i | \(-0.736897\pi\) | ||||
−0.677409 | + | 0.735607i | \(0.736897\pi\) | |||||||
\(702\) | 4.41519 | 0.166641 | ||||||||
\(703\) | 31.7980 | 1.19928 | ||||||||
\(704\) | 3.87352 | 0.145989 | ||||||||
\(705\) | 8.26336 | 0.311216 | ||||||||
\(706\) | 34.7883 | 1.30927 | ||||||||
\(707\) | −39.3480 | −1.47984 | ||||||||
\(708\) | 4.51323 | 0.169617 | ||||||||
\(709\) | −18.5313 | −0.695958 | −0.347979 | − | 0.937502i | \(-0.613132\pi\) | ||||
−0.347979 | + | 0.937502i | \(0.613132\pi\) | |||||||
\(710\) | 1.24853 | 0.0468566 | ||||||||
\(711\) | 51.5092 | 1.93174 | ||||||||
\(712\) | 5.22657 | 0.195874 | ||||||||
\(713\) | 1.59143 | 0.0595995 | ||||||||
\(714\) | 111.446 | 4.17075 | ||||||||
\(715\) | −0.383013 | −0.0143239 | ||||||||
\(716\) | 1.73209 | 0.0647313 | ||||||||
\(717\) | 59.8840 | 2.23641 | ||||||||
\(718\) | 50.8305 | 1.89698 | ||||||||
\(719\) | −29.8646 | −1.11376 | −0.556882 | − | 0.830592i | \(-0.688002\pi\) | ||||
−0.556882 | + | 0.830592i | \(0.688002\pi\) | |||||||
\(720\) | 14.2027 | 0.529302 | ||||||||
\(721\) | −20.0957 | −0.748404 | ||||||||
\(722\) | 0.293222 | 0.0109126 | ||||||||
\(723\) | 32.4774 | 1.20785 | ||||||||
\(724\) | 3.60517 | 0.133985 | ||||||||
\(725\) | −5.42938 | −0.201642 | ||||||||
\(726\) | −42.5618 | −1.57962 | ||||||||
\(727\) | 5.10520 | 0.189342 | 0.0946708 | − | 0.995509i | \(-0.469820\pi\) | ||||
0.0946708 | + | 0.995509i | \(0.469820\pi\) | |||||||
\(728\) | −11.3715 | −0.421457 | ||||||||
\(729\) | −42.7006 | −1.58150 | ||||||||
\(730\) | 6.43099 | 0.238022 | ||||||||
\(731\) | 37.2761 | 1.37871 | ||||||||
\(732\) | 0.705777 | 0.0260863 | ||||||||
\(733\) | 19.6414 | 0.725471 | 0.362735 | − | 0.931892i | \(-0.381843\pi\) | ||||
0.362735 | + | 0.931892i | \(0.381843\pi\) | |||||||
\(734\) | 38.5928 | 1.42449 | ||||||||
\(735\) | −30.9587 | −1.14193 | ||||||||
\(736\) | −1.11685 | −0.0411676 | ||||||||
\(737\) | −3.07166 | −0.113146 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 21.4364 | 0.788552 | 0.394276 | − | 0.918992i | \(-0.370995\pi\) | ||||
0.394276 | + | 0.918992i | \(0.370995\pi\) | |||||||
\(740\) | 1.06332 | 0.0390883 | ||||||||
\(741\) | −10.6865 | −0.392578 | ||||||||
\(742\) | −37.0461 | −1.36001 | ||||||||
\(743\) | 26.6988 | 0.979485 | 0.489742 | − | 0.871867i | \(-0.337091\pi\) | ||||
0.489742 | + | 0.871867i | \(0.337091\pi\) | |||||||
\(744\) | −10.9467 | −0.401326 | ||||||||
\(745\) | −6.13728 | −0.224852 | ||||||||
\(746\) | 14.9421 | 0.547069 | ||||||||
\(747\) | −55.5709 | −2.03323 | ||||||||
\(748\) | 0.617950 | 0.0225945 | ||||||||
\(749\) | −57.9225 | −2.11644 | ||||||||
\(750\) | 28.9473 | 1.05701 | ||||||||
\(751\) | 18.3027 | 0.667876 | 0.333938 | − | 0.942595i | \(-0.391622\pi\) | ||||
0.333938 | + | 0.942595i | \(0.391622\pi\) | |||||||
\(752\) | 17.2421 | 0.628753 | ||||||||
\(753\) | 21.3558 | 0.778249 | ||||||||
\(754\) | 1.65667 | 0.0603325 | ||||||||
\(755\) | 16.0086 | 0.582614 | ||||||||
\(756\) | 2.91003 | 0.105837 | ||||||||
\(757\) | −17.8721 | −0.649571 | −0.324785 | − | 0.945788i | \(-0.605292\pi\) | ||||
−0.324785 | + | 0.945788i | \(0.605292\pi\) | |||||||
\(758\) | −19.5808 | −0.711207 | ||||||||
\(759\) | 1.53355 | 0.0556645 | ||||||||
\(760\) | −9.09049 | −0.329747 | ||||||||
\(761\) | −6.49099 | −0.235298 | −0.117649 | − | 0.993055i | \(-0.537536\pi\) | ||||
−0.117649 | + | 0.993055i | \(0.537536\pi\) | |||||||
\(762\) | 39.7428 | 1.43973 | ||||||||
\(763\) | 8.09239 | 0.292964 | ||||||||
\(764\) | 2.13162 | 0.0771193 | ||||||||
\(765\) | −19.5969 | −0.708527 | ||||||||
\(766\) | −10.1777 | −0.367735 | ||||||||
\(767\) | 8.05374 | 0.290804 | ||||||||
\(768\) | 12.0990 | 0.436587 | ||||||||
\(769\) | 14.8889 | 0.536907 | 0.268454 | − | 0.963293i | \(-0.413487\pi\) | ||||
0.268454 | + | 0.963293i | \(0.413487\pi\) | |||||||
\(770\) | −2.92080 | −0.105258 | ||||||||
\(771\) | 63.1754 | 2.27521 | ||||||||
\(772\) | −2.21236 | −0.0796245 | ||||||||
\(773\) | 33.2262 | 1.19506 | 0.597532 | − | 0.801845i | \(-0.296148\pi\) | ||||
0.597532 | + | 0.801845i | \(0.296148\pi\) | |||||||
\(774\) | 38.8755 | 1.39735 | ||||||||
\(775\) | −6.68939 | −0.240290 | ||||||||
\(776\) | −5.20499 | −0.186848 | ||||||||
\(777\) | −91.2261 | −3.27272 | ||||||||
\(778\) | 45.1527 | 1.61880 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −0.357353 | −0.0127953 | ||||||||
\(781\) | −0.593946 | −0.0212531 | ||||||||
\(782\) | 9.28116 | 0.331894 | ||||||||
\(783\) | 4.05730 | 0.144996 | ||||||||
\(784\) | −64.5974 | −2.30705 | ||||||||
\(785\) | 9.34676 | 0.333600 | ||||||||
\(786\) | 3.24061 | 0.115589 | ||||||||
\(787\) | −51.6698 | −1.84183 | −0.920914 | − | 0.389765i | \(-0.872556\pi\) | ||||
−0.920914 | + | 0.389765i | \(0.872556\pi\) | |||||||
\(788\) | −1.91213 | −0.0681168 | ||||||||
\(789\) | −57.4586 | −2.04558 | ||||||||
\(790\) | −13.9734 | −0.497152 | ||||||||
\(791\) | 5.46209 | 0.194210 | ||||||||
\(792\) | −6.16765 | −0.219158 | ||||||||
\(793\) | 1.25944 | 0.0447241 | ||||||||
\(794\) | −35.5611 | −1.26202 | ||||||||
\(795\) | 11.1415 | 0.395147 | ||||||||
\(796\) | −1.59232 | −0.0564382 | ||||||||
\(797\) | 14.3536 | 0.508431 | 0.254216 | − | 0.967148i | \(-0.418183\pi\) | ||||
0.254216 | + | 0.967148i | \(0.418183\pi\) | |||||||
\(798\) | −81.4936 | −2.88484 | ||||||||
\(799\) | −23.7907 | −0.841654 | ||||||||
\(800\) | 4.69455 | 0.165977 | ||||||||
\(801\) | −8.23904 | −0.291112 | ||||||||
\(802\) | −7.05221 | −0.249022 | ||||||||
\(803\) | −3.05932 | −0.107961 | ||||||||
\(804\) | −2.86588 | −0.101072 | ||||||||
\(805\) | −3.79150 | −0.133633 | ||||||||
\(806\) | 2.04114 | 0.0718962 | ||||||||
\(807\) | 72.6601 | 2.55776 | ||||||||
\(808\) | 22.5402 | 0.792963 | ||||||||
\(809\) | 44.1719 | 1.55300 | 0.776501 | − | 0.630116i | \(-0.216993\pi\) | ||||
0.776501 | + | 0.630116i | \(0.216993\pi\) | |||||||
\(810\) | 4.39120 | 0.154291 | ||||||||
\(811\) | 27.7113 | 0.973074 | 0.486537 | − | 0.873660i | \(-0.338260\pi\) | ||||
0.486537 | + | 0.873660i | \(0.338260\pi\) | |||||||
\(812\) | 1.09191 | 0.0383184 | ||||||||
\(813\) | 32.0842 | 1.12524 | ||||||||
\(814\) | −5.85261 | −0.205134 | ||||||||
\(815\) | −1.54942 | −0.0542738 | ||||||||
\(816\) | −69.9351 | −2.44822 | ||||||||
\(817\) | −27.2578 | −0.953630 | ||||||||
\(818\) | 54.9108 | 1.91991 | ||||||||
\(819\) | 17.9258 | 0.626378 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.1582 | 0.389424 | 0.194712 | − | 0.980860i | \(-0.437623\pi\) | ||||
0.194712 | + | 0.980860i | \(0.437623\pi\) | |||||||
\(822\) | 17.1152 | 0.596962 | ||||||||
\(823\) | 40.3927 | 1.40800 | 0.704000 | − | 0.710200i | \(-0.251396\pi\) | ||||
0.704000 | + | 0.710200i | \(0.251396\pi\) | |||||||
\(824\) | 11.5117 | 0.401029 | ||||||||
\(825\) | −6.44612 | −0.224425 | ||||||||
\(826\) | 61.4167 | 2.13696 | ||||||||
\(827\) | −2.11653 | −0.0735990 | −0.0367995 | − | 0.999323i | \(-0.511716\pi\) | ||||
−0.0367995 | + | 0.999323i | \(0.511716\pi\) | |||||||
\(828\) | 0.836580 | 0.0290732 | ||||||||
\(829\) | −22.5376 | −0.782765 | −0.391382 | − | 0.920228i | \(-0.628003\pi\) | ||||
−0.391382 | + | 0.920228i | \(0.628003\pi\) | |||||||
\(830\) | 15.0753 | 0.523271 | ||||||||
\(831\) | −39.4193 | −1.36744 | ||||||||
\(832\) | 6.44912 | 0.223583 | ||||||||
\(833\) | 89.1317 | 3.08823 | ||||||||
\(834\) | 19.9792 | 0.691824 | ||||||||
\(835\) | 14.8083 | 0.512464 | ||||||||
\(836\) | −0.451870 | −0.0156283 | ||||||||
\(837\) | 4.99888 | 0.172787 | ||||||||
\(838\) | 16.6119 | 0.573850 | ||||||||
\(839\) | −30.3508 | −1.04783 | −0.523913 | − | 0.851772i | \(-0.675528\pi\) | ||||
−0.523913 | + | 0.851772i | \(0.675528\pi\) | |||||||
\(840\) | 26.0800 | 0.899844 | ||||||||
\(841\) | −27.4776 | −0.947504 | ||||||||
\(842\) | 25.0750 | 0.864143 | ||||||||
\(843\) | −28.7484 | −0.990149 | ||||||||
\(844\) | −2.45671 | −0.0845633 | ||||||||
\(845\) | 9.42906 | 0.324370 | ||||||||
\(846\) | −24.8115 | −0.853036 | ||||||||
\(847\) | −50.0585 | −1.72003 | ||||||||
\(848\) | 23.2474 | 0.798320 | ||||||||
\(849\) | −51.2624 | −1.75932 | ||||||||
\(850\) | −39.0123 | −1.33811 | ||||||||
\(851\) | −7.59728 | −0.260431 | ||||||||
\(852\) | −0.554154 | −0.0189850 | ||||||||
\(853\) | −18.6542 | −0.638708 | −0.319354 | − | 0.947635i | \(-0.603466\pi\) | ||||
−0.319354 | + | 0.947635i | \(0.603466\pi\) | |||||||
\(854\) | 9.60432 | 0.328653 | ||||||||
\(855\) | 14.3300 | 0.490077 | ||||||||
\(856\) | 33.1805 | 1.13409 | ||||||||
\(857\) | 48.1230 | 1.64385 | 0.821926 | − | 0.569595i | \(-0.192900\pi\) | ||||
0.821926 | + | 0.569595i | \(0.192900\pi\) | |||||||
\(858\) | 1.96691 | 0.0671493 | ||||||||
\(859\) | −17.9691 | −0.613098 | −0.306549 | − | 0.951855i | \(-0.599174\pi\) | ||||
−0.306549 | + | 0.951855i | \(0.599174\pi\) | |||||||
\(860\) | −0.911495 | −0.0310817 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 30.1105 | 1.02557 | ||||||||
\(863\) | 33.8047 | 1.15073 | 0.575363 | − | 0.817898i | \(-0.304861\pi\) | ||||
0.575363 | + | 0.817898i | \(0.304861\pi\) | |||||||
\(864\) | −3.50817 | −0.119350 | ||||||||
\(865\) | 4.64920 | 0.158078 | ||||||||
\(866\) | −31.3659 | −1.06586 | ||||||||
\(867\) | 50.8066 | 1.72548 | ||||||||
\(868\) | 1.34531 | 0.0456627 | ||||||||
\(869\) | 6.64737 | 0.225496 | ||||||||
\(870\) | −3.79949 | −0.128815 | ||||||||
\(871\) | −5.11409 | −0.173284 | ||||||||
\(872\) | −4.63567 | −0.156983 | ||||||||
\(873\) | 8.20502 | 0.277698 | ||||||||
\(874\) | −6.78676 | −0.229566 | ||||||||
\(875\) | 34.0460 | 1.15097 | ||||||||
\(876\) | −2.85436 | −0.0964399 | ||||||||
\(877\) | −27.0528 | −0.913507 | −0.456753 | − | 0.889593i | \(-0.650988\pi\) | ||||
−0.456753 | + | 0.889593i | \(0.650988\pi\) | |||||||
\(878\) | 30.5793 | 1.03200 | ||||||||
\(879\) | 69.7143 | 2.35140 | ||||||||
\(880\) | 1.83288 | 0.0617864 | ||||||||
\(881\) | −16.7259 | −0.563510 | −0.281755 | − | 0.959486i | \(-0.590916\pi\) | ||||
−0.281755 | + | 0.959486i | \(0.590916\pi\) | |||||||
\(882\) | 92.9561 | 3.13000 | ||||||||
\(883\) | 25.5414 | 0.859536 | 0.429768 | − | 0.902939i | \(-0.358595\pi\) | ||||
0.429768 | + | 0.902939i | \(0.358595\pi\) | |||||||
\(884\) | 1.02884 | 0.0346036 | ||||||||
\(885\) | −18.4708 | −0.620889 | ||||||||
\(886\) | 32.1116 | 1.07881 | ||||||||
\(887\) | 40.0127 | 1.34349 | 0.671747 | − | 0.740780i | \(-0.265544\pi\) | ||||
0.671747 | + | 0.740780i | \(0.265544\pi\) | |||||||
\(888\) | 52.2582 | 1.75367 | ||||||||
\(889\) | 46.7430 | 1.56771 | ||||||||
\(890\) | 2.23509 | 0.0749203 | ||||||||
\(891\) | −2.08896 | −0.0699827 | ||||||||
\(892\) | −3.31085 | −0.110855 | ||||||||
\(893\) | 17.3967 | 0.582159 | ||||||||
\(894\) | 31.5172 | 1.05409 | ||||||||
\(895\) | −7.08875 | −0.236951 | ||||||||
\(896\) | 59.1597 | 1.97639 | ||||||||
\(897\) | 2.55325 | 0.0852506 | ||||||||
\(898\) | −8.21615 | −0.274177 | ||||||||
\(899\) | 1.87569 | 0.0625577 | ||||||||
\(900\) | −3.51647 | −0.117216 | ||||||||
\(901\) | −32.0769 | −1.06864 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 78.2007 | 2.60236 | ||||||||
\(904\) | −3.12892 | −0.104066 | ||||||||
\(905\) | −14.7545 | −0.490457 | ||||||||
\(906\) | −82.2102 | −2.73125 | ||||||||
\(907\) | −24.3470 | −0.808428 | −0.404214 | − | 0.914664i | \(-0.632455\pi\) | ||||
−0.404214 | + | 0.914664i | \(0.632455\pi\) | |||||||
\(908\) | −5.15418 | −0.171047 | ||||||||
\(909\) | −35.5319 | −1.17852 | ||||||||
\(910\) | −4.86292 | −0.161204 | ||||||||
\(911\) | 24.0894 | 0.798118 | 0.399059 | − | 0.916925i | \(-0.369337\pi\) | ||||
0.399059 | + | 0.916925i | \(0.369337\pi\) | |||||||
\(912\) | 51.1394 | 1.69339 | ||||||||
\(913\) | −7.17154 | −0.237343 | ||||||||
\(914\) | −57.2859 | −1.89485 | ||||||||
\(915\) | −2.88846 | −0.0954895 | ||||||||
\(916\) | −4.28273 | −0.141505 | ||||||||
\(917\) | 3.81141 | 0.125864 | ||||||||
\(918\) | 29.1533 | 0.962202 | ||||||||
\(919\) | 7.19903 | 0.237474 | 0.118737 | − | 0.992926i | \(-0.462115\pi\) | ||||
0.118737 | + | 0.992926i | \(0.462115\pi\) | |||||||
\(920\) | 2.17193 | 0.0716065 | ||||||||
\(921\) | −23.2672 | −0.766679 | ||||||||
\(922\) | 7.53175 | 0.248045 | ||||||||
\(923\) | −0.988875 | −0.0325492 | ||||||||
\(924\) | 1.29638 | 0.0426479 | ||||||||
\(925\) | 31.9343 | 1.04999 | ||||||||
\(926\) | 4.26671 | 0.140213 | ||||||||
\(927\) | −18.1468 | −0.596018 | ||||||||
\(928\) | −1.31634 | −0.0432110 | ||||||||
\(929\) | 6.89462 | 0.226205 | 0.113102 | − | 0.993583i | \(-0.463921\pi\) | ||||
0.113102 | + | 0.993583i | \(0.463921\pi\) | |||||||
\(930\) | −4.68125 | −0.153504 | ||||||||
\(931\) | −65.1768 | −2.13608 | ||||||||
\(932\) | 4.58087 | 0.150051 | ||||||||
\(933\) | −21.7137 | −0.710873 | ||||||||
\(934\) | 54.5325 | 1.78436 | ||||||||
\(935\) | −2.52902 | −0.0827078 | ||||||||
\(936\) | −10.2687 | −0.335642 | ||||||||
\(937\) | −57.9860 | −1.89432 | −0.947160 | − | 0.320762i | \(-0.896061\pi\) | ||||
−0.947160 | + | 0.320762i | \(0.896061\pi\) | |||||||
\(938\) | −38.9993 | −1.27337 | ||||||||
\(939\) | −9.27583 | −0.302705 | ||||||||
\(940\) | 0.581742 | 0.0189743 | ||||||||
\(941\) | 40.7464 | 1.32829 | 0.664147 | − | 0.747602i | \(-0.268795\pi\) | ||||
0.664147 | + | 0.747602i | \(0.268795\pi\) | |||||||
\(942\) | −47.9991 | −1.56389 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −38.5406 | −1.25439 | ||||||||
\(945\) | −11.9096 | −0.387418 | ||||||||
\(946\) | 5.01697 | 0.163116 | ||||||||
\(947\) | −28.0328 | −0.910945 | −0.455472 | − | 0.890250i | \(-0.650530\pi\) | ||||
−0.455472 | + | 0.890250i | \(0.650530\pi\) | |||||||
\(948\) | 6.20203 | 0.201432 | ||||||||
\(949\) | −5.09353 | −0.165343 | ||||||||
\(950\) | 28.5274 | 0.925550 | ||||||||
\(951\) | 75.0294 | 2.43300 | ||||||||
\(952\) | −75.0857 | −2.43354 | ||||||||
\(953\) | 38.5353 | 1.24828 | 0.624140 | − | 0.781312i | \(-0.285449\pi\) | ||||
0.624140 | + | 0.781312i | \(0.285449\pi\) | |||||||
\(954\) | −33.4532 | −1.08309 | ||||||||
\(955\) | −8.72386 | −0.282298 | ||||||||
\(956\) | 4.21584 | 0.136350 | ||||||||
\(957\) | 1.80748 | 0.0584274 | ||||||||
\(958\) | −47.2020 | −1.52503 | ||||||||
\(959\) | 20.1299 | 0.650028 | ||||||||
\(960\) | −14.7907 | −0.477368 | ||||||||
\(961\) | −28.6890 | −0.925452 | ||||||||
\(962\) | −9.74416 | −0.314164 | ||||||||
\(963\) | −52.3049 | −1.68550 | ||||||||
\(964\) | 2.28641 | 0.0736404 | ||||||||
\(965\) | 9.05429 | 0.291468 | ||||||||
\(966\) | 19.4707 | 0.626461 | ||||||||
\(967\) | 42.2286 | 1.35798 | 0.678990 | − | 0.734147i | \(-0.262418\pi\) | ||||
0.678990 | + | 0.734147i | \(0.262418\pi\) | |||||||
\(968\) | 28.6757 | 0.921672 | ||||||||
\(969\) | −70.5624 | −2.26679 | ||||||||
\(970\) | −2.22586 | −0.0714681 | ||||||||
\(971\) | −2.08564 | −0.0669315 | −0.0334657 | − | 0.999440i | \(-0.510654\pi\) | ||||
−0.0334657 | + | 0.999440i | \(0.510654\pi\) | |||||||
\(972\) | −3.81557 | −0.122385 | ||||||||
\(973\) | 23.4984 | 0.753323 | ||||||||
\(974\) | −26.5322 | −0.850146 | ||||||||
\(975\) | −10.7323 | −0.343709 | ||||||||
\(976\) | −6.02697 | −0.192918 | ||||||||
\(977\) | −29.8162 | −0.953904 | −0.476952 | − | 0.878929i | \(-0.658258\pi\) | ||||
−0.476952 | + | 0.878929i | \(0.658258\pi\) | |||||||
\(978\) | 7.95684 | 0.254432 | ||||||||
\(979\) | −1.06326 | −0.0339821 | ||||||||
\(980\) | −2.17949 | −0.0696214 | ||||||||
\(981\) | 7.30756 | 0.233312 | ||||||||
\(982\) | −37.0154 | −1.18121 | ||||||||
\(983\) | 36.2484 | 1.15615 | 0.578073 | − | 0.815985i | \(-0.303805\pi\) | ||||
0.578073 | + | 0.815985i | \(0.303805\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.82557 | 0.249343 | ||||||||
\(986\) | 10.9390 | 0.348367 | ||||||||
\(987\) | −49.9099 | −1.58865 | ||||||||
\(988\) | −0.752330 | −0.0239348 | ||||||||
\(989\) | 6.51253 | 0.207087 | ||||||||
\(990\) | −2.63753 | −0.0838263 | ||||||||
\(991\) | 13.5186 | 0.429433 | 0.214717 | − | 0.976676i | \(-0.431117\pi\) | ||||
0.214717 | + | 0.976676i | \(0.431117\pi\) | |||||||
\(992\) | −1.62183 | −0.0514930 | ||||||||
\(993\) | 60.6821 | 1.92569 | ||||||||
\(994\) | −7.54102 | −0.239187 | ||||||||
\(995\) | 6.51672 | 0.206594 | ||||||||
\(996\) | −6.69109 | −0.212015 | ||||||||
\(997\) | −27.8577 | −0.882262 | −0.441131 | − | 0.897443i | \(-0.645423\pi\) | ||||
−0.441131 | + | 0.897443i | \(0.645423\pi\) | |||||||
\(998\) | 38.2058 | 1.20938 | ||||||||
\(999\) | −23.8640 | −0.755024 |
(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 | 1681.2.a.m.1.18 | 24 | ||
41.17 | odd | 40 | 41.2.g.a.2.2 | ✓ | 24 | ||
41.29 | odd | 40 | 41.2.g.a.21.2 | yes | 24 | ||
41.40 | even | 2 | inner | 1681.2.a.m.1.17 | 24 | ||
123.17 | even | 40 | 369.2.u.a.289.2 | 24 | |||
123.29 | even | 40 | 369.2.u.a.226.2 | 24 | |||
164.99 | even | 40 | 656.2.bs.d.289.3 | 24 | |||
164.111 | even | 40 | 656.2.bs.d.513.3 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
41.2.g.a.2.2 | ✓ | 24 | 41.17 | odd | 40 | ||
41.2.g.a.21.2 | yes | 24 | 41.29 | odd | 40 | ||
369.2.u.a.226.2 | 24 | 123.29 | even | 40 | |||
369.2.u.a.289.2 | 24 | 123.17 | even | 40 | |||
656.2.bs.d.289.3 | 24 | 164.99 | even | 40 | |||
656.2.bs.d.513.3 | 24 | 164.111 | even | 40 | |||
1681.2.a.m.1.17 | 24 | 41.40 | even | 2 | inner | ||
1681.2.a.m.1.18 | 24 | 1.1 | even | 1 | trivial |