Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [671,2,Mod(1,671)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(671, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("671.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 671 = 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 671.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: | \(5.35796197563\) |
Analytic rank: | \(0\) |
Dimension: | \(21\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 671.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.404310 | −0.285891 | −0.142945 | − | 0.989731i | \(-0.545657\pi\) | ||||
−0.142945 | + | 0.989731i | \(0.545657\pi\) | |||||||
\(3\) | 1.66838 | 0.963242 | 0.481621 | − | 0.876380i | \(-0.340048\pi\) | ||||
0.481621 | + | 0.876380i | \(0.340048\pi\) | |||||||
\(4\) | −1.83653 | −0.918267 | ||||||||
\(5\) | 0.0975766 | 0.0436376 | 0.0218188 | − | 0.999762i | \(-0.493054\pi\) | ||||
0.0218188 | + | 0.999762i | \(0.493054\pi\) | |||||||
\(6\) | −0.674545 | −0.275382 | ||||||||
\(7\) | 1.38056 | 0.521804 | 0.260902 | − | 0.965365i | \(-0.415980\pi\) | ||||
0.260902 | + | 0.965365i | \(0.415980\pi\) | |||||||
\(8\) | 1.55115 | 0.548414 | ||||||||
\(9\) | −0.216497 | −0.0721657 | ||||||||
\(10\) | −0.0394512 | −0.0124756 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −3.06404 | −0.884512 | ||||||||
\(13\) | 1.91382 | 0.530799 | 0.265399 | − | 0.964139i | \(-0.414496\pi\) | ||||
0.265399 | + | 0.964139i | \(0.414496\pi\) | |||||||
\(14\) | −0.558177 | −0.149179 | ||||||||
\(15\) | 0.162795 | 0.0420335 | ||||||||
\(16\) | 3.04592 | 0.761480 | ||||||||
\(17\) | 6.39070 | 1.54997 | 0.774986 | − | 0.631979i | \(-0.217757\pi\) | ||||
0.774986 | + | 0.631979i | \(0.217757\pi\) | |||||||
\(18\) | 0.0875320 | 0.0206315 | ||||||||
\(19\) | 2.68107 | 0.615080 | 0.307540 | − | 0.951535i | \(-0.400494\pi\) | ||||
0.307540 | + | 0.951535i | \(0.400494\pi\) | |||||||
\(20\) | −0.179203 | −0.0400709 | ||||||||
\(21\) | 2.30331 | 0.502624 | ||||||||
\(22\) | 0.404310 | 0.0861993 | ||||||||
\(23\) | 3.27987 | 0.683901 | 0.341951 | − | 0.939718i | \(-0.388912\pi\) | ||||
0.341951 | + | 0.939718i | \(0.388912\pi\) | |||||||
\(24\) | 2.58791 | 0.528256 | ||||||||
\(25\) | −4.99048 | −0.998096 | ||||||||
\(26\) | −0.773778 | −0.151750 | ||||||||
\(27\) | −5.36635 | −1.03275 | ||||||||
\(28\) | −2.53545 | −0.479156 | ||||||||
\(29\) | 3.68854 | 0.684945 | 0.342472 | − | 0.939528i | \(-0.388736\pi\) | ||||
0.342472 | + | 0.939528i | \(0.388736\pi\) | |||||||
\(30\) | −0.0658198 | −0.0120170 | ||||||||
\(31\) | 8.77643 | 1.57629 | 0.788147 | − | 0.615487i | \(-0.211041\pi\) | ||||
0.788147 | + | 0.615487i | \(0.211041\pi\) | |||||||
\(32\) | −4.33380 | −0.766114 | ||||||||
\(33\) | −1.66838 | −0.290428 | ||||||||
\(34\) | −2.58383 | −0.443122 | ||||||||
\(35\) | 0.134711 | 0.0227703 | ||||||||
\(36\) | 0.397604 | 0.0662674 | ||||||||
\(37\) | 8.11523 | 1.33414 | 0.667068 | − | 0.744997i | \(-0.267549\pi\) | ||||
0.667068 | + | 0.744997i | \(0.267549\pi\) | |||||||
\(38\) | −1.08399 | −0.175846 | ||||||||
\(39\) | 3.19299 | 0.511287 | ||||||||
\(40\) | 0.151356 | 0.0239315 | ||||||||
\(41\) | −7.68669 | −1.20046 | −0.600230 | − | 0.799827i | \(-0.704924\pi\) | ||||
−0.600230 | + | 0.799827i | \(0.704924\pi\) | |||||||
\(42\) | −0.931253 | −0.143695 | ||||||||
\(43\) | 0.587590 | 0.0896067 | 0.0448033 | − | 0.998996i | \(-0.485734\pi\) | ||||
0.0448033 | + | 0.998996i | \(0.485734\pi\) | |||||||
\(44\) | 1.83653 | 0.276868 | ||||||||
\(45\) | −0.0211251 | −0.00314914 | ||||||||
\(46\) | −1.32609 | −0.195521 | ||||||||
\(47\) | −3.82618 | −0.558106 | −0.279053 | − | 0.960276i | \(-0.590020\pi\) | ||||
−0.279053 | + | 0.960276i | \(0.590020\pi\) | |||||||
\(48\) | 5.08176 | 0.733489 | ||||||||
\(49\) | −5.09404 | −0.727720 | ||||||||
\(50\) | 2.01770 | 0.285346 | ||||||||
\(51\) | 10.6621 | 1.49300 | ||||||||
\(52\) | −3.51480 | −0.487415 | ||||||||
\(53\) | 12.1754 | 1.67242 | 0.836210 | − | 0.548410i | \(-0.184767\pi\) | ||||
0.836210 | + | 0.548410i | \(0.184767\pi\) | |||||||
\(54\) | 2.16967 | 0.295255 | ||||||||
\(55\) | −0.0975766 | −0.0131572 | ||||||||
\(56\) | 2.14146 | 0.286165 | ||||||||
\(57\) | 4.47306 | 0.592471 | ||||||||
\(58\) | −1.49132 | −0.195819 | ||||||||
\(59\) | 4.38430 | 0.570787 | 0.285394 | − | 0.958410i | \(-0.407876\pi\) | ||||
0.285394 | + | 0.958410i | \(0.407876\pi\) | |||||||
\(60\) | −0.298979 | −0.0385980 | ||||||||
\(61\) | 1.00000 | 0.128037 | ||||||||
\(62\) | −3.54840 | −0.450648 | ||||||||
\(63\) | −0.298888 | −0.0376564 | ||||||||
\(64\) | −4.33964 | −0.542455 | ||||||||
\(65\) | 0.186744 | 0.0231628 | ||||||||
\(66\) | 0.674545 | 0.0830307 | ||||||||
\(67\) | 2.09197 | 0.255575 | 0.127787 | − | 0.991802i | \(-0.459212\pi\) | ||||
0.127787 | + | 0.991802i | \(0.459212\pi\) | |||||||
\(68\) | −11.7367 | −1.42329 | ||||||||
\(69\) | 5.47209 | 0.658762 | ||||||||
\(70\) | −0.0544650 | −0.00650981 | ||||||||
\(71\) | −7.30897 | −0.867416 | −0.433708 | − | 0.901054i | \(-0.642795\pi\) | ||||
−0.433708 | + | 0.901054i | \(0.642795\pi\) | |||||||
\(72\) | −0.335820 | −0.0395767 | ||||||||
\(73\) | 7.39795 | 0.865865 | 0.432933 | − | 0.901426i | \(-0.357479\pi\) | ||||
0.432933 | + | 0.901426i | \(0.357479\pi\) | |||||||
\(74\) | −3.28107 | −0.381417 | ||||||||
\(75\) | −8.32603 | −0.961407 | ||||||||
\(76\) | −4.92388 | −0.564807 | ||||||||
\(77\) | −1.38056 | −0.157330 | ||||||||
\(78\) | −1.29096 | −0.146172 | ||||||||
\(79\) | −15.9826 | −1.79819 | −0.899093 | − | 0.437757i | \(-0.855773\pi\) | ||||
−0.899093 | + | 0.437757i | \(0.855773\pi\) | |||||||
\(80\) | 0.297210 | 0.0332291 | ||||||||
\(81\) | −8.30364 | −0.922626 | ||||||||
\(82\) | 3.10781 | 0.343200 | ||||||||
\(83\) | −0.649661 | −0.0713096 | −0.0356548 | − | 0.999364i | \(-0.511352\pi\) | ||||
−0.0356548 | + | 0.999364i | \(0.511352\pi\) | |||||||
\(84\) | −4.23011 | −0.461543 | ||||||||
\(85\) | 0.623582 | 0.0676370 | ||||||||
\(86\) | −0.237569 | −0.0256177 | ||||||||
\(87\) | 6.15390 | 0.659767 | ||||||||
\(88\) | −1.55115 | −0.165353 | ||||||||
\(89\) | −8.11324 | −0.860001 | −0.430001 | − | 0.902829i | \(-0.641487\pi\) | ||||
−0.430001 | + | 0.902829i | \(0.641487\pi\) | |||||||
\(90\) | 0.00854108 | 0.000900309 0 | ||||||||
\(91\) | 2.64215 | 0.276973 | ||||||||
\(92\) | −6.02360 | −0.628004 | ||||||||
\(93\) | 14.6425 | 1.51835 | ||||||||
\(94\) | 1.54696 | 0.159557 | ||||||||
\(95\) | 0.261610 | 0.0268406 | ||||||||
\(96\) | −7.23044 | −0.737953 | ||||||||
\(97\) | 6.04986 | 0.614271 | 0.307135 | − | 0.951666i | \(-0.400630\pi\) | ||||
0.307135 | + | 0.951666i | \(0.400630\pi\) | |||||||
\(98\) | 2.05957 | 0.208048 | ||||||||
\(99\) | 0.216497 | 0.0217588 | ||||||||
\(100\) | 9.16518 | 0.916518 | ||||||||
\(101\) | −13.4229 | −1.33563 | −0.667815 | − | 0.744327i | \(-0.732770\pi\) | ||||
−0.667815 | + | 0.744327i | \(0.732770\pi\) | |||||||
\(102\) | −4.31081 | −0.426834 | ||||||||
\(103\) | 13.3184 | 1.31230 | 0.656151 | − | 0.754630i | \(-0.272183\pi\) | ||||
0.656151 | + | 0.754630i | \(0.272183\pi\) | |||||||
\(104\) | 2.96863 | 0.291098 | ||||||||
\(105\) | 0.224749 | 0.0219333 | ||||||||
\(106\) | −4.92264 | −0.478129 | ||||||||
\(107\) | −11.4259 | −1.10458 | −0.552290 | − | 0.833652i | \(-0.686246\pi\) | ||||
−0.552290 | + | 0.833652i | \(0.686246\pi\) | |||||||
\(108\) | 9.85548 | 0.948344 | ||||||||
\(109\) | −19.4090 | −1.85904 | −0.929521 | − | 0.368768i | \(-0.879780\pi\) | ||||
−0.929521 | + | 0.368768i | \(0.879780\pi\) | |||||||
\(110\) | 0.0394512 | 0.00376153 | ||||||||
\(111\) | 13.5393 | 1.28510 | ||||||||
\(112\) | 4.20509 | 0.397344 | ||||||||
\(113\) | 11.7630 | 1.10657 | 0.553286 | − | 0.832992i | \(-0.313374\pi\) | ||||
0.553286 | + | 0.832992i | \(0.313374\pi\) | |||||||
\(114\) | −1.80850 | −0.169382 | ||||||||
\(115\) | 0.320039 | 0.0298438 | ||||||||
\(116\) | −6.77413 | −0.628962 | ||||||||
\(117\) | −0.414337 | −0.0383055 | ||||||||
\(118\) | −1.77262 | −0.163183 | ||||||||
\(119\) | 8.82277 | 0.808782 | ||||||||
\(120\) | 0.252520 | 0.0230518 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −0.404310 | −0.0366045 | ||||||||
\(123\) | −12.8244 | −1.15633 | ||||||||
\(124\) | −16.1182 | −1.44746 | ||||||||
\(125\) | −0.974837 | −0.0871921 | ||||||||
\(126\) | 0.120844 | 0.0107656 | ||||||||
\(127\) | 12.7715 | 1.13329 | 0.566645 | − | 0.823962i | \(-0.308241\pi\) | ||||
0.566645 | + | 0.823962i | \(0.308241\pi\) | |||||||
\(128\) | 10.4222 | 0.921197 | ||||||||
\(129\) | 0.980326 | 0.0863129 | ||||||||
\(130\) | −0.0755026 | −0.00662202 | ||||||||
\(131\) | 11.1301 | 0.972440 | 0.486220 | − | 0.873836i | \(-0.338375\pi\) | ||||
0.486220 | + | 0.873836i | \(0.338375\pi\) | |||||||
\(132\) | 3.06404 | 0.266691 | ||||||||
\(133\) | 3.70139 | 0.320952 | ||||||||
\(134\) | −0.845806 | −0.0730665 | ||||||||
\(135\) | −0.523630 | −0.0450669 | ||||||||
\(136\) | 9.91293 | 0.850027 | ||||||||
\(137\) | −6.41607 | −0.548162 | −0.274081 | − | 0.961707i | \(-0.588374\pi\) | ||||
−0.274081 | + | 0.961707i | \(0.588374\pi\) | |||||||
\(138\) | −2.21242 | −0.188334 | ||||||||
\(139\) | 10.3340 | 0.876518 | 0.438259 | − | 0.898849i | \(-0.355595\pi\) | ||||
0.438259 | + | 0.898849i | \(0.355595\pi\) | |||||||
\(140\) | −0.247401 | −0.0209092 | ||||||||
\(141\) | −6.38354 | −0.537591 | ||||||||
\(142\) | 2.95509 | 0.247986 | ||||||||
\(143\) | −1.91382 | −0.160042 | ||||||||
\(144\) | −0.659433 | −0.0549527 | ||||||||
\(145\) | 0.359915 | 0.0298893 | ||||||||
\(146\) | −2.99107 | −0.247543 | ||||||||
\(147\) | −8.49881 | −0.700970 | ||||||||
\(148\) | −14.9039 | −1.22509 | ||||||||
\(149\) | −10.9469 | −0.896806 | −0.448403 | − | 0.893832i | \(-0.648007\pi\) | ||||
−0.448403 | + | 0.893832i | \(0.648007\pi\) | |||||||
\(150\) | 3.36630 | 0.274857 | ||||||||
\(151\) | −14.0261 | −1.14143 | −0.570715 | − | 0.821149i | \(-0.693334\pi\) | ||||
−0.570715 | + | 0.821149i | \(0.693334\pi\) | |||||||
\(152\) | 4.15875 | 0.337319 | ||||||||
\(153\) | −1.38357 | −0.111855 | ||||||||
\(154\) | 0.558177 | 0.0449792 | ||||||||
\(155\) | 0.856375 | 0.0687857 | ||||||||
\(156\) | −5.86403 | −0.469498 | ||||||||
\(157\) | −20.5792 | −1.64240 | −0.821201 | − | 0.570639i | \(-0.806695\pi\) | ||||
−0.821201 | + | 0.570639i | \(0.806695\pi\) | |||||||
\(158\) | 6.46194 | 0.514085 | ||||||||
\(159\) | 20.3132 | 1.61094 | ||||||||
\(160\) | −0.422877 | −0.0334314 | ||||||||
\(161\) | 4.52808 | 0.356863 | ||||||||
\(162\) | 3.35725 | 0.263770 | ||||||||
\(163\) | 1.51365 | 0.118559 | 0.0592793 | − | 0.998241i | \(-0.481120\pi\) | ||||
0.0592793 | + | 0.998241i | \(0.481120\pi\) | |||||||
\(164\) | 14.1169 | 1.10234 | ||||||||
\(165\) | −0.162795 | −0.0126736 | ||||||||
\(166\) | 0.262665 | 0.0203867 | ||||||||
\(167\) | −16.5914 | −1.28388 | −0.641941 | − | 0.766754i | \(-0.721870\pi\) | ||||
−0.641941 | + | 0.766754i | \(0.721870\pi\) | |||||||
\(168\) | 3.57278 | 0.275646 | ||||||||
\(169\) | −9.33729 | −0.718253 | ||||||||
\(170\) | −0.252121 | −0.0193368 | ||||||||
\(171\) | −0.580444 | −0.0443877 | ||||||||
\(172\) | −1.07913 | −0.0822828 | ||||||||
\(173\) | −17.7599 | −1.35026 | −0.675128 | − | 0.737700i | \(-0.735912\pi\) | ||||
−0.675128 | + | 0.737700i | \(0.735912\pi\) | |||||||
\(174\) | −2.48809 | −0.188621 | ||||||||
\(175\) | −6.88968 | −0.520811 | ||||||||
\(176\) | −3.04592 | −0.229595 | ||||||||
\(177\) | 7.31469 | 0.549806 | ||||||||
\(178\) | 3.28027 | 0.245866 | ||||||||
\(179\) | −19.8327 | −1.48236 | −0.741181 | − | 0.671305i | \(-0.765734\pi\) | ||||
−0.741181 | + | 0.671305i | \(0.765734\pi\) | |||||||
\(180\) | 0.0387969 | 0.00289175 | ||||||||
\(181\) | 7.18951 | 0.534392 | 0.267196 | − | 0.963642i | \(-0.413903\pi\) | ||||
0.267196 | + | 0.963642i | \(0.413903\pi\) | |||||||
\(182\) | −1.06825 | −0.0791840 | ||||||||
\(183\) | 1.66838 | 0.123330 | ||||||||
\(184\) | 5.08758 | 0.375061 | ||||||||
\(185\) | 0.791857 | 0.0582185 | ||||||||
\(186\) | −5.92010 | −0.434083 | ||||||||
\(187\) | −6.39070 | −0.467334 | ||||||||
\(188\) | 7.02691 | 0.512490 | ||||||||
\(189\) | −7.40859 | −0.538896 | ||||||||
\(190\) | −0.105772 | −0.00767348 | ||||||||
\(191\) | −10.4136 | −0.753503 | −0.376751 | − | 0.926314i | \(-0.622959\pi\) | ||||
−0.376751 | + | 0.926314i | \(0.622959\pi\) | |||||||
\(192\) | −7.24018 | −0.522515 | ||||||||
\(193\) | −6.92074 | −0.498166 | −0.249083 | − | 0.968482i | \(-0.580129\pi\) | ||||
−0.249083 | + | 0.968482i | \(0.580129\pi\) | |||||||
\(194\) | −2.44602 | −0.175614 | ||||||||
\(195\) | 0.311561 | 0.0223113 | ||||||||
\(196\) | 9.35537 | 0.668241 | ||||||||
\(197\) | 5.12309 | 0.365005 | 0.182502 | − | 0.983205i | \(-0.441580\pi\) | ||||
0.182502 | + | 0.983205i | \(0.441580\pi\) | |||||||
\(198\) | −0.0875320 | −0.00622063 | ||||||||
\(199\) | −9.17574 | −0.650451 | −0.325226 | − | 0.945636i | \(-0.605440\pi\) | ||||
−0.325226 | + | 0.945636i | \(0.605440\pi\) | |||||||
\(200\) | −7.74098 | −0.547370 | ||||||||
\(201\) | 3.49021 | 0.246180 | ||||||||
\(202\) | 5.42702 | 0.381844 | ||||||||
\(203\) | 5.09227 | 0.357407 | ||||||||
\(204\) | −19.5814 | −1.37097 | ||||||||
\(205\) | −0.750041 | −0.0523852 | ||||||||
\(206\) | −5.38477 | −0.375175 | ||||||||
\(207\) | −0.710083 | −0.0493542 | ||||||||
\(208\) | 5.82935 | 0.404193 | ||||||||
\(209\) | −2.68107 | −0.185454 | ||||||||
\(210\) | −0.0908685 | −0.00627052 | ||||||||
\(211\) | 10.0749 | 0.693588 | 0.346794 | − | 0.937941i | \(-0.387270\pi\) | ||||
0.346794 | + | 0.937941i | \(0.387270\pi\) | |||||||
\(212\) | −22.3605 | −1.53573 | ||||||||
\(213\) | −12.1942 | −0.835531 | ||||||||
\(214\) | 4.61959 | 0.315789 | ||||||||
\(215\) | 0.0573350 | 0.00391022 | ||||||||
\(216\) | −8.32402 | −0.566378 | ||||||||
\(217\) | 12.1164 | 0.822517 | ||||||||
\(218\) | 7.84725 | 0.531483 | ||||||||
\(219\) | 12.3426 | 0.834037 | ||||||||
\(220\) | 0.179203 | 0.0120818 | ||||||||
\(221\) | 12.2307 | 0.822723 | ||||||||
\(222\) | −5.47409 | −0.367397 | ||||||||
\(223\) | 25.6563 | 1.71807 | 0.859037 | − | 0.511913i | \(-0.171063\pi\) | ||||
0.859037 | + | 0.511913i | \(0.171063\pi\) | |||||||
\(224\) | −5.98309 | −0.399762 | ||||||||
\(225\) | 1.08042 | 0.0720283 | ||||||||
\(226\) | −4.75591 | −0.316358 | ||||||||
\(227\) | −22.7936 | −1.51286 | −0.756431 | − | 0.654074i | \(-0.773059\pi\) | ||||
−0.756431 | + | 0.654074i | \(0.773059\pi\) | |||||||
\(228\) | −8.21491 | −0.544046 | ||||||||
\(229\) | 22.0797 | 1.45907 | 0.729535 | − | 0.683943i | \(-0.239736\pi\) | ||||
0.729535 | + | 0.683943i | \(0.239736\pi\) | |||||||
\(230\) | −0.129395 | −0.00853206 | ||||||||
\(231\) | −2.30331 | −0.151547 | ||||||||
\(232\) | 5.72148 | 0.375634 | ||||||||
\(233\) | 24.2302 | 1.58737 | 0.793686 | − | 0.608327i | \(-0.208159\pi\) | ||||
0.793686 | + | 0.608327i | \(0.208159\pi\) | |||||||
\(234\) | 0.167521 | 0.0109512 | ||||||||
\(235\) | −0.373346 | −0.0243544 | ||||||||
\(236\) | −8.05191 | −0.524135 | ||||||||
\(237\) | −26.6652 | −1.73209 | ||||||||
\(238\) | −3.56714 | −0.231223 | ||||||||
\(239\) | −22.4004 | −1.44896 | −0.724481 | − | 0.689295i | \(-0.757920\pi\) | ||||
−0.724481 | + | 0.689295i | \(0.757920\pi\) | |||||||
\(240\) | 0.495861 | 0.0320077 | ||||||||
\(241\) | 17.1080 | 1.10202 | 0.551011 | − | 0.834498i | \(-0.314242\pi\) | ||||
0.551011 | + | 0.834498i | \(0.314242\pi\) | |||||||
\(242\) | −0.404310 | −0.0259901 | ||||||||
\(243\) | 2.24540 | 0.144042 | ||||||||
\(244\) | −1.83653 | −0.117572 | ||||||||
\(245\) | −0.497059 | −0.0317559 | ||||||||
\(246\) | 5.18502 | 0.330585 | ||||||||
\(247\) | 5.13109 | 0.326484 | ||||||||
\(248\) | 13.6136 | 0.864463 | ||||||||
\(249\) | −1.08388 | −0.0686883 | ||||||||
\(250\) | 0.394137 | 0.0249274 | ||||||||
\(251\) | −21.1591 | −1.33555 | −0.667774 | − | 0.744364i | \(-0.732753\pi\) | ||||
−0.667774 | + | 0.744364i | \(0.732753\pi\) | |||||||
\(252\) | 0.548918 | 0.0345786 | ||||||||
\(253\) | −3.27987 | −0.206204 | ||||||||
\(254\) | −5.16366 | −0.323997 | ||||||||
\(255\) | 1.04037 | 0.0651508 | ||||||||
\(256\) | 4.46549 | 0.279093 | ||||||||
\(257\) | 18.3294 | 1.14336 | 0.571680 | − | 0.820477i | \(-0.306292\pi\) | ||||
0.571680 | + | 0.820477i | \(0.306292\pi\) | |||||||
\(258\) | −0.396356 | −0.0246760 | ||||||||
\(259\) | 11.2036 | 0.696158 | ||||||||
\(260\) | −0.342962 | −0.0212696 | ||||||||
\(261\) | −0.798558 | −0.0494295 | ||||||||
\(262\) | −4.50001 | −0.278012 | ||||||||
\(263\) | −7.41077 | −0.456968 | −0.228484 | − | 0.973548i | \(-0.573377\pi\) | ||||
−0.228484 | + | 0.973548i | \(0.573377\pi\) | |||||||
\(264\) | −2.58791 | −0.159275 | ||||||||
\(265\) | 1.18803 | 0.0729803 | ||||||||
\(266\) | −1.49651 | −0.0917570 | ||||||||
\(267\) | −13.5360 | −0.828389 | ||||||||
\(268\) | −3.84197 | −0.234686 | ||||||||
\(269\) | −28.5189 | −1.73883 | −0.869415 | − | 0.494082i | \(-0.835504\pi\) | ||||
−0.869415 | + | 0.494082i | \(0.835504\pi\) | |||||||
\(270\) | 0.211709 | 0.0128842 | ||||||||
\(271\) | 23.7868 | 1.44495 | 0.722473 | − | 0.691399i | \(-0.243005\pi\) | ||||
0.722473 | + | 0.691399i | \(0.243005\pi\) | |||||||
\(272\) | 19.4655 | 1.18027 | ||||||||
\(273\) | 4.40813 | 0.266792 | ||||||||
\(274\) | 2.59408 | 0.156714 | ||||||||
\(275\) | 4.99048 | 0.300937 | ||||||||
\(276\) | −10.0497 | −0.604919 | ||||||||
\(277\) | 10.2932 | 0.618460 | 0.309230 | − | 0.950987i | \(-0.399929\pi\) | ||||
0.309230 | + | 0.950987i | \(0.399929\pi\) | |||||||
\(278\) | −4.17814 | −0.250588 | ||||||||
\(279\) | −1.90007 | −0.113754 | ||||||||
\(280\) | 0.208957 | 0.0124876 | ||||||||
\(281\) | −20.1829 | −1.20401 | −0.602004 | − | 0.798493i | \(-0.705631\pi\) | ||||
−0.602004 | + | 0.798493i | \(0.705631\pi\) | |||||||
\(282\) | 2.58093 | 0.153692 | ||||||||
\(283\) | 5.16490 | 0.307021 | 0.153511 | − | 0.988147i | \(-0.450942\pi\) | ||||
0.153511 | + | 0.988147i | \(0.450942\pi\) | |||||||
\(284\) | 13.4232 | 0.796519 | ||||||||
\(285\) | 0.436465 | 0.0258540 | ||||||||
\(286\) | 0.773778 | 0.0457545 | ||||||||
\(287\) | −10.6120 | −0.626405 | ||||||||
\(288\) | 0.938255 | 0.0552872 | ||||||||
\(289\) | 23.8410 | 1.40241 | ||||||||
\(290\) | −0.145517 | −0.00854508 | ||||||||
\(291\) | 10.0935 | 0.591691 | ||||||||
\(292\) | −13.5866 | −0.795095 | ||||||||
\(293\) | 1.92764 | 0.112614 | 0.0563071 | − | 0.998413i | \(-0.482067\pi\) | ||||
0.0563071 | + | 0.998413i | \(0.482067\pi\) | |||||||
\(294\) | 3.43616 | 0.200401 | ||||||||
\(295\) | 0.427805 | 0.0249078 | ||||||||
\(296\) | 12.5879 | 0.731660 | ||||||||
\(297\) | 5.36635 | 0.311387 | ||||||||
\(298\) | 4.42595 | 0.256388 | ||||||||
\(299\) | 6.27710 | 0.363014 | ||||||||
\(300\) | 15.2910 | 0.882828 | ||||||||
\(301\) | 0.811206 | 0.0467572 | ||||||||
\(302\) | 5.67090 | 0.326324 | ||||||||
\(303\) | −22.3946 | −1.28653 | ||||||||
\(304\) | 8.16633 | 0.468371 | ||||||||
\(305\) | 0.0975766 | 0.00558722 | ||||||||
\(306\) | 0.559391 | 0.0319782 | ||||||||
\(307\) | 11.9619 | 0.682699 | 0.341350 | − | 0.939936i | \(-0.389116\pi\) | ||||
0.341350 | + | 0.939936i | \(0.389116\pi\) | |||||||
\(308\) | 2.53545 | 0.144471 | ||||||||
\(309\) | 22.2202 | 1.26406 | ||||||||
\(310\) | −0.346241 | −0.0196652 | ||||||||
\(311\) | 8.08067 | 0.458213 | 0.229106 | − | 0.973401i | \(-0.426420\pi\) | ||||
0.229106 | + | 0.973401i | \(0.426420\pi\) | |||||||
\(312\) | 4.95280 | 0.280397 | ||||||||
\(313\) | 29.4242 | 1.66316 | 0.831578 | − | 0.555408i | \(-0.187438\pi\) | ||||
0.831578 | + | 0.555408i | \(0.187438\pi\) | |||||||
\(314\) | 8.32040 | 0.469547 | ||||||||
\(315\) | −0.0291645 | −0.00164323 | ||||||||
\(316\) | 29.3526 | 1.65121 | ||||||||
\(317\) | 22.5448 | 1.26624 | 0.633120 | − | 0.774054i | \(-0.281774\pi\) | ||||
0.633120 | + | 0.774054i | \(0.281774\pi\) | |||||||
\(318\) | −8.21285 | −0.460554 | ||||||||
\(319\) | −3.68854 | −0.206519 | ||||||||
\(320\) | −0.423447 | −0.0236714 | ||||||||
\(321\) | −19.0627 | −1.06398 | ||||||||
\(322\) | −1.83075 | −0.102024 | ||||||||
\(323\) | 17.1339 | 0.953357 | ||||||||
\(324\) | 15.2499 | 0.847217 | ||||||||
\(325\) | −9.55089 | −0.529788 | ||||||||
\(326\) | −0.611986 | −0.0338948 | ||||||||
\(327\) | −32.3816 | −1.79071 | ||||||||
\(328\) | −11.9232 | −0.658350 | ||||||||
\(329\) | −5.28229 | −0.291222 | ||||||||
\(330\) | 0.0658198 | 0.00362326 | ||||||||
\(331\) | 11.1529 | 0.613020 | 0.306510 | − | 0.951867i | \(-0.400839\pi\) | ||||
0.306510 | + | 0.951867i | \(0.400839\pi\) | |||||||
\(332\) | 1.19312 | 0.0654812 | ||||||||
\(333\) | −1.75692 | −0.0962789 | ||||||||
\(334\) | 6.70808 | 0.367050 | ||||||||
\(335\) | 0.204127 | 0.0111527 | ||||||||
\(336\) | 7.01570 | 0.382738 | ||||||||
\(337\) | −14.9848 | −0.816274 | −0.408137 | − | 0.912921i | \(-0.633821\pi\) | ||||
−0.408137 | + | 0.912921i | \(0.633821\pi\) | |||||||
\(338\) | 3.77516 | 0.205342 | ||||||||
\(339\) | 19.6252 | 1.06590 | ||||||||
\(340\) | −1.14523 | −0.0621088 | ||||||||
\(341\) | −8.77643 | −0.475271 | ||||||||
\(342\) | 0.234680 | 0.0126900 | ||||||||
\(343\) | −16.6966 | −0.901532 | ||||||||
\(344\) | 0.911441 | 0.0491416 | ||||||||
\(345\) | 0.533948 | 0.0287468 | ||||||||
\(346\) | 7.18049 | 0.386026 | ||||||||
\(347\) | 14.5439 | 0.780760 | 0.390380 | − | 0.920654i | \(-0.372344\pi\) | ||||
0.390380 | + | 0.920654i | \(0.372344\pi\) | |||||||
\(348\) | −11.3018 | −0.605842 | ||||||||
\(349\) | 15.7833 | 0.844863 | 0.422431 | − | 0.906395i | \(-0.361177\pi\) | ||||
0.422431 | + | 0.906395i | \(0.361177\pi\) | |||||||
\(350\) | 2.78557 | 0.148895 | ||||||||
\(351\) | −10.2702 | −0.548185 | ||||||||
\(352\) | 4.33380 | 0.230992 | ||||||||
\(353\) | 11.2517 | 0.598869 | 0.299434 | − | 0.954117i | \(-0.403202\pi\) | ||||
0.299434 | + | 0.954117i | \(0.403202\pi\) | |||||||
\(354\) | −2.95741 | −0.157184 | ||||||||
\(355\) | −0.713185 | −0.0378519 | ||||||||
\(356\) | 14.9002 | 0.789710 | ||||||||
\(357\) | 14.7198 | 0.779052 | ||||||||
\(358\) | 8.01855 | 0.423793 | ||||||||
\(359\) | −10.7378 | −0.566721 | −0.283360 | − | 0.959013i | \(-0.591449\pi\) | ||||
−0.283360 | + | 0.959013i | \(0.591449\pi\) | |||||||
\(360\) | −0.0327681 | −0.00172703 | ||||||||
\(361\) | −11.8119 | −0.621677 | ||||||||
\(362\) | −2.90679 | −0.152778 | ||||||||
\(363\) | 1.66838 | 0.0875674 | ||||||||
\(364\) | −4.85240 | −0.254335 | ||||||||
\(365\) | 0.721867 | 0.0377843 | ||||||||
\(366\) | −0.674545 | −0.0352590 | ||||||||
\(367\) | −31.2795 | −1.63278 | −0.816388 | − | 0.577503i | \(-0.804027\pi\) | ||||
−0.816388 | + | 0.577503i | \(0.804027\pi\) | |||||||
\(368\) | 9.99024 | 0.520777 | ||||||||
\(369\) | 1.66415 | 0.0866320 | ||||||||
\(370\) | −0.320156 | −0.0166441 | ||||||||
\(371\) | 16.8089 | 0.872676 | ||||||||
\(372\) | −26.8914 | −1.39425 | ||||||||
\(373\) | −6.69105 | −0.346449 | −0.173225 | − | 0.984882i | \(-0.555419\pi\) | ||||
−0.173225 | + | 0.984882i | \(0.555419\pi\) | |||||||
\(374\) | 2.58383 | 0.133606 | ||||||||
\(375\) | −1.62640 | −0.0839870 | ||||||||
\(376\) | −5.93498 | −0.306073 | ||||||||
\(377\) | 7.05921 | 0.363568 | ||||||||
\(378\) | 2.99537 | 0.154065 | ||||||||
\(379\) | 17.4406 | 0.895866 | 0.447933 | − | 0.894067i | \(-0.352160\pi\) | ||||
0.447933 | + | 0.894067i | \(0.352160\pi\) | |||||||
\(380\) | −0.480455 | −0.0246468 | ||||||||
\(381\) | 21.3078 | 1.09163 | ||||||||
\(382\) | 4.21033 | 0.215419 | ||||||||
\(383\) | −11.5754 | −0.591473 | −0.295736 | − | 0.955270i | \(-0.595565\pi\) | ||||
−0.295736 | + | 0.955270i | \(0.595565\pi\) | |||||||
\(384\) | 17.3882 | 0.887335 | ||||||||
\(385\) | −0.134711 | −0.00686550 | ||||||||
\(386\) | 2.79813 | 0.142421 | ||||||||
\(387\) | −0.127212 | −0.00646653 | ||||||||
\(388\) | −11.1108 | −0.564064 | ||||||||
\(389\) | 14.2848 | 0.724266 | 0.362133 | − | 0.932126i | \(-0.382049\pi\) | ||||
0.362133 | + | 0.932126i | \(0.382049\pi\) | |||||||
\(390\) | −0.125967 | −0.00637860 | ||||||||
\(391\) | 20.9607 | 1.06003 | ||||||||
\(392\) | −7.90162 | −0.399092 | ||||||||
\(393\) | 18.5692 | 0.936695 | ||||||||
\(394\) | −2.07132 | −0.104352 | ||||||||
\(395\) | −1.55953 | −0.0784685 | ||||||||
\(396\) | −0.397604 | −0.0199804 | ||||||||
\(397\) | 27.6351 | 1.38696 | 0.693482 | − | 0.720474i | \(-0.256075\pi\) | ||||
0.693482 | + | 0.720474i | \(0.256075\pi\) | |||||||
\(398\) | 3.70985 | 0.185958 | ||||||||
\(399\) | 6.17534 | 0.309154 | ||||||||
\(400\) | −15.2006 | −0.760030 | ||||||||
\(401\) | 24.1900 | 1.20799 | 0.603996 | − | 0.796987i | \(-0.293574\pi\) | ||||
0.603996 | + | 0.796987i | \(0.293574\pi\) | |||||||
\(402\) | −1.41113 | −0.0703807 | ||||||||
\(403\) | 16.7965 | 0.836695 | ||||||||
\(404\) | 24.6516 | 1.22646 | ||||||||
\(405\) | −0.810241 | −0.0402612 | ||||||||
\(406\) | −2.05886 | −0.102179 | ||||||||
\(407\) | −8.11523 | −0.402257 | ||||||||
\(408\) | 16.5386 | 0.818781 | ||||||||
\(409\) | 7.93089 | 0.392157 | 0.196079 | − | 0.980588i | \(-0.437179\pi\) | ||||
0.196079 | + | 0.980588i | \(0.437179\pi\) | |||||||
\(410\) | 0.303250 | 0.0149764 | ||||||||
\(411\) | −10.7045 | −0.528012 | ||||||||
\(412\) | −24.4597 | −1.20504 | ||||||||
\(413\) | 6.05281 | 0.297839 | ||||||||
\(414\) | 0.287094 | 0.0141099 | ||||||||
\(415\) | −0.0633917 | −0.00311178 | ||||||||
\(416\) | −8.29412 | −0.406653 | ||||||||
\(417\) | 17.2411 | 0.844299 | ||||||||
\(418\) | 1.08399 | 0.0530195 | ||||||||
\(419\) | 10.8385 | 0.529496 | 0.264748 | − | 0.964318i | \(-0.414711\pi\) | ||||
0.264748 | + | 0.964318i | \(0.414711\pi\) | |||||||
\(420\) | −0.412759 | −0.0201406 | ||||||||
\(421\) | −10.7357 | −0.523228 | −0.261614 | − | 0.965173i | \(-0.584255\pi\) | ||||
−0.261614 | + | 0.965173i | \(0.584255\pi\) | |||||||
\(422\) | −4.07341 | −0.198290 | ||||||||
\(423\) | 0.828357 | 0.0402761 | ||||||||
\(424\) | 18.8859 | 0.917179 | ||||||||
\(425\) | −31.8926 | −1.54702 | ||||||||
\(426\) | 4.93023 | 0.238870 | ||||||||
\(427\) | 1.38056 | 0.0668102 | ||||||||
\(428\) | 20.9840 | 1.01430 | ||||||||
\(429\) | −3.19299 | −0.154159 | ||||||||
\(430\) | −0.0231812 | −0.00111789 | ||||||||
\(431\) | −30.2153 | −1.45542 | −0.727710 | − | 0.685885i | \(-0.759415\pi\) | ||||
−0.727710 | + | 0.685885i | \(0.759415\pi\) | |||||||
\(432\) | −16.3455 | −0.786422 | ||||||||
\(433\) | 17.6507 | 0.848237 | 0.424119 | − | 0.905607i | \(-0.360584\pi\) | ||||
0.424119 | + | 0.905607i | \(0.360584\pi\) | |||||||
\(434\) | −4.89880 | −0.235150 | ||||||||
\(435\) | 0.600476 | 0.0287906 | ||||||||
\(436\) | 35.6452 | 1.70710 | ||||||||
\(437\) | 8.79358 | 0.420654 | ||||||||
\(438\) | −4.99025 | −0.238443 | ||||||||
\(439\) | −19.7097 | −0.940693 | −0.470347 | − | 0.882482i | \(-0.655871\pi\) | ||||
−0.470347 | + | 0.882482i | \(0.655871\pi\) | |||||||
\(440\) | −0.151356 | −0.00721561 | ||||||||
\(441\) | 1.10285 | 0.0525164 | ||||||||
\(442\) | −4.94498 | −0.235209 | ||||||||
\(443\) | −36.4139 | −1.73008 | −0.865038 | − | 0.501706i | \(-0.832706\pi\) | ||||
−0.865038 | + | 0.501706i | \(0.832706\pi\) | |||||||
\(444\) | −24.8654 | −1.18006 | ||||||||
\(445\) | −0.791662 | −0.0375284 | ||||||||
\(446\) | −10.3731 | −0.491181 | ||||||||
\(447\) | −18.2636 | −0.863840 | ||||||||
\(448\) | −5.99115 | −0.283055 | ||||||||
\(449\) | −7.81784 | −0.368947 | −0.184473 | − | 0.982838i | \(-0.559058\pi\) | ||||
−0.184473 | + | 0.982838i | \(0.559058\pi\) | |||||||
\(450\) | −0.436827 | −0.0205922 | ||||||||
\(451\) | 7.68669 | 0.361952 | ||||||||
\(452\) | −21.6032 | −1.01613 | ||||||||
\(453\) | −23.4009 | −1.09947 | ||||||||
\(454\) | 9.21567 | 0.432513 | ||||||||
\(455\) | 0.257812 | 0.0120864 | ||||||||
\(456\) | 6.93838 | 0.324919 | ||||||||
\(457\) | 1.28959 | 0.0603245 | 0.0301622 | − | 0.999545i | \(-0.490398\pi\) | ||||
0.0301622 | + | 0.999545i | \(0.490398\pi\) | |||||||
\(458\) | −8.92707 | −0.417135 | ||||||||
\(459\) | −34.2947 | −1.60074 | ||||||||
\(460\) | −0.587762 | −0.0274046 | ||||||||
\(461\) | −12.1738 | −0.566991 | −0.283495 | − | 0.958974i | \(-0.591494\pi\) | ||||
−0.283495 | + | 0.958974i | \(0.591494\pi\) | |||||||
\(462\) | 0.931253 | 0.0433258 | ||||||||
\(463\) | 33.2077 | 1.54329 | 0.771647 | − | 0.636050i | \(-0.219433\pi\) | ||||
0.771647 | + | 0.636050i | \(0.219433\pi\) | |||||||
\(464\) | 11.2350 | 0.521572 | ||||||||
\(465\) | 1.42876 | 0.0662572 | ||||||||
\(466\) | −9.79652 | −0.453815 | ||||||||
\(467\) | −25.1563 | −1.16410 | −0.582048 | − | 0.813154i | \(-0.697748\pi\) | ||||
−0.582048 | + | 0.813154i | \(0.697748\pi\) | |||||||
\(468\) | 0.760943 | 0.0351746 | ||||||||
\(469\) | 2.88810 | 0.133360 | ||||||||
\(470\) | 0.150948 | 0.00696269 | ||||||||
\(471\) | −34.3340 | −1.58203 | ||||||||
\(472\) | 6.80071 | 0.313028 | ||||||||
\(473\) | −0.587590 | −0.0270174 | ||||||||
\(474\) | 10.7810 | 0.495188 | ||||||||
\(475\) | −13.3798 | −0.613909 | ||||||||
\(476\) | −16.2033 | −0.742677 | ||||||||
\(477\) | −2.63594 | −0.120691 | ||||||||
\(478\) | 9.05672 | 0.414245 | ||||||||
\(479\) | −14.0023 | −0.639779 | −0.319890 | − | 0.947455i | \(-0.603646\pi\) | ||||
−0.319890 | + | 0.947455i | \(0.603646\pi\) | |||||||
\(480\) | −0.705521 | −0.0322025 | ||||||||
\(481\) | 15.5311 | 0.708158 | ||||||||
\(482\) | −6.91694 | −0.315058 | ||||||||
\(483\) | 7.55457 | 0.343745 | ||||||||
\(484\) | −1.83653 | −0.0834788 | ||||||||
\(485\) | 0.590325 | 0.0268053 | ||||||||
\(486\) | −0.907839 | −0.0411804 | ||||||||
\(487\) | −28.1486 | −1.27553 | −0.637767 | − | 0.770229i | \(-0.720142\pi\) | ||||
−0.637767 | + | 0.770229i | \(0.720142\pi\) | |||||||
\(488\) | 1.55115 | 0.0702173 | ||||||||
\(489\) | 2.52536 | 0.114201 | ||||||||
\(490\) | 0.200966 | 0.00907873 | ||||||||
\(491\) | 27.6795 | 1.24916 | 0.624580 | − | 0.780961i | \(-0.285270\pi\) | ||||
0.624580 | + | 0.780961i | \(0.285270\pi\) | |||||||
\(492\) | 23.5523 | 1.06182 | ||||||||
\(493\) | 23.5723 | 1.06164 | ||||||||
\(494\) | −2.07455 | −0.0933386 | ||||||||
\(495\) | 0.0211251 | 0.000949500 0 | ||||||||
\(496\) | 26.7323 | 1.20032 | ||||||||
\(497\) | −10.0905 | −0.452621 | ||||||||
\(498\) | 0.438225 | 0.0196374 | ||||||||
\(499\) | −14.1755 | −0.634582 | −0.317291 | − | 0.948328i | \(-0.602773\pi\) | ||||
−0.317291 | + | 0.948328i | \(0.602773\pi\) | |||||||
\(500\) | 1.79032 | 0.0800655 | ||||||||
\(501\) | −27.6808 | −1.23669 | ||||||||
\(502\) | 8.55483 | 0.381821 | ||||||||
\(503\) | 26.0229 | 1.16030 | 0.580152 | − | 0.814508i | \(-0.302993\pi\) | ||||
0.580152 | + | 0.814508i | \(0.302993\pi\) | |||||||
\(504\) | −0.463621 | −0.0206513 | ||||||||
\(505\) | −1.30976 | −0.0582836 | ||||||||
\(506\) | 1.32609 | 0.0589518 | ||||||||
\(507\) | −15.5782 | −0.691851 | ||||||||
\(508\) | −23.4553 | −1.04066 | ||||||||
\(509\) | 7.54307 | 0.334341 | 0.167170 | − | 0.985928i | \(-0.446537\pi\) | ||||
0.167170 | + | 0.985928i | \(0.446537\pi\) | |||||||
\(510\) | −0.420634 | −0.0186260 | ||||||||
\(511\) | 10.2134 | 0.451812 | ||||||||
\(512\) | −22.6498 | −1.00099 | ||||||||
\(513\) | −14.3876 | −0.635227 | ||||||||
\(514\) | −7.41079 | −0.326876 | ||||||||
\(515\) | 1.29957 | 0.0572657 | ||||||||
\(516\) | −1.80040 | −0.0792582 | ||||||||
\(517\) | 3.82618 | 0.168275 | ||||||||
\(518\) | −4.52973 | −0.199025 | ||||||||
\(519\) | −29.6302 | −1.30062 | ||||||||
\(520\) | 0.289668 | 0.0127028 | ||||||||
\(521\) | 33.3174 | 1.45966 | 0.729831 | − | 0.683628i | \(-0.239599\pi\) | ||||
0.729831 | + | 0.683628i | \(0.239599\pi\) | |||||||
\(522\) | 0.322865 | 0.0141314 | ||||||||
\(523\) | −39.4616 | −1.72554 | −0.862768 | − | 0.505601i | \(-0.831271\pi\) | ||||
−0.862768 | + | 0.505601i | \(0.831271\pi\) | |||||||
\(524\) | −20.4408 | −0.892959 | ||||||||
\(525\) | −11.4946 | −0.501667 | ||||||||
\(526\) | 2.99625 | 0.130643 | ||||||||
\(527\) | 56.0875 | 2.44321 | ||||||||
\(528\) | −5.08176 | −0.221155 | ||||||||
\(529\) | −12.2424 | −0.532279 | ||||||||
\(530\) | −0.480334 | −0.0208644 | ||||||||
\(531\) | −0.949188 | −0.0411913 | ||||||||
\(532\) | −6.79773 | −0.294719 | ||||||||
\(533\) | −14.7110 | −0.637202 | ||||||||
\(534\) | 5.47274 | 0.236829 | ||||||||
\(535\) | −1.11490 | −0.0482012 | ||||||||
\(536\) | 3.24496 | 0.140161 | ||||||||
\(537\) | −33.0885 | −1.42787 | ||||||||
\(538\) | 11.5305 | 0.497115 | ||||||||
\(539\) | 5.09404 | 0.219416 | ||||||||
\(540\) | 0.961664 | 0.0413834 | ||||||||
\(541\) | −13.8024 | −0.593409 | −0.296705 | − | 0.954969i | \(-0.595888\pi\) | ||||
−0.296705 | + | 0.954969i | \(0.595888\pi\) | |||||||
\(542\) | −9.61726 | −0.413097 | ||||||||
\(543\) | 11.9949 | 0.514748 | ||||||||
\(544\) | −27.6960 | −1.18746 | ||||||||
\(545\) | −1.89386 | −0.0811241 | ||||||||
\(546\) | −1.78225 | −0.0762733 | ||||||||
\(547\) | −24.3353 | −1.04050 | −0.520250 | − | 0.854014i | \(-0.674161\pi\) | ||||
−0.520250 | + | 0.854014i | \(0.674161\pi\) | |||||||
\(548\) | 11.7833 | 0.503358 | ||||||||
\(549\) | −0.216497 | −0.00923987 | ||||||||
\(550\) | −2.01770 | −0.0860351 | ||||||||
\(551\) | 9.88924 | 0.421296 | ||||||||
\(552\) | 8.48803 | 0.361275 | ||||||||
\(553\) | −22.0651 | −0.938302 | ||||||||
\(554\) | −4.16166 | −0.176812 | ||||||||
\(555\) | 1.32112 | 0.0560785 | ||||||||
\(556\) | −18.9787 | −0.804877 | ||||||||
\(557\) | 0.570434 | 0.0241701 | 0.0120850 | − | 0.999927i | \(-0.496153\pi\) | ||||
0.0120850 | + | 0.999927i | \(0.496153\pi\) | |||||||
\(558\) | 0.768219 | 0.0325213 | ||||||||
\(559\) | 1.12454 | 0.0475631 | ||||||||
\(560\) | 0.410318 | 0.0173391 | ||||||||
\(561\) | −10.6621 | −0.450156 | ||||||||
\(562\) | 8.16014 | 0.344215 | ||||||||
\(563\) | 26.8221 | 1.13042 | 0.565209 | − | 0.824948i | \(-0.308796\pi\) | ||||
0.565209 | + | 0.824948i | \(0.308796\pi\) | |||||||
\(564\) | 11.7236 | 0.493652 | ||||||||
\(565\) | 1.14779 | 0.0482881 | ||||||||
\(566\) | −2.08822 | −0.0877745 | ||||||||
\(567\) | −11.4637 | −0.481431 | ||||||||
\(568\) | −11.3373 | −0.475703 | ||||||||
\(569\) | −1.76168 | −0.0738534 | −0.0369267 | − | 0.999318i | \(-0.511757\pi\) | ||||
−0.0369267 | + | 0.999318i | \(0.511757\pi\) | |||||||
\(570\) | −0.176468 | −0.00739141 | ||||||||
\(571\) | −26.0955 | −1.09206 | −0.546031 | − | 0.837765i | \(-0.683862\pi\) | ||||
−0.546031 | + | 0.837765i | \(0.683862\pi\) | |||||||
\(572\) | 3.51480 | 0.146961 | ||||||||
\(573\) | −17.3739 | −0.725805 | ||||||||
\(574\) | 4.29053 | 0.179083 | ||||||||
\(575\) | −16.3681 | −0.682599 | ||||||||
\(576\) | 0.939520 | 0.0391467 | ||||||||
\(577\) | 17.7705 | 0.739794 | 0.369897 | − | 0.929073i | \(-0.379393\pi\) | ||||
0.369897 | + | 0.929073i | \(0.379393\pi\) | |||||||
\(578\) | −9.63916 | −0.400936 | ||||||||
\(579\) | −11.5464 | −0.479854 | ||||||||
\(580\) | −0.660996 | −0.0274464 | ||||||||
\(581\) | −0.896899 | −0.0372096 | ||||||||
\(582\) | −4.08090 | −0.169159 | ||||||||
\(583\) | −12.1754 | −0.504253 | ||||||||
\(584\) | 11.4753 | 0.474853 | ||||||||
\(585\) | −0.0404296 | −0.00167156 | ||||||||
\(586\) | −0.779367 | −0.0321953 | ||||||||
\(587\) | −13.5033 | −0.557339 | −0.278669 | − | 0.960387i | \(-0.589893\pi\) | ||||
−0.278669 | + | 0.960387i | \(0.589893\pi\) | |||||||
\(588\) | 15.6084 | 0.643678 | ||||||||
\(589\) | 23.5303 | 0.969547 | ||||||||
\(590\) | −0.172966 | −0.00712090 | ||||||||
\(591\) | 8.54728 | 0.351588 | ||||||||
\(592\) | 24.7184 | 1.01592 | ||||||||
\(593\) | 9.48660 | 0.389568 | 0.194784 | − | 0.980846i | \(-0.437599\pi\) | ||||
0.194784 | + | 0.980846i | \(0.437599\pi\) | |||||||
\(594\) | −2.16967 | −0.0890227 | ||||||||
\(595\) | 0.860896 | 0.0352933 | ||||||||
\(596\) | 20.1044 | 0.823507 | ||||||||
\(597\) | −15.3087 | −0.626542 | ||||||||
\(598\) | −2.53790 | −0.103782 | ||||||||
\(599\) | −5.01686 | −0.204983 | −0.102492 | − | 0.994734i | \(-0.532681\pi\) | ||||
−0.102492 | + | 0.994734i | \(0.532681\pi\) | |||||||
\(600\) | −12.9149 | −0.527250 | ||||||||
\(601\) | 9.73474 | 0.397088 | 0.198544 | − | 0.980092i | \(-0.436379\pi\) | ||||
0.198544 | + | 0.980092i | \(0.436379\pi\) | |||||||
\(602\) | −0.327979 | −0.0133674 | ||||||||
\(603\) | −0.452906 | −0.0184437 | ||||||||
\(604\) | 25.7594 | 1.04814 | ||||||||
\(605\) | 0.0975766 | 0.00396705 | ||||||||
\(606\) | 9.05436 | 0.367808 | ||||||||
\(607\) | 20.1566 | 0.818130 | 0.409065 | − | 0.912505i | \(-0.365855\pi\) | ||||
0.409065 | + | 0.912505i | \(0.365855\pi\) | |||||||
\(608\) | −11.6192 | −0.471222 | ||||||||
\(609\) | 8.49585 | 0.344269 | ||||||||
\(610\) | −0.0394512 | −0.00159733 | ||||||||
\(611\) | −7.32263 | −0.296242 | ||||||||
\(612\) | 2.54097 | 0.102713 | ||||||||
\(613\) | 1.56278 | 0.0631202 | 0.0315601 | − | 0.999502i | \(-0.489952\pi\) | ||||
0.0315601 | + | 0.999502i | \(0.489952\pi\) | |||||||
\(614\) | −4.83630 | −0.195177 | ||||||||
\(615\) | −1.25136 | −0.0504596 | ||||||||
\(616\) | −2.14146 | −0.0862820 | ||||||||
\(617\) | −28.1019 | −1.13134 | −0.565670 | − | 0.824632i | \(-0.691382\pi\) | ||||
−0.565670 | + | 0.824632i | \(0.691382\pi\) | |||||||
\(618\) | −8.98387 | −0.361384 | ||||||||
\(619\) | 7.18499 | 0.288789 | 0.144394 | − | 0.989520i | \(-0.453877\pi\) | ||||
0.144394 | + | 0.989520i | \(0.453877\pi\) | |||||||
\(620\) | −1.57276 | −0.0631636 | ||||||||
\(621\) | −17.6010 | −0.706302 | ||||||||
\(622\) | −3.26710 | −0.130999 | ||||||||
\(623\) | −11.2008 | −0.448753 | ||||||||
\(624\) | 9.72559 | 0.389335 | ||||||||
\(625\) | 24.8573 | 0.994291 | ||||||||
\(626\) | −11.8965 | −0.475481 | ||||||||
\(627\) | −4.47306 | −0.178637 | ||||||||
\(628\) | 37.7944 | 1.50816 | ||||||||
\(629\) | 51.8620 | 2.06787 | ||||||||
\(630\) | 0.0117915 | 0.000469785 0 | ||||||||
\(631\) | −41.4917 | −1.65176 | −0.825879 | − | 0.563848i | \(-0.809321\pi\) | ||||
−0.825879 | + | 0.563848i | \(0.809321\pi\) | |||||||
\(632\) | −24.7915 | −0.986152 | ||||||||
\(633\) | 16.8089 | 0.668093 | ||||||||
\(634\) | −9.11508 | −0.362006 | ||||||||
\(635\) | 1.24620 | 0.0494540 | ||||||||
\(636\) | −37.3059 | −1.47928 | ||||||||
\(637\) | −9.74909 | −0.386273 | ||||||||
\(638\) | 1.49132 | 0.0590417 | ||||||||
\(639\) | 1.58237 | 0.0625977 | ||||||||
\(640\) | 1.01696 | 0.0401988 | ||||||||
\(641\) | 5.36615 | 0.211950 | 0.105975 | − | 0.994369i | \(-0.466204\pi\) | ||||
0.105975 | + | 0.994369i | \(0.466204\pi\) | |||||||
\(642\) | 7.70725 | 0.304181 | ||||||||
\(643\) | −16.8713 | −0.665341 | −0.332670 | − | 0.943043i | \(-0.607950\pi\) | ||||
−0.332670 | + | 0.943043i | \(0.607950\pi\) | |||||||
\(644\) | −8.31597 | −0.327695 | ||||||||
\(645\) | 0.0956568 | 0.00376648 | ||||||||
\(646\) | −6.92742 | −0.272556 | ||||||||
\(647\) | 15.1912 | 0.597229 | 0.298614 | − | 0.954374i | \(-0.403476\pi\) | ||||
0.298614 | + | 0.954374i | \(0.403476\pi\) | |||||||
\(648\) | −12.8802 | −0.505982 | ||||||||
\(649\) | −4.38430 | −0.172099 | ||||||||
\(650\) | 3.86152 | 0.151461 | ||||||||
\(651\) | 20.2149 | 0.792283 | ||||||||
\(652\) | −2.77988 | −0.108868 | ||||||||
\(653\) | 10.8434 | 0.424334 | 0.212167 | − | 0.977233i | \(-0.431948\pi\) | ||||
0.212167 | + | 0.977233i | \(0.431948\pi\) | |||||||
\(654\) | 13.0922 | 0.511946 | ||||||||
\(655\) | 1.08604 | 0.0424349 | ||||||||
\(656\) | −23.4131 | −0.914126 | ||||||||
\(657\) | −1.60164 | −0.0624858 | ||||||||
\(658\) | 2.13569 | 0.0832577 | ||||||||
\(659\) | −39.8700 | −1.55312 | −0.776558 | − | 0.630046i | \(-0.783036\pi\) | ||||
−0.776558 | + | 0.630046i | \(0.783036\pi\) | |||||||
\(660\) | 0.298979 | 0.0116377 | ||||||||
\(661\) | 2.58629 | 0.100595 | 0.0502975 | − | 0.998734i | \(-0.483983\pi\) | ||||
0.0502975 | + | 0.998734i | \(0.483983\pi\) | |||||||
\(662\) | −4.50924 | −0.175257 | ||||||||
\(663\) | 20.4054 | 0.792481 | ||||||||
\(664\) | −1.00772 | −0.0391072 | ||||||||
\(665\) | 0.361169 | 0.0140055 | ||||||||
\(666\) | 0.710343 | 0.0275252 | ||||||||
\(667\) | 12.0979 | 0.468434 | ||||||||
\(668\) | 30.4707 | 1.17895 | ||||||||
\(669\) | 42.8046 | 1.65492 | ||||||||
\(670\) | −0.0825308 | −0.00318844 | ||||||||
\(671\) | −1.00000 | −0.0386046 | ||||||||
\(672\) | −9.98209 | −0.385067 | ||||||||
\(673\) | −40.7325 | −1.57012 | −0.785060 | − | 0.619419i | \(-0.787368\pi\) | ||||
−0.785060 | + | 0.619419i | \(0.787368\pi\) | |||||||
\(674\) | 6.05851 | 0.233365 | ||||||||
\(675\) | 26.7807 | 1.03079 | ||||||||
\(676\) | 17.1482 | 0.659548 | ||||||||
\(677\) | 42.3469 | 1.62752 | 0.813761 | − | 0.581199i | \(-0.197416\pi\) | ||||
0.813761 | + | 0.581199i | \(0.197416\pi\) | |||||||
\(678\) | −7.93468 | −0.304730 | ||||||||
\(679\) | 8.35223 | 0.320529 | ||||||||
\(680\) | 0.967270 | 0.0370931 | ||||||||
\(681\) | −38.0284 | −1.45725 | ||||||||
\(682\) | 3.54840 | 0.135875 | ||||||||
\(683\) | −11.4726 | −0.438985 | −0.219492 | − | 0.975614i | \(-0.570440\pi\) | ||||
−0.219492 | + | 0.975614i | \(0.570440\pi\) | |||||||
\(684\) | 1.06601 | 0.0407597 | ||||||||
\(685\) | −0.626058 | −0.0239204 | ||||||||
\(686\) | 6.75061 | 0.257740 | ||||||||
\(687\) | 36.8375 | 1.40544 | ||||||||
\(688\) | 1.78975 | 0.0682337 | ||||||||
\(689\) | 23.3015 | 0.887718 | ||||||||
\(690\) | −0.215881 | −0.00821844 | ||||||||
\(691\) | −4.48114 | −0.170471 | −0.0852354 | − | 0.996361i | \(-0.527164\pi\) | ||||
−0.0852354 | + | 0.996361i | \(0.527164\pi\) | |||||||
\(692\) | 32.6166 | 1.23990 | ||||||||
\(693\) | 0.298888 | 0.0113538 | ||||||||
\(694\) | −5.88027 | −0.223212 | ||||||||
\(695\) | 1.00836 | 0.0382491 | ||||||||
\(696\) | 9.54562 | 0.361826 | ||||||||
\(697\) | −49.1233 | −1.86068 | ||||||||
\(698\) | −6.38137 | −0.241538 | ||||||||
\(699\) | 40.4252 | 1.52902 | ||||||||
\(700\) | 12.6531 | 0.478243 | ||||||||
\(701\) | −23.8141 | −0.899445 | −0.449722 | − | 0.893168i | \(-0.648477\pi\) | ||||
−0.449722 | + | 0.893168i | \(0.648477\pi\) | |||||||
\(702\) | 4.15236 | 0.156721 | ||||||||
\(703\) | 21.7575 | 0.820601 | ||||||||
\(704\) | 4.33964 | 0.163556 | ||||||||
\(705\) | −0.622884 | −0.0234592 | ||||||||
\(706\) | −4.54919 | −0.171211 | ||||||||
\(707\) | −18.5312 | −0.696937 | ||||||||
\(708\) | −13.4337 | −0.504868 | ||||||||
\(709\) | 40.1995 | 1.50972 | 0.754862 | − | 0.655884i | \(-0.227704\pi\) | ||||
0.754862 | + | 0.655884i | \(0.227704\pi\) | |||||||
\(710\) | 0.288348 | 0.0108215 | ||||||||
\(711\) | 3.46019 | 0.129767 | ||||||||
\(712\) | −12.5849 | −0.471637 | ||||||||
\(713\) | 28.7856 | 1.07803 | ||||||||
\(714\) | −5.95135 | −0.222724 | ||||||||
\(715\) | −0.186744 | −0.00698384 | ||||||||
\(716\) | 36.4233 | 1.36120 | ||||||||
\(717\) | −37.3725 | −1.39570 | ||||||||
\(718\) | 4.34142 | 0.162020 | ||||||||
\(719\) | −20.7734 | −0.774719 | −0.387359 | − | 0.921929i | \(-0.626613\pi\) | ||||
−0.387359 | + | 0.921929i | \(0.626613\pi\) | |||||||
\(720\) | −0.0643452 | −0.00239800 | ||||||||
\(721\) | 18.3869 | 0.684765 | ||||||||
\(722\) | 4.77566 | 0.177732 | ||||||||
\(723\) | 28.5427 | 1.06151 | ||||||||
\(724\) | −13.2038 | −0.490714 | ||||||||
\(725\) | −18.4076 | −0.683640 | ||||||||
\(726\) | −0.674545 | −0.0250347 | ||||||||
\(727\) | −22.1783 | −0.822549 | −0.411275 | − | 0.911512i | \(-0.634916\pi\) | ||||
−0.411275 | + | 0.911512i | \(0.634916\pi\) | |||||||
\(728\) | 4.09838 | 0.151896 | ||||||||
\(729\) | 28.6571 | 1.06137 | ||||||||
\(730\) | −0.291858 | −0.0108022 | ||||||||
\(731\) | 3.75511 | 0.138888 | ||||||||
\(732\) | −3.06404 | −0.113250 | ||||||||
\(733\) | −22.3172 | −0.824304 | −0.412152 | − | 0.911115i | \(-0.635223\pi\) | ||||
−0.412152 | + | 0.911115i | \(0.635223\pi\) | |||||||
\(734\) | 12.6466 | 0.466796 | ||||||||
\(735\) | −0.829285 | −0.0305886 | ||||||||
\(736\) | −14.2143 | −0.523947 | ||||||||
\(737\) | −2.09197 | −0.0770587 | ||||||||
\(738\) | −0.672832 | −0.0247673 | ||||||||
\(739\) | −48.0693 | −1.76826 | −0.884129 | − | 0.467243i | \(-0.845247\pi\) | ||||
−0.884129 | + | 0.467243i | \(0.845247\pi\) | |||||||
\(740\) | −1.45427 | −0.0534601 | ||||||||
\(741\) | 8.56063 | 0.314483 | ||||||||
\(742\) | −6.79602 | −0.249490 | ||||||||
\(743\) | −25.5828 | −0.938542 | −0.469271 | − | 0.883054i | \(-0.655483\pi\) | ||||
−0.469271 | + | 0.883054i | \(0.655483\pi\) | |||||||
\(744\) | 22.7127 | 0.832686 | ||||||||
\(745\) | −1.06816 | −0.0391344 | ||||||||
\(746\) | 2.70526 | 0.0990467 | ||||||||
\(747\) | 0.140650 | 0.00514611 | ||||||||
\(748\) | 11.7367 | 0.429137 | ||||||||
\(749\) | −15.7741 | −0.576374 | ||||||||
\(750\) | 0.657571 | 0.0240111 | ||||||||
\(751\) | 45.0859 | 1.64521 | 0.822604 | − | 0.568615i | \(-0.192521\pi\) | ||||
0.822604 | + | 0.568615i | \(0.192521\pi\) | |||||||
\(752\) | −11.6542 | −0.424986 | ||||||||
\(753\) | −35.3014 | −1.28646 | ||||||||
\(754\) | −2.85411 | −0.103941 | ||||||||
\(755\) | −1.36862 | −0.0498092 | ||||||||
\(756\) | 13.6061 | 0.494850 | ||||||||
\(757\) | −8.81976 | −0.320560 | −0.160280 | − | 0.987072i | \(-0.551240\pi\) | ||||
−0.160280 | + | 0.987072i | \(0.551240\pi\) | |||||||
\(758\) | −7.05143 | −0.256120 | ||||||||
\(759\) | −5.47209 | −0.198624 | ||||||||
\(760\) | 0.405796 | 0.0147198 | ||||||||
\(761\) | 43.9572 | 1.59345 | 0.796723 | − | 0.604344i | \(-0.206565\pi\) | ||||
0.796723 | + | 0.604344i | \(0.206565\pi\) | |||||||
\(762\) | −8.61497 | −0.312087 | ||||||||
\(763\) | −26.7953 | −0.970057 | ||||||||
\(764\) | 19.1249 | 0.691916 | ||||||||
\(765\) | −0.135004 | −0.00488107 | ||||||||
\(766\) | 4.68004 | 0.169097 | ||||||||
\(767\) | 8.39077 | 0.302973 | ||||||||
\(768\) | 7.45015 | 0.268834 | ||||||||
\(769\) | 3.56562 | 0.128580 | 0.0642898 | − | 0.997931i | \(-0.479522\pi\) | ||||
0.0642898 | + | 0.997931i | \(0.479522\pi\) | |||||||
\(770\) | 0.0544650 | 0.00196278 | ||||||||
\(771\) | 30.5805 | 1.10133 | ||||||||
\(772\) | 12.7102 | 0.457449 | ||||||||
\(773\) | −47.7439 | −1.71723 | −0.858614 | − | 0.512622i | \(-0.828674\pi\) | ||||
−0.858614 | + | 0.512622i | \(0.828674\pi\) | |||||||
\(774\) | 0.0514330 | 0.00184872 | ||||||||
\(775\) | −43.7986 | −1.57329 | ||||||||
\(776\) | 9.38425 | 0.336875 | ||||||||
\(777\) | 18.6919 | 0.670569 | ||||||||
\(778\) | −5.77548 | −0.207061 | ||||||||
\(779\) | −20.6086 | −0.738379 | ||||||||
\(780\) | −0.572192 | −0.0204878 | ||||||||
\(781\) | 7.30897 | 0.261536 | ||||||||
\(782\) | −8.47462 | −0.303052 | ||||||||
\(783\) | −19.7940 | −0.707380 | ||||||||
\(784\) | −15.5160 | −0.554144 | ||||||||
\(785\) | −2.00805 | −0.0716704 | ||||||||
\(786\) | −7.50774 | −0.267792 | ||||||||
\(787\) | −14.5262 | −0.517803 | −0.258902 | − | 0.965904i | \(-0.583361\pi\) | ||||
−0.258902 | + | 0.965904i | \(0.583361\pi\) | |||||||
\(788\) | −9.40872 | −0.335172 | ||||||||
\(789\) | −12.3640 | −0.440170 | ||||||||
\(790\) | 0.630535 | 0.0224334 | ||||||||
\(791\) | 16.2396 | 0.577414 | ||||||||
\(792\) | 0.335820 | 0.0119328 | ||||||||
\(793\) | 1.91382 | 0.0679618 | ||||||||
\(794\) | −11.1732 | −0.396520 | ||||||||
\(795\) | 1.98210 | 0.0702977 | ||||||||
\(796\) | 16.8516 | 0.597288 | ||||||||
\(797\) | −25.7378 | −0.911679 | −0.455839 | − | 0.890062i | \(-0.650661\pi\) | ||||
−0.455839 | + | 0.890062i | \(0.650661\pi\) | |||||||
\(798\) | −2.49676 | −0.0883842 | ||||||||
\(799\) | −24.4520 | −0.865048 | ||||||||
\(800\) | 21.6277 | 0.764656 | ||||||||
\(801\) | 1.75649 | 0.0620626 | ||||||||
\(802\) | −9.78028 | −0.345354 | ||||||||
\(803\) | −7.39795 | −0.261068 | ||||||||
\(804\) | −6.40988 | −0.226059 | ||||||||
\(805\) | 0.441835 | 0.0155726 | ||||||||
\(806\) | −6.79101 | −0.239203 | ||||||||
\(807\) | −47.5805 | −1.67491 | ||||||||
\(808\) | −20.8210 | −0.732479 | ||||||||
\(809\) | 16.1314 | 0.567150 | 0.283575 | − | 0.958950i | \(-0.408479\pi\) | ||||
0.283575 | + | 0.958950i | \(0.408479\pi\) | |||||||
\(810\) | 0.327589 | 0.0115103 | ||||||||
\(811\) | −37.2088 | −1.30658 | −0.653289 | − | 0.757108i | \(-0.726611\pi\) | ||||
−0.653289 | + | 0.757108i | \(0.726611\pi\) | |||||||
\(812\) | −9.35212 | −0.328195 | ||||||||
\(813\) | 39.6855 | 1.39183 | ||||||||
\(814\) | 3.28107 | 0.115002 | ||||||||
\(815\) | 0.147697 | 0.00517361 | ||||||||
\(816\) | 32.4760 | 1.13689 | ||||||||
\(817\) | 1.57537 | 0.0551153 | ||||||||
\(818\) | −3.20654 | −0.112114 | ||||||||
\(819\) | −0.572019 | −0.0199880 | ||||||||
\(820\) | 1.37748 | 0.0481035 | ||||||||
\(821\) | −24.8527 | −0.867366 | −0.433683 | − | 0.901065i | \(-0.642786\pi\) | ||||
−0.433683 | + | 0.901065i | \(0.642786\pi\) | |||||||
\(822\) | 4.32792 | 0.150954 | ||||||||
\(823\) | −27.3472 | −0.953262 | −0.476631 | − | 0.879104i | \(-0.658142\pi\) | ||||
−0.476631 | + | 0.879104i | \(0.658142\pi\) | |||||||
\(824\) | 20.6589 | 0.719685 | ||||||||
\(825\) | 8.32603 | 0.289875 | ||||||||
\(826\) | −2.44721 | −0.0851495 | ||||||||
\(827\) | 3.62847 | 0.126174 | 0.0630871 | − | 0.998008i | \(-0.479905\pi\) | ||||
0.0630871 | + | 0.998008i | \(0.479905\pi\) | |||||||
\(828\) | 1.30409 | 0.0453203 | ||||||||
\(829\) | 26.8941 | 0.934070 | 0.467035 | − | 0.884239i | \(-0.345322\pi\) | ||||
0.467035 | + | 0.884239i | \(0.345322\pi\) | |||||||
\(830\) | 0.0256299 | 0.000889628 0 | ||||||||
\(831\) | 17.1731 | 0.595727 | ||||||||
\(832\) | −8.30530 | −0.287934 | ||||||||
\(833\) | −32.5545 | −1.12795 | ||||||||
\(834\) | −6.97074 | −0.241377 | ||||||||
\(835\) | −1.61893 | −0.0560255 | ||||||||
\(836\) | 4.92388 | 0.170296 | ||||||||
\(837\) | −47.0974 | −1.62792 | ||||||||
\(838\) | −4.38212 | −0.151378 | ||||||||
\(839\) | 8.01173 | 0.276596 | 0.138298 | − | 0.990391i | \(-0.455837\pi\) | ||||
0.138298 | + | 0.990391i | \(0.455837\pi\) | |||||||
\(840\) | 0.348620 | 0.0120285 | ||||||||
\(841\) | −15.3947 | −0.530851 | ||||||||
\(842\) | 4.34057 | 0.149586 | ||||||||
\(843\) | −33.6728 | −1.15975 | ||||||||
\(844\) | −18.5030 | −0.636899 | ||||||||
\(845\) | −0.911101 | −0.0313428 | ||||||||
\(846\) | −0.334913 | −0.0115146 | ||||||||
\(847\) | 1.38056 | 0.0474368 | ||||||||
\(848\) | 37.0853 | 1.27351 | ||||||||
\(849\) | 8.61703 | 0.295736 | ||||||||
\(850\) | 12.8945 | 0.442279 | ||||||||
\(851\) | 26.6170 | 0.912417 | ||||||||
\(852\) | 22.3950 | 0.767240 | ||||||||
\(853\) | 27.7986 | 0.951807 | 0.475904 | − | 0.879497i | \(-0.342121\pi\) | ||||
0.475904 | + | 0.879497i | \(0.342121\pi\) | |||||||
\(854\) | −0.558177 | −0.0191004 | ||||||||
\(855\) | −0.0566378 | −0.00193697 | ||||||||
\(856\) | −17.7232 | −0.605767 | ||||||||
\(857\) | −36.1854 | −1.23607 | −0.618035 | − | 0.786150i | \(-0.712071\pi\) | ||||
−0.618035 | + | 0.786150i | \(0.712071\pi\) | |||||||
\(858\) | 1.29096 | 0.0440726 | ||||||||
\(859\) | −36.5369 | −1.24662 | −0.623312 | − | 0.781974i | \(-0.714213\pi\) | ||||
−0.623312 | + | 0.781974i | \(0.714213\pi\) | |||||||
\(860\) | −0.105298 | −0.00359062 | ||||||||
\(861\) | −17.7048 | −0.603380 | ||||||||
\(862\) | 12.2164 | 0.416091 | ||||||||
\(863\) | 17.8996 | 0.609309 | 0.304655 | − | 0.952463i | \(-0.401459\pi\) | ||||
0.304655 | + | 0.952463i | \(0.401459\pi\) | |||||||
\(864\) | 23.2567 | 0.791208 | ||||||||
\(865\) | −1.73295 | −0.0589219 | ||||||||
\(866\) | −7.13635 | −0.242503 | ||||||||
\(867\) | 39.7759 | 1.35086 | ||||||||
\(868\) | −22.2522 | −0.755290 | ||||||||
\(869\) | 15.9826 | 0.542174 | ||||||||
\(870\) | −0.242779 | −0.00823097 | ||||||||
\(871\) | 4.00366 | 0.135659 | ||||||||
\(872\) | −30.1062 | −1.01953 | ||||||||
\(873\) | −1.30978 | −0.0443293 | ||||||||
\(874\) | −3.55534 | −0.120261 | ||||||||
\(875\) | −1.34583 | −0.0454972 | ||||||||
\(876\) | −22.6676 | −0.765868 | ||||||||
\(877\) | −28.7263 | −0.970019 | −0.485009 | − | 0.874509i | \(-0.661184\pi\) | ||||
−0.485009 | + | 0.874509i | \(0.661184\pi\) | |||||||
\(878\) | 7.96884 | 0.268935 | ||||||||
\(879\) | 3.21605 | 0.108475 | ||||||||
\(880\) | −0.297210 | −0.0100190 | ||||||||
\(881\) | 18.4462 | 0.621467 | 0.310734 | − | 0.950497i | \(-0.399425\pi\) | ||||
0.310734 | + | 0.950497i | \(0.399425\pi\) | |||||||
\(882\) | −0.445892 | −0.0150140 | ||||||||
\(883\) | −8.21016 | −0.276294 | −0.138147 | − | 0.990412i | \(-0.544115\pi\) | ||||
−0.138147 | + | 0.990412i | \(0.544115\pi\) | |||||||
\(884\) | −22.4620 | −0.755479 | ||||||||
\(885\) | 0.713743 | 0.0239922 | ||||||||
\(886\) | 14.7225 | 0.494613 | ||||||||
\(887\) | −1.69374 | −0.0568703 | −0.0284352 | − | 0.999596i | \(-0.509052\pi\) | ||||
−0.0284352 | + | 0.999596i | \(0.509052\pi\) | |||||||
\(888\) | 21.0015 | 0.704765 | ||||||||
\(889\) | 17.6319 | 0.591356 | ||||||||
\(890\) | 0.320077 | 0.0107290 | ||||||||
\(891\) | 8.30364 | 0.278182 | ||||||||
\(892\) | −47.1187 | −1.57765 | ||||||||
\(893\) | −10.2583 | −0.343280 | ||||||||
\(894\) | 7.38418 | 0.246964 | ||||||||
\(895\) | −1.93520 | −0.0646867 | ||||||||
\(896\) | 14.3885 | 0.480685 | ||||||||
\(897\) | 10.4726 | 0.349670 | ||||||||
\(898\) | 3.16083 | 0.105478 | ||||||||
\(899\) | 32.3722 | 1.07967 | ||||||||
\(900\) | −1.98424 | −0.0661412 | ||||||||
\(901\) | 77.8093 | 2.59220 | ||||||||
\(902\) | −3.10781 | −0.103479 | ||||||||
\(903\) | 1.35340 | 0.0450384 | ||||||||
\(904\) | 18.2462 | 0.606860 | ||||||||
\(905\) | 0.701527 | 0.0233196 | ||||||||
\(906\) | 9.46124 | 0.314329 | ||||||||
\(907\) | 41.0996 | 1.36469 | 0.682345 | − | 0.731031i | \(-0.260960\pi\) | ||||
0.682345 | + | 0.731031i | \(0.260960\pi\) | |||||||
\(908\) | 41.8611 | 1.38921 | ||||||||
\(909\) | 2.90602 | 0.0963867 | ||||||||
\(910\) | −0.104236 | −0.00345540 | ||||||||
\(911\) | −10.5470 | −0.349437 | −0.174719 | − | 0.984618i | \(-0.555902\pi\) | ||||
−0.174719 | + | 0.984618i | \(0.555902\pi\) | |||||||
\(912\) | 13.6246 | 0.451155 | ||||||||
\(913\) | 0.649661 | 0.0215006 | ||||||||
\(914\) | −0.521395 | −0.0172462 | ||||||||
\(915\) | 0.162795 | 0.00538184 | ||||||||
\(916\) | −40.5502 | −1.33982 | ||||||||
\(917\) | 15.3658 | 0.507424 | ||||||||
\(918\) | 13.8657 | 0.457637 | ||||||||
\(919\) | −2.90139 | −0.0957080 | −0.0478540 | − | 0.998854i | \(-0.515238\pi\) | ||||
−0.0478540 | + | 0.998854i | \(0.515238\pi\) | |||||||
\(920\) | 0.496429 | 0.0163668 | ||||||||
\(921\) | 19.9570 | 0.657604 | ||||||||
\(922\) | 4.92200 | 0.162097 | ||||||||
\(923\) | −13.9881 | −0.460423 | ||||||||
\(924\) | 4.23011 | 0.139160 | ||||||||
\(925\) | −40.4989 | −1.33160 | ||||||||
\(926\) | −13.4262 | −0.441214 | ||||||||
\(927\) | −2.88340 | −0.0947032 | ||||||||
\(928\) | −15.9854 | −0.524746 | ||||||||
\(929\) | −37.3322 | −1.22483 | −0.612416 | − | 0.790536i | \(-0.709802\pi\) | ||||
−0.612416 | + | 0.790536i | \(0.709802\pi\) | |||||||
\(930\) | −0.577663 | −0.0189423 | ||||||||
\(931\) | −13.6575 | −0.447606 | ||||||||
\(932\) | −44.4995 | −1.45763 | ||||||||
\(933\) | 13.4817 | 0.441370 | ||||||||
\(934\) | 10.1710 | 0.332804 | ||||||||
\(935\) | −0.623582 | −0.0203933 | ||||||||
\(936\) | −0.642699 | −0.0210073 | ||||||||
\(937\) | 1.64643 | 0.0537867 | 0.0268933 | − | 0.999638i | \(-0.491439\pi\) | ||||
0.0268933 | + | 0.999638i | \(0.491439\pi\) | |||||||
\(938\) | −1.16769 | −0.0381264 | ||||||||
\(939\) | 49.0909 | 1.60202 | ||||||||
\(940\) | 0.685662 | 0.0223638 | ||||||||
\(941\) | −55.6461 | −1.81401 | −0.907005 | − | 0.421120i | \(-0.861637\pi\) | ||||
−0.907005 | + | 0.421120i | \(0.861637\pi\) | |||||||
\(942\) | 13.8816 | 0.452287 | ||||||||
\(943\) | −25.2114 | −0.820996 | ||||||||
\(944\) | 13.3542 | 0.434643 | ||||||||
\(945\) | −0.722905 | −0.0235161 | ||||||||
\(946\) | 0.237569 | 0.00772403 | ||||||||
\(947\) | −27.5185 | −0.894230 | −0.447115 | − | 0.894476i | \(-0.647549\pi\) | ||||
−0.447115 | + | 0.894476i | \(0.647549\pi\) | |||||||
\(948\) | 48.9714 | 1.59052 | ||||||||
\(949\) | 14.1584 | 0.459600 | ||||||||
\(950\) | 5.40961 | 0.175511 | ||||||||
\(951\) | 37.6133 | 1.21970 | ||||||||
\(952\) | 13.6854 | 0.443548 | ||||||||
\(953\) | 26.8576 | 0.870003 | 0.435002 | − | 0.900430i | \(-0.356748\pi\) | ||||
0.435002 | + | 0.900430i | \(0.356748\pi\) | |||||||
\(954\) | 1.06574 | 0.0345045 | ||||||||
\(955\) | −1.01612 | −0.0328810 | ||||||||
\(956\) | 41.1391 | 1.33053 | ||||||||
\(957\) | −6.15390 | −0.198927 | ||||||||
\(958\) | 5.66126 | 0.182907 | ||||||||
\(959\) | −8.85780 | −0.286033 | ||||||||
\(960\) | −0.706472 | −0.0228013 | ||||||||
\(961\) | 46.0258 | 1.48470 | ||||||||
\(962\) | −6.27939 | −0.202456 | ||||||||
\(963\) | 2.47367 | 0.0797128 | ||||||||
\(964\) | −31.4194 | −1.01195 | ||||||||
\(965\) | −0.675302 | −0.0217387 | ||||||||
\(966\) | −3.05439 | −0.0982735 | ||||||||
\(967\) | −7.13631 | −0.229488 | −0.114744 | − | 0.993395i | \(-0.536605\pi\) | ||||
−0.114744 | + | 0.993395i | \(0.536605\pi\) | |||||||
\(968\) | 1.55115 | 0.0498559 | ||||||||
\(969\) | 28.5859 | 0.918313 | ||||||||
\(970\) | −0.238675 | −0.00766338 | ||||||||
\(971\) | 48.6208 | 1.56032 | 0.780158 | − | 0.625582i | \(-0.215138\pi\) | ||||
0.780158 | + | 0.625582i | \(0.215138\pi\) | |||||||
\(972\) | −4.12375 | −0.132269 | ||||||||
\(973\) | 14.2668 | 0.457371 | ||||||||
\(974\) | 11.3808 | 0.364663 | ||||||||
\(975\) | −15.9345 | −0.510314 | ||||||||
\(976\) | 3.04592 | 0.0974975 | ||||||||
\(977\) | 37.7471 | 1.20764 | 0.603819 | − | 0.797122i | \(-0.293645\pi\) | ||||
0.603819 | + | 0.797122i | \(0.293645\pi\) | |||||||
\(978\) | −1.02103 | −0.0326489 | ||||||||
\(979\) | 8.11324 | 0.259300 | ||||||||
\(980\) | 0.912866 | 0.0291604 | ||||||||
\(981\) | 4.20199 | 0.134159 | ||||||||
\(982\) | −11.1911 | −0.357123 | ||||||||
\(983\) | −31.2734 | −0.997467 | −0.498734 | − | 0.866755i | \(-0.666201\pi\) | ||||
−0.498734 | + | 0.866755i | \(0.666201\pi\) | |||||||
\(984\) | −19.8925 | −0.634150 | ||||||||
\(985\) | 0.499894 | 0.0159279 | ||||||||
\(986\) | −9.53054 | −0.303514 | ||||||||
\(987\) | −8.81289 | −0.280517 | ||||||||
\(988\) | −9.42342 | −0.299799 | ||||||||
\(989\) | 1.92722 | 0.0612821 | ||||||||
\(990\) | −0.00854108 | −0.000271453 0 | ||||||||
\(991\) | −34.5374 | −1.09712 | −0.548558 | − | 0.836112i | \(-0.684823\pi\) | ||||
−0.548558 | + | 0.836112i | \(0.684823\pi\) | |||||||
\(992\) | −38.0353 | −1.20762 | ||||||||
\(993\) | 18.6074 | 0.590487 | ||||||||
\(994\) | 4.07970 | 0.129400 | ||||||||
\(995\) | −0.895338 | −0.0283841 | ||||||||
\(996\) | 1.99059 | 0.0630742 | ||||||||
\(997\) | 1.18905 | 0.0376577 | 0.0188288 | − | 0.999823i | \(-0.494006\pi\) | ||||
0.0188288 | + | 0.999823i | \(0.494006\pi\) | |||||||
\(998\) | 5.73130 | 0.181421 | ||||||||
\(999\) | −43.5492 | −1.37784 |
(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 | 671.2.a.d.1.10 | ✓ | 21 | |
3.2 | odd | 2 | 6039.2.a.l.1.12 | 21 | |||
11.10 | odd | 2 | 7381.2.a.j.1.12 | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
671.2.a.d.1.10 | ✓ | 21 | 1.1 | even | 1 | trivial | |
6039.2.a.l.1.12 | 21 | 3.2 | odd | 2 | |||
7381.2.a.j.1.12 | 21 | 11.10 | odd | 2 |