Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8042,2,Mod(1,8042)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8042, 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("8042.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8042 = 2 \cdot 4021 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8042.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.2156933055\) |
Analytic rank: | \(1\) |
Dimension: | \(67\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 8042.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −2.60646 | −1.50484 | −0.752419 | − | 0.658684i | \(-0.771113\pi\) | ||||
−0.752419 | + | 0.658684i | \(0.771113\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.616826 | −0.275853 | −0.137927 | − | 0.990442i | \(-0.544044\pi\) | ||||
−0.137927 | + | 0.990442i | \(0.544044\pi\) | |||||||
\(6\) | −2.60646 | −1.06408 | ||||||||
\(7\) | −3.04419 | −1.15059 | −0.575297 | − | 0.817944i | \(-0.695114\pi\) | ||||
−0.575297 | + | 0.817944i | \(0.695114\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 3.79362 | 1.26454 | ||||||||
\(10\) | −0.616826 | −0.195058 | ||||||||
\(11\) | −0.708752 | −0.213697 | −0.106848 | − | 0.994275i | \(-0.534076\pi\) | ||||
−0.106848 | + | 0.994275i | \(0.534076\pi\) | |||||||
\(12\) | −2.60646 | −0.752419 | ||||||||
\(13\) | 4.52204 | 1.25419 | 0.627095 | − | 0.778943i | \(-0.284244\pi\) | ||||
0.627095 | + | 0.778943i | \(0.284244\pi\) | |||||||
\(14\) | −3.04419 | −0.813593 | ||||||||
\(15\) | 1.60773 | 0.415114 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −7.53136 | −1.82662 | −0.913311 | − | 0.407263i | \(-0.866483\pi\) | ||||
−0.913311 | + | 0.407263i | \(0.866483\pi\) | |||||||
\(18\) | 3.79362 | 0.894165 | ||||||||
\(19\) | 1.15378 | 0.264696 | 0.132348 | − | 0.991203i | \(-0.457748\pi\) | ||||
0.132348 | + | 0.991203i | \(0.457748\pi\) | |||||||
\(20\) | −0.616826 | −0.137927 | ||||||||
\(21\) | 7.93454 | 1.73146 | ||||||||
\(22\) | −0.708752 | −0.151106 | ||||||||
\(23\) | 6.01283 | 1.25376 | 0.626881 | − | 0.779115i | \(-0.284331\pi\) | ||||
0.626881 | + | 0.779115i | \(0.284331\pi\) | |||||||
\(24\) | −2.60646 | −0.532041 | ||||||||
\(25\) | −4.61953 | −0.923905 | ||||||||
\(26\) | 4.52204 | 0.886846 | ||||||||
\(27\) | −2.06853 | −0.398090 | ||||||||
\(28\) | −3.04419 | −0.575297 | ||||||||
\(29\) | 3.05269 | 0.566871 | 0.283436 | − | 0.958991i | \(-0.408526\pi\) | ||||
0.283436 | + | 0.958991i | \(0.408526\pi\) | |||||||
\(30\) | 1.60773 | 0.293530 | ||||||||
\(31\) | −4.59808 | −0.825839 | −0.412920 | − | 0.910767i | \(-0.635491\pi\) | ||||
−0.412920 | + | 0.910767i | \(0.635491\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 1.84733 | 0.321579 | ||||||||
\(34\) | −7.53136 | −1.29162 | ||||||||
\(35\) | 1.87773 | 0.317395 | ||||||||
\(36\) | 3.79362 | 0.632270 | ||||||||
\(37\) | 0.716683 | 0.117822 | 0.0589110 | − | 0.998263i | \(-0.481237\pi\) | ||||
0.0589110 | + | 0.998263i | \(0.481237\pi\) | |||||||
\(38\) | 1.15378 | 0.187168 | ||||||||
\(39\) | −11.7865 | −1.88735 | ||||||||
\(40\) | −0.616826 | −0.0975288 | ||||||||
\(41\) | 5.61551 | 0.876996 | 0.438498 | − | 0.898732i | \(-0.355511\pi\) | ||||
0.438498 | + | 0.898732i | \(0.355511\pi\) | |||||||
\(42\) | 7.93454 | 1.22433 | ||||||||
\(43\) | 1.06760 | 0.162807 | 0.0814035 | − | 0.996681i | \(-0.474060\pi\) | ||||
0.0814035 | + | 0.996681i | \(0.474060\pi\) | |||||||
\(44\) | −0.708752 | −0.106848 | ||||||||
\(45\) | −2.34000 | −0.348827 | ||||||||
\(46\) | 6.01283 | 0.886544 | ||||||||
\(47\) | 5.03724 | 0.734757 | 0.367378 | − | 0.930072i | \(-0.380255\pi\) | ||||
0.367378 | + | 0.930072i | \(0.380255\pi\) | |||||||
\(48\) | −2.60646 | −0.376210 | ||||||||
\(49\) | 2.26707 | 0.323868 | ||||||||
\(50\) | −4.61953 | −0.653300 | ||||||||
\(51\) | 19.6302 | 2.74877 | ||||||||
\(52\) | 4.52204 | 0.627095 | ||||||||
\(53\) | −6.45049 | −0.886043 | −0.443021 | − | 0.896511i | \(-0.646093\pi\) | ||||
−0.443021 | + | 0.896511i | \(0.646093\pi\) | |||||||
\(54\) | −2.06853 | −0.281492 | ||||||||
\(55\) | 0.437177 | 0.0589489 | ||||||||
\(56\) | −3.04419 | −0.406797 | ||||||||
\(57\) | −3.00729 | −0.398325 | ||||||||
\(58\) | 3.05269 | 0.400838 | ||||||||
\(59\) | 1.48533 | 0.193373 | 0.0966866 | − | 0.995315i | \(-0.469176\pi\) | ||||
0.0966866 | + | 0.995315i | \(0.469176\pi\) | |||||||
\(60\) | 1.60773 | 0.207557 | ||||||||
\(61\) | −1.93080 | −0.247214 | −0.123607 | − | 0.992331i | \(-0.539446\pi\) | ||||
−0.123607 | + | 0.992331i | \(0.539446\pi\) | |||||||
\(62\) | −4.59808 | −0.583957 | ||||||||
\(63\) | −11.5485 | −1.45497 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.78932 | −0.345972 | ||||||||
\(66\) | 1.84733 | 0.227391 | ||||||||
\(67\) | −2.98628 | −0.364832 | −0.182416 | − | 0.983221i | \(-0.558392\pi\) | ||||
−0.182416 | + | 0.983221i | \(0.558392\pi\) | |||||||
\(68\) | −7.53136 | −0.913311 | ||||||||
\(69\) | −15.6722 | −1.88671 | ||||||||
\(70\) | 1.87773 | 0.224432 | ||||||||
\(71\) | 11.7144 | 1.39025 | 0.695124 | − | 0.718890i | \(-0.255349\pi\) | ||||
0.695124 | + | 0.718890i | \(0.255349\pi\) | |||||||
\(72\) | 3.79362 | 0.447082 | ||||||||
\(73\) | 5.50758 | 0.644614 | 0.322307 | − | 0.946635i | \(-0.395542\pi\) | ||||
0.322307 | + | 0.946635i | \(0.395542\pi\) | |||||||
\(74\) | 0.716683 | 0.0833127 | ||||||||
\(75\) | 12.0406 | 1.39033 | ||||||||
\(76\) | 1.15378 | 0.132348 | ||||||||
\(77\) | 2.15757 | 0.245878 | ||||||||
\(78\) | −11.7865 | −1.33456 | ||||||||
\(79\) | 10.9722 | 1.23447 | 0.617236 | − | 0.786778i | \(-0.288252\pi\) | ||||
0.617236 | + | 0.786778i | \(0.288252\pi\) | |||||||
\(80\) | −0.616826 | −0.0689633 | ||||||||
\(81\) | −5.98931 | −0.665479 | ||||||||
\(82\) | 5.61551 | 0.620130 | ||||||||
\(83\) | −1.61518 | −0.177289 | −0.0886443 | − | 0.996063i | \(-0.528253\pi\) | ||||
−0.0886443 | + | 0.996063i | \(0.528253\pi\) | |||||||
\(84\) | 7.93454 | 0.865730 | ||||||||
\(85\) | 4.64554 | 0.503879 | ||||||||
\(86\) | 1.06760 | 0.115122 | ||||||||
\(87\) | −7.95672 | −0.853050 | ||||||||
\(88\) | −0.708752 | −0.0755532 | ||||||||
\(89\) | 2.45925 | 0.260680 | 0.130340 | − | 0.991469i | \(-0.458393\pi\) | ||||
0.130340 | + | 0.991469i | \(0.458393\pi\) | |||||||
\(90\) | −2.34000 | −0.246658 | ||||||||
\(91\) | −13.7659 | −1.44306 | ||||||||
\(92\) | 6.01283 | 0.626881 | ||||||||
\(93\) | 11.9847 | 1.24275 | ||||||||
\(94\) | 5.03724 | 0.519552 | ||||||||
\(95\) | −0.711684 | −0.0730173 | ||||||||
\(96\) | −2.60646 | −0.266020 | ||||||||
\(97\) | 12.5402 | 1.27326 | 0.636632 | − | 0.771168i | \(-0.280327\pi\) | ||||
0.636632 | + | 0.771168i | \(0.280327\pi\) | |||||||
\(98\) | 2.26707 | 0.229009 | ||||||||
\(99\) | −2.68873 | −0.270228 | ||||||||
\(100\) | −4.61953 | −0.461953 | ||||||||
\(101\) | −13.5576 | −1.34904 | −0.674518 | − | 0.738258i | \(-0.735648\pi\) | ||||
−0.674518 | + | 0.738258i | \(0.735648\pi\) | |||||||
\(102\) | 19.6302 | 1.94367 | ||||||||
\(103\) | 19.5165 | 1.92302 | 0.961508 | − | 0.274778i | \(-0.0886042\pi\) | ||||
0.961508 | + | 0.274778i | \(0.0886042\pi\) | |||||||
\(104\) | 4.52204 | 0.443423 | ||||||||
\(105\) | −4.89423 | −0.477628 | ||||||||
\(106\) | −6.45049 | −0.626527 | ||||||||
\(107\) | −12.9180 | −1.24883 | −0.624417 | − | 0.781091i | \(-0.714664\pi\) | ||||
−0.624417 | + | 0.781091i | \(0.714664\pi\) | |||||||
\(108\) | −2.06853 | −0.199045 | ||||||||
\(109\) | −3.93185 | −0.376603 | −0.188301 | − | 0.982111i | \(-0.560298\pi\) | ||||
−0.188301 | + | 0.982111i | \(0.560298\pi\) | |||||||
\(110\) | 0.437177 | 0.0416832 | ||||||||
\(111\) | −1.86800 | −0.177303 | ||||||||
\(112\) | −3.04419 | −0.287649 | ||||||||
\(113\) | −18.6937 | −1.75856 | −0.879279 | − | 0.476307i | \(-0.841975\pi\) | ||||
−0.879279 | + | 0.476307i | \(0.841975\pi\) | |||||||
\(114\) | −3.00729 | −0.281658 | ||||||||
\(115\) | −3.70887 | −0.345854 | ||||||||
\(116\) | 3.05269 | 0.283436 | ||||||||
\(117\) | 17.1549 | 1.58597 | ||||||||
\(118\) | 1.48533 | 0.136735 | ||||||||
\(119\) | 22.9269 | 2.10170 | ||||||||
\(120\) | 1.60773 | 0.146765 | ||||||||
\(121\) | −10.4977 | −0.954334 | ||||||||
\(122\) | −1.93080 | −0.174807 | ||||||||
\(123\) | −14.6366 | −1.31974 | ||||||||
\(124\) | −4.59808 | −0.412920 | ||||||||
\(125\) | 5.93358 | 0.530715 | ||||||||
\(126\) | −11.5485 | −1.02882 | ||||||||
\(127\) | −5.47636 | −0.485949 | −0.242974 | − | 0.970033i | \(-0.578123\pi\) | ||||
−0.242974 | + | 0.970033i | \(0.578123\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −2.78265 | −0.244998 | ||||||||
\(130\) | −2.78932 | −0.244639 | ||||||||
\(131\) | 19.0650 | 1.66572 | 0.832859 | − | 0.553485i | \(-0.186702\pi\) | ||||
0.832859 | + | 0.553485i | \(0.186702\pi\) | |||||||
\(132\) | 1.84733 | 0.160790 | ||||||||
\(133\) | −3.51233 | −0.304558 | ||||||||
\(134\) | −2.98628 | −0.257976 | ||||||||
\(135\) | 1.27593 | 0.109814 | ||||||||
\(136\) | −7.53136 | −0.645808 | ||||||||
\(137\) | −15.1802 | −1.29693 | −0.648466 | − | 0.761244i | \(-0.724589\pi\) | ||||
−0.648466 | + | 0.761244i | \(0.724589\pi\) | |||||||
\(138\) | −15.6722 | −1.33411 | ||||||||
\(139\) | −6.26425 | −0.531327 | −0.265664 | − | 0.964066i | \(-0.585591\pi\) | ||||
−0.265664 | + | 0.964066i | \(0.585591\pi\) | |||||||
\(140\) | 1.87773 | 0.158698 | ||||||||
\(141\) | −13.1293 | −1.10569 | ||||||||
\(142\) | 11.7144 | 0.983054 | ||||||||
\(143\) | −3.20501 | −0.268016 | ||||||||
\(144\) | 3.79362 | 0.316135 | ||||||||
\(145\) | −1.88298 | −0.156373 | ||||||||
\(146\) | 5.50758 | 0.455811 | ||||||||
\(147\) | −5.90903 | −0.487368 | ||||||||
\(148\) | 0.716683 | 0.0589110 | ||||||||
\(149\) | 14.4738 | 1.18574 | 0.592872 | − | 0.805297i | \(-0.297994\pi\) | ||||
0.592872 | + | 0.805297i | \(0.297994\pi\) | |||||||
\(150\) | 12.0406 | 0.983110 | ||||||||
\(151\) | −0.119120 | −0.00969382 | −0.00484691 | − | 0.999988i | \(-0.501543\pi\) | ||||
−0.00484691 | + | 0.999988i | \(0.501543\pi\) | |||||||
\(152\) | 1.15378 | 0.0935842 | ||||||||
\(153\) | −28.5711 | −2.30984 | ||||||||
\(154\) | 2.15757 | 0.173862 | ||||||||
\(155\) | 2.83622 | 0.227810 | ||||||||
\(156\) | −11.7865 | −0.943676 | ||||||||
\(157\) | 15.5116 | 1.23796 | 0.618978 | − | 0.785408i | \(-0.287547\pi\) | ||||
0.618978 | + | 0.785408i | \(0.287547\pi\) | |||||||
\(158\) | 10.9722 | 0.872904 | ||||||||
\(159\) | 16.8129 | 1.33335 | ||||||||
\(160\) | −0.616826 | −0.0487644 | ||||||||
\(161\) | −18.3042 | −1.44257 | ||||||||
\(162\) | −5.98931 | −0.470565 | ||||||||
\(163\) | −15.0880 | −1.18178 | −0.590890 | − | 0.806752i | \(-0.701223\pi\) | ||||
−0.590890 | + | 0.806752i | \(0.701223\pi\) | |||||||
\(164\) | 5.61551 | 0.438498 | ||||||||
\(165\) | −1.13948 | −0.0887086 | ||||||||
\(166\) | −1.61518 | −0.125362 | ||||||||
\(167\) | 14.4544 | 1.11851 | 0.559257 | − | 0.828994i | \(-0.311086\pi\) | ||||
0.559257 | + | 0.828994i | \(0.311086\pi\) | |||||||
\(168\) | 7.93454 | 0.612163 | ||||||||
\(169\) | 7.44888 | 0.572991 | ||||||||
\(170\) | 4.64554 | 0.356296 | ||||||||
\(171\) | 4.37702 | 0.334719 | ||||||||
\(172\) | 1.06760 | 0.0814035 | ||||||||
\(173\) | −13.1084 | −0.996610 | −0.498305 | − | 0.867002i | \(-0.666044\pi\) | ||||
−0.498305 | + | 0.867002i | \(0.666044\pi\) | |||||||
\(174\) | −7.95672 | −0.603197 | ||||||||
\(175\) | 14.0627 | 1.06304 | ||||||||
\(176\) | −0.708752 | −0.0534242 | ||||||||
\(177\) | −3.87144 | −0.290995 | ||||||||
\(178\) | 2.45925 | 0.184329 | ||||||||
\(179\) | −5.73901 | −0.428954 | −0.214477 | − | 0.976729i | \(-0.568805\pi\) | ||||
−0.214477 | + | 0.976729i | \(0.568805\pi\) | |||||||
\(180\) | −2.34000 | −0.174414 | ||||||||
\(181\) | −4.15790 | −0.309054 | −0.154527 | − | 0.987989i | \(-0.549385\pi\) | ||||
−0.154527 | + | 0.987989i | \(0.549385\pi\) | |||||||
\(182\) | −13.7659 | −1.02040 | ||||||||
\(183\) | 5.03255 | 0.372017 | ||||||||
\(184\) | 6.01283 | 0.443272 | ||||||||
\(185\) | −0.442069 | −0.0325016 | ||||||||
\(186\) | 11.9847 | 0.878760 | ||||||||
\(187\) | 5.33786 | 0.390343 | ||||||||
\(188\) | 5.03724 | 0.367378 | ||||||||
\(189\) | 6.29700 | 0.458040 | ||||||||
\(190\) | −0.711684 | −0.0516310 | ||||||||
\(191\) | −10.2417 | −0.741062 | −0.370531 | − | 0.928820i | \(-0.620824\pi\) | ||||
−0.370531 | + | 0.928820i | \(0.620824\pi\) | |||||||
\(192\) | −2.60646 | −0.188105 | ||||||||
\(193\) | −1.58131 | −0.113825 | −0.0569127 | − | 0.998379i | \(-0.518126\pi\) | ||||
−0.0569127 | + | 0.998379i | \(0.518126\pi\) | |||||||
\(194\) | 12.5402 | 0.900334 | ||||||||
\(195\) | 7.27023 | 0.520632 | ||||||||
\(196\) | 2.26707 | 0.161934 | ||||||||
\(197\) | 0.465375 | 0.0331566 | 0.0165783 | − | 0.999863i | \(-0.494723\pi\) | ||||
0.0165783 | + | 0.999863i | \(0.494723\pi\) | |||||||
\(198\) | −2.68873 | −0.191080 | ||||||||
\(199\) | 0.780673 | 0.0553404 | 0.0276702 | − | 0.999617i | \(-0.491191\pi\) | ||||
0.0276702 | + | 0.999617i | \(0.491191\pi\) | |||||||
\(200\) | −4.61953 | −0.326650 | ||||||||
\(201\) | 7.78362 | 0.549014 | ||||||||
\(202\) | −13.5576 | −0.953912 | ||||||||
\(203\) | −9.29297 | −0.652239 | ||||||||
\(204\) | 19.6302 | 1.37439 | ||||||||
\(205\) | −3.46380 | −0.241922 | ||||||||
\(206\) | 19.5165 | 1.35978 | ||||||||
\(207\) | 22.8104 | 1.58543 | ||||||||
\(208\) | 4.52204 | 0.313547 | ||||||||
\(209\) | −0.817747 | −0.0565647 | ||||||||
\(210\) | −4.89423 | −0.337734 | ||||||||
\(211\) | −24.0924 | −1.65859 | −0.829296 | − | 0.558809i | \(-0.811258\pi\) | ||||
−0.829296 | + | 0.558809i | \(0.811258\pi\) | |||||||
\(212\) | −6.45049 | −0.443021 | ||||||||
\(213\) | −30.5332 | −2.09210 | ||||||||
\(214\) | −12.9180 | −0.883059 | ||||||||
\(215\) | −0.658522 | −0.0449108 | ||||||||
\(216\) | −2.06853 | −0.140746 | ||||||||
\(217\) | 13.9974 | 0.950206 | ||||||||
\(218\) | −3.93185 | −0.266299 | ||||||||
\(219\) | −14.3553 | −0.970040 | ||||||||
\(220\) | 0.437177 | 0.0294745 | ||||||||
\(221\) | −34.0571 | −2.29093 | ||||||||
\(222\) | −1.86800 | −0.125372 | ||||||||
\(223\) | −18.9446 | −1.26862 | −0.634312 | − | 0.773077i | \(-0.718716\pi\) | ||||
−0.634312 | + | 0.773077i | \(0.718716\pi\) | |||||||
\(224\) | −3.04419 | −0.203398 | ||||||||
\(225\) | −17.5247 | −1.16831 | ||||||||
\(226\) | −18.6937 | −1.24349 | ||||||||
\(227\) | −21.2732 | −1.41195 | −0.705975 | − | 0.708237i | \(-0.749491\pi\) | ||||
−0.705975 | + | 0.708237i | \(0.749491\pi\) | |||||||
\(228\) | −3.00729 | −0.199163 | ||||||||
\(229\) | 9.46496 | 0.625462 | 0.312731 | − | 0.949842i | \(-0.398756\pi\) | ||||
0.312731 | + | 0.949842i | \(0.398756\pi\) | |||||||
\(230\) | −3.70887 | −0.244556 | ||||||||
\(231\) | −5.62362 | −0.370007 | ||||||||
\(232\) | 3.05269 | 0.200419 | ||||||||
\(233\) | −7.44251 | −0.487575 | −0.243787 | − | 0.969829i | \(-0.578390\pi\) | ||||
−0.243787 | + | 0.969829i | \(0.578390\pi\) | |||||||
\(234\) | 17.1549 | 1.12145 | ||||||||
\(235\) | −3.10710 | −0.202685 | ||||||||
\(236\) | 1.48533 | 0.0966866 | ||||||||
\(237\) | −28.5986 | −1.85768 | ||||||||
\(238\) | 22.9269 | 1.48613 | ||||||||
\(239\) | 23.9371 | 1.54837 | 0.774183 | − | 0.632962i | \(-0.218161\pi\) | ||||
0.774183 | + | 0.632962i | \(0.218161\pi\) | |||||||
\(240\) | 1.60773 | 0.103779 | ||||||||
\(241\) | −7.34849 | −0.473358 | −0.236679 | − | 0.971588i | \(-0.576059\pi\) | ||||
−0.236679 | + | 0.971588i | \(0.576059\pi\) | |||||||
\(242\) | −10.4977 | −0.674816 | ||||||||
\(243\) | 21.8165 | 1.39953 | ||||||||
\(244\) | −1.93080 | −0.123607 | ||||||||
\(245\) | −1.39839 | −0.0893399 | ||||||||
\(246\) | −14.6366 | −0.933195 | ||||||||
\(247\) | 5.21746 | 0.331979 | ||||||||
\(248\) | −4.59808 | −0.291978 | ||||||||
\(249\) | 4.20989 | 0.266791 | ||||||||
\(250\) | 5.93358 | 0.375272 | ||||||||
\(251\) | 23.0951 | 1.45775 | 0.728876 | − | 0.684646i | \(-0.240043\pi\) | ||||
0.728876 | + | 0.684646i | \(0.240043\pi\) | |||||||
\(252\) | −11.5485 | −0.727486 | ||||||||
\(253\) | −4.26161 | −0.267925 | ||||||||
\(254\) | −5.47636 | −0.343618 | ||||||||
\(255\) | −12.1084 | −0.758257 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −15.9746 | −0.996469 | −0.498235 | − | 0.867042i | \(-0.666018\pi\) | ||||
−0.498235 | + | 0.867042i | \(0.666018\pi\) | |||||||
\(258\) | −2.78265 | −0.173240 | ||||||||
\(259\) | −2.18172 | −0.135565 | ||||||||
\(260\) | −2.78932 | −0.172986 | ||||||||
\(261\) | 11.5808 | 0.716831 | ||||||||
\(262\) | 19.0650 | 1.17784 | ||||||||
\(263\) | −20.7078 | −1.27690 | −0.638450 | − | 0.769663i | \(-0.720424\pi\) | ||||
−0.638450 | + | 0.769663i | \(0.720424\pi\) | |||||||
\(264\) | 1.84733 | 0.113695 | ||||||||
\(265\) | 3.97883 | 0.244418 | ||||||||
\(266\) | −3.51233 | −0.215355 | ||||||||
\(267\) | −6.40994 | −0.392282 | ||||||||
\(268\) | −2.98628 | −0.182416 | ||||||||
\(269\) | −30.4598 | −1.85716 | −0.928582 | − | 0.371127i | \(-0.878972\pi\) | ||||
−0.928582 | + | 0.371127i | \(0.878972\pi\) | |||||||
\(270\) | 1.27593 | 0.0776504 | ||||||||
\(271\) | −21.4757 | −1.30456 | −0.652278 | − | 0.757980i | \(-0.726186\pi\) | ||||
−0.652278 | + | 0.757980i | \(0.726186\pi\) | |||||||
\(272\) | −7.53136 | −0.456655 | ||||||||
\(273\) | 35.8804 | 2.17158 | ||||||||
\(274\) | −15.1802 | −0.917069 | ||||||||
\(275\) | 3.27410 | 0.197436 | ||||||||
\(276\) | −15.6722 | −0.943355 | ||||||||
\(277\) | −13.6355 | −0.819276 | −0.409638 | − | 0.912248i | \(-0.634345\pi\) | ||||
−0.409638 | + | 0.912248i | \(0.634345\pi\) | |||||||
\(278\) | −6.26425 | −0.375705 | ||||||||
\(279\) | −17.4434 | −1.04431 | ||||||||
\(280\) | 1.87773 | 0.112216 | ||||||||
\(281\) | −6.77677 | −0.404268 | −0.202134 | − | 0.979358i | \(-0.564788\pi\) | ||||
−0.202134 | + | 0.979358i | \(0.564788\pi\) | |||||||
\(282\) | −13.1293 | −0.781841 | ||||||||
\(283\) | 5.42191 | 0.322299 | 0.161150 | − | 0.986930i | \(-0.448480\pi\) | ||||
0.161150 | + | 0.986930i | \(0.448480\pi\) | |||||||
\(284\) | 11.7144 | 0.695124 | ||||||||
\(285\) | 1.85497 | 0.109879 | ||||||||
\(286\) | −3.20501 | −0.189516 | ||||||||
\(287\) | −17.0947 | −1.00907 | ||||||||
\(288\) | 3.79362 | 0.223541 | ||||||||
\(289\) | 39.7213 | 2.33655 | ||||||||
\(290\) | −1.88298 | −0.110573 | ||||||||
\(291\) | −32.6855 | −1.91606 | ||||||||
\(292\) | 5.50758 | 0.322307 | ||||||||
\(293\) | 2.48853 | 0.145382 | 0.0726908 | − | 0.997355i | \(-0.476841\pi\) | ||||
0.0726908 | + | 0.997355i | \(0.476841\pi\) | |||||||
\(294\) | −5.90903 | −0.344622 | ||||||||
\(295\) | −0.916189 | −0.0533426 | ||||||||
\(296\) | 0.716683 | 0.0416564 | ||||||||
\(297\) | 1.46608 | 0.0850704 | ||||||||
\(298\) | 14.4738 | 0.838447 | ||||||||
\(299\) | 27.1903 | 1.57246 | ||||||||
\(300\) | 12.0406 | 0.695164 | ||||||||
\(301\) | −3.24996 | −0.187325 | ||||||||
\(302\) | −0.119120 | −0.00685457 | ||||||||
\(303\) | 35.3374 | 2.03008 | ||||||||
\(304\) | 1.15378 | 0.0661740 | ||||||||
\(305\) | 1.19097 | 0.0681947 | ||||||||
\(306\) | −28.5711 | −1.63330 | ||||||||
\(307\) | −14.6098 | −0.833828 | −0.416914 | − | 0.908946i | \(-0.636888\pi\) | ||||
−0.416914 | + | 0.908946i | \(0.636888\pi\) | |||||||
\(308\) | 2.15757 | 0.122939 | ||||||||
\(309\) | −50.8689 | −2.89383 | ||||||||
\(310\) | 2.83622 | 0.161086 | ||||||||
\(311\) | −11.7922 | −0.668677 | −0.334338 | − | 0.942453i | \(-0.608513\pi\) | ||||
−0.334338 | + | 0.942453i | \(0.608513\pi\) | |||||||
\(312\) | −11.7865 | −0.667280 | ||||||||
\(313\) | −5.04499 | −0.285160 | −0.142580 | − | 0.989783i | \(-0.545540\pi\) | ||||
−0.142580 | + | 0.989783i | \(0.545540\pi\) | |||||||
\(314\) | 15.5116 | 0.875368 | ||||||||
\(315\) | 7.12341 | 0.401359 | ||||||||
\(316\) | 10.9722 | 0.617236 | ||||||||
\(317\) | −11.4506 | −0.643131 | −0.321566 | − | 0.946887i | \(-0.604209\pi\) | ||||
−0.321566 | + | 0.946887i | \(0.604209\pi\) | |||||||
\(318\) | 16.8129 | 0.942822 | ||||||||
\(319\) | −2.16360 | −0.121139 | ||||||||
\(320\) | −0.616826 | −0.0344816 | ||||||||
\(321\) | 33.6703 | 1.87929 | ||||||||
\(322\) | −18.3042 | −1.02005 | ||||||||
\(323\) | −8.68956 | −0.483500 | ||||||||
\(324\) | −5.98931 | −0.332740 | ||||||||
\(325\) | −20.8897 | −1.15875 | ||||||||
\(326\) | −15.0880 | −0.835645 | ||||||||
\(327\) | 10.2482 | 0.566727 | ||||||||
\(328\) | 5.61551 | 0.310065 | ||||||||
\(329\) | −15.3343 | −0.845407 | ||||||||
\(330\) | −1.13948 | −0.0627265 | ||||||||
\(331\) | −23.9042 | −1.31390 | −0.656948 | − | 0.753936i | \(-0.728153\pi\) | ||||
−0.656948 | + | 0.753936i | \(0.728153\pi\) | |||||||
\(332\) | −1.61518 | −0.0886443 | ||||||||
\(333\) | 2.71882 | 0.148991 | ||||||||
\(334\) | 14.4544 | 0.790909 | ||||||||
\(335\) | 1.84202 | 0.100640 | ||||||||
\(336\) | 7.93454 | 0.432865 | ||||||||
\(337\) | −17.9843 | −0.979667 | −0.489833 | − | 0.871816i | \(-0.662942\pi\) | ||||
−0.489833 | + | 0.871816i | \(0.662942\pi\) | |||||||
\(338\) | 7.44888 | 0.405166 | ||||||||
\(339\) | 48.7244 | 2.64635 | ||||||||
\(340\) | 4.64554 | 0.251940 | ||||||||
\(341\) | 3.25890 | 0.176479 | ||||||||
\(342\) | 4.37702 | 0.236682 | ||||||||
\(343\) | 14.4079 | 0.777954 | ||||||||
\(344\) | 1.06760 | 0.0575610 | ||||||||
\(345\) | 9.66702 | 0.520455 | ||||||||
\(346\) | −13.1084 | −0.704710 | ||||||||
\(347\) | 17.4068 | 0.934447 | 0.467224 | − | 0.884139i | \(-0.345254\pi\) | ||||
0.467224 | + | 0.884139i | \(0.345254\pi\) | |||||||
\(348\) | −7.95672 | −0.426525 | ||||||||
\(349\) | −29.2073 | −1.56343 | −0.781716 | − | 0.623635i | \(-0.785655\pi\) | ||||
−0.781716 | + | 0.623635i | \(0.785655\pi\) | |||||||
\(350\) | 14.0627 | 0.751683 | ||||||||
\(351\) | −9.35400 | −0.499280 | ||||||||
\(352\) | −0.708752 | −0.0377766 | ||||||||
\(353\) | −18.7365 | −0.997242 | −0.498621 | − | 0.866820i | \(-0.666160\pi\) | ||||
−0.498621 | + | 0.866820i | \(0.666160\pi\) | |||||||
\(354\) | −3.87144 | −0.205765 | ||||||||
\(355\) | −7.22578 | −0.383504 | ||||||||
\(356\) | 2.45925 | 0.130340 | ||||||||
\(357\) | −59.7579 | −3.16272 | ||||||||
\(358\) | −5.73901 | −0.303316 | ||||||||
\(359\) | 26.8376 | 1.41643 | 0.708216 | − | 0.705995i | \(-0.249500\pi\) | ||||
0.708216 | + | 0.705995i | \(0.249500\pi\) | |||||||
\(360\) | −2.34000 | −0.123329 | ||||||||
\(361\) | −17.6688 | −0.929936 | ||||||||
\(362\) | −4.15790 | −0.218535 | ||||||||
\(363\) | 27.3617 | 1.43612 | ||||||||
\(364\) | −13.7659 | −0.721532 | ||||||||
\(365\) | −3.39722 | −0.177819 | ||||||||
\(366\) | 5.03255 | 0.263056 | ||||||||
\(367\) | 17.6152 | 0.919505 | 0.459752 | − | 0.888047i | \(-0.347938\pi\) | ||||
0.459752 | + | 0.888047i | \(0.347938\pi\) | |||||||
\(368\) | 6.01283 | 0.313441 | ||||||||
\(369\) | 21.3031 | 1.10900 | ||||||||
\(370\) | −0.442069 | −0.0229821 | ||||||||
\(371\) | 19.6365 | 1.01948 | ||||||||
\(372\) | 11.9847 | 0.621377 | ||||||||
\(373\) | 37.0947 | 1.92069 | 0.960346 | − | 0.278811i | \(-0.0899404\pi\) | ||||
0.960346 | + | 0.278811i | \(0.0899404\pi\) | |||||||
\(374\) | 5.33786 | 0.276014 | ||||||||
\(375\) | −15.4656 | −0.798641 | ||||||||
\(376\) | 5.03724 | 0.259776 | ||||||||
\(377\) | 13.8044 | 0.710964 | ||||||||
\(378\) | 6.29700 | 0.323883 | ||||||||
\(379\) | 11.6444 | 0.598131 | 0.299065 | − | 0.954233i | \(-0.403325\pi\) | ||||
0.299065 | + | 0.954233i | \(0.403325\pi\) | |||||||
\(380\) | −0.711684 | −0.0365086 | ||||||||
\(381\) | 14.2739 | 0.731275 | ||||||||
\(382\) | −10.2417 | −0.524010 | ||||||||
\(383\) | 7.91835 | 0.404609 | 0.202304 | − | 0.979323i | \(-0.435157\pi\) | ||||
0.202304 | + | 0.979323i | \(0.435157\pi\) | |||||||
\(384\) | −2.60646 | −0.133010 | ||||||||
\(385\) | −1.33085 | −0.0678263 | ||||||||
\(386\) | −1.58131 | −0.0804867 | ||||||||
\(387\) | 4.05006 | 0.205876 | ||||||||
\(388\) | 12.5402 | 0.636632 | ||||||||
\(389\) | 22.7545 | 1.15370 | 0.576849 | − | 0.816851i | \(-0.304282\pi\) | ||||
0.576849 | + | 0.816851i | \(0.304282\pi\) | |||||||
\(390\) | 7.27023 | 0.368143 | ||||||||
\(391\) | −45.2848 | −2.29015 | ||||||||
\(392\) | 2.26707 | 0.114504 | ||||||||
\(393\) | −49.6922 | −2.50664 | ||||||||
\(394\) | 0.465375 | 0.0234453 | ||||||||
\(395\) | −6.76796 | −0.340533 | ||||||||
\(396\) | −2.68873 | −0.135114 | ||||||||
\(397\) | −20.7737 | −1.04260 | −0.521302 | − | 0.853372i | \(-0.674553\pi\) | ||||
−0.521302 | + | 0.853372i | \(0.674553\pi\) | |||||||
\(398\) | 0.780673 | 0.0391316 | ||||||||
\(399\) | 9.15475 | 0.458311 | ||||||||
\(400\) | −4.61953 | −0.230976 | ||||||||
\(401\) | −23.2179 | −1.15945 | −0.579724 | − | 0.814813i | \(-0.696840\pi\) | ||||
−0.579724 | + | 0.814813i | \(0.696840\pi\) | |||||||
\(402\) | 7.78362 | 0.388212 | ||||||||
\(403\) | −20.7927 | −1.03576 | ||||||||
\(404\) | −13.5576 | −0.674518 | ||||||||
\(405\) | 3.69437 | 0.183574 | ||||||||
\(406\) | −9.29297 | −0.461202 | ||||||||
\(407\) | −0.507951 | −0.0251782 | ||||||||
\(408\) | 19.6302 | 0.971837 | ||||||||
\(409\) | −11.9253 | −0.589669 | −0.294835 | − | 0.955548i | \(-0.595265\pi\) | ||||
−0.294835 | + | 0.955548i | \(0.595265\pi\) | |||||||
\(410\) | −3.46380 | −0.171065 | ||||||||
\(411\) | 39.5665 | 1.95167 | ||||||||
\(412\) | 19.5165 | 0.961508 | ||||||||
\(413\) | −4.52161 | −0.222494 | ||||||||
\(414\) | 22.8104 | 1.12107 | ||||||||
\(415\) | 0.996283 | 0.0489056 | ||||||||
\(416\) | 4.52204 | 0.221711 | ||||||||
\(417\) | 16.3275 | 0.799562 | ||||||||
\(418\) | −0.817747 | −0.0399973 | ||||||||
\(419\) | 27.7954 | 1.35790 | 0.678948 | − | 0.734187i | \(-0.262436\pi\) | ||||
0.678948 | + | 0.734187i | \(0.262436\pi\) | |||||||
\(420\) | −4.89423 | −0.238814 | ||||||||
\(421\) | −34.8715 | −1.69953 | −0.849765 | − | 0.527161i | \(-0.823256\pi\) | ||||
−0.849765 | + | 0.527161i | \(0.823256\pi\) | |||||||
\(422\) | −24.0924 | −1.17280 | ||||||||
\(423\) | 19.1094 | 0.929129 | ||||||||
\(424\) | −6.45049 | −0.313264 | ||||||||
\(425\) | 34.7913 | 1.68763 | ||||||||
\(426\) | −30.5332 | −1.47934 | ||||||||
\(427\) | 5.87772 | 0.284443 | ||||||||
\(428\) | −12.9180 | −0.624417 | ||||||||
\(429\) | 8.35372 | 0.403321 | ||||||||
\(430\) | −0.658522 | −0.0317567 | ||||||||
\(431\) | −14.4154 | −0.694365 | −0.347183 | − | 0.937798i | \(-0.612862\pi\) | ||||
−0.347183 | + | 0.937798i | \(0.612862\pi\) | |||||||
\(432\) | −2.06853 | −0.0995224 | ||||||||
\(433\) | −13.7117 | −0.658940 | −0.329470 | − | 0.944166i | \(-0.606870\pi\) | ||||
−0.329470 | + | 0.944166i | \(0.606870\pi\) | |||||||
\(434\) | 13.9974 | 0.671897 | ||||||||
\(435\) | 4.90791 | 0.235316 | ||||||||
\(436\) | −3.93185 | −0.188301 | ||||||||
\(437\) | 6.93751 | 0.331866 | ||||||||
\(438\) | −14.3553 | −0.685922 | ||||||||
\(439\) | 14.5141 | 0.692721 | 0.346360 | − | 0.938102i | \(-0.387417\pi\) | ||||
0.346360 | + | 0.938102i | \(0.387417\pi\) | |||||||
\(440\) | 0.437177 | 0.0208416 | ||||||||
\(441\) | 8.60041 | 0.409543 | ||||||||
\(442\) | −34.0571 | −1.61993 | ||||||||
\(443\) | −34.0471 | −1.61762 | −0.808812 | − | 0.588067i | \(-0.799889\pi\) | ||||
−0.808812 | + | 0.588067i | \(0.799889\pi\) | |||||||
\(444\) | −1.86800 | −0.0886515 | ||||||||
\(445\) | −1.51693 | −0.0719095 | ||||||||
\(446\) | −18.9446 | −0.897052 | ||||||||
\(447\) | −37.7255 | −1.78435 | ||||||||
\(448\) | −3.04419 | −0.143824 | ||||||||
\(449\) | 14.4308 | 0.681032 | 0.340516 | − | 0.940239i | \(-0.389398\pi\) | ||||
0.340516 | + | 0.940239i | \(0.389398\pi\) | |||||||
\(450\) | −17.5247 | −0.826123 | ||||||||
\(451\) | −3.98001 | −0.187411 | ||||||||
\(452\) | −18.6937 | −0.879279 | ||||||||
\(453\) | 0.310480 | 0.0145876 | ||||||||
\(454\) | −21.2732 | −0.998399 | ||||||||
\(455\) | 8.49120 | 0.398074 | ||||||||
\(456\) | −3.00729 | −0.140829 | ||||||||
\(457\) | −17.7909 | −0.832223 | −0.416111 | − | 0.909314i | \(-0.636607\pi\) | ||||
−0.416111 | + | 0.909314i | \(0.636607\pi\) | |||||||
\(458\) | 9.46496 | 0.442269 | ||||||||
\(459\) | 15.5789 | 0.727159 | ||||||||
\(460\) | −3.70887 | −0.172927 | ||||||||
\(461\) | 27.0926 | 1.26183 | 0.630915 | − | 0.775852i | \(-0.282680\pi\) | ||||
0.630915 | + | 0.775852i | \(0.282680\pi\) | |||||||
\(462\) | −5.62362 | −0.261635 | ||||||||
\(463\) | −32.5408 | −1.51230 | −0.756150 | − | 0.654398i | \(-0.772922\pi\) | ||||
−0.756150 | + | 0.654398i | \(0.772922\pi\) | |||||||
\(464\) | 3.05269 | 0.141718 | ||||||||
\(465\) | −7.39247 | −0.342818 | ||||||||
\(466\) | −7.44251 | −0.344767 | ||||||||
\(467\) | −4.16093 | −0.192545 | −0.0962724 | − | 0.995355i | \(-0.530692\pi\) | ||||
−0.0962724 | + | 0.995355i | \(0.530692\pi\) | |||||||
\(468\) | 17.1549 | 0.792986 | ||||||||
\(469\) | 9.09080 | 0.419774 | ||||||||
\(470\) | −3.10710 | −0.143320 | ||||||||
\(471\) | −40.4302 | −1.86293 | ||||||||
\(472\) | 1.48533 | 0.0683677 | ||||||||
\(473\) | −0.756661 | −0.0347913 | ||||||||
\(474\) | −28.5986 | −1.31358 | ||||||||
\(475\) | −5.32993 | −0.244554 | ||||||||
\(476\) | 22.9269 | 1.05085 | ||||||||
\(477\) | −24.4707 | −1.12044 | ||||||||
\(478\) | 23.9371 | 1.09486 | ||||||||
\(479\) | −29.7519 | −1.35940 | −0.679698 | − | 0.733492i | \(-0.737889\pi\) | ||||
−0.679698 | + | 0.733492i | \(0.737889\pi\) | |||||||
\(480\) | 1.60773 | 0.0733826 | ||||||||
\(481\) | 3.24087 | 0.147771 | ||||||||
\(482\) | −7.34849 | −0.334714 | ||||||||
\(483\) | 47.7091 | 2.17084 | ||||||||
\(484\) | −10.4977 | −0.477167 | ||||||||
\(485\) | −7.73513 | −0.351234 | ||||||||
\(486\) | 21.8165 | 0.989616 | ||||||||
\(487\) | 31.3125 | 1.41890 | 0.709452 | − | 0.704754i | \(-0.248943\pi\) | ||||
0.709452 | + | 0.704754i | \(0.248943\pi\) | |||||||
\(488\) | −1.93080 | −0.0874033 | ||||||||
\(489\) | 39.3261 | 1.77839 | ||||||||
\(490\) | −1.39839 | −0.0631728 | ||||||||
\(491\) | 2.57433 | 0.116178 | 0.0580889 | − | 0.998311i | \(-0.481499\pi\) | ||||
0.0580889 | + | 0.998311i | \(0.481499\pi\) | |||||||
\(492\) | −14.6366 | −0.659869 | ||||||||
\(493\) | −22.9909 | −1.03546 | ||||||||
\(494\) | 5.21746 | 0.234745 | ||||||||
\(495\) | 1.65848 | 0.0745432 | ||||||||
\(496\) | −4.59808 | −0.206460 | ||||||||
\(497\) | −35.6610 | −1.59961 | ||||||||
\(498\) | 4.20989 | 0.188649 | ||||||||
\(499\) | −31.6113 | −1.41512 | −0.707559 | − | 0.706654i | \(-0.750204\pi\) | ||||
−0.707559 | + | 0.706654i | \(0.750204\pi\) | |||||||
\(500\) | 5.93358 | 0.265358 | ||||||||
\(501\) | −37.6748 | −1.68318 | ||||||||
\(502\) | 23.0951 | 1.03079 | ||||||||
\(503\) | −14.2842 | −0.636902 | −0.318451 | − | 0.947939i | \(-0.603163\pi\) | ||||
−0.318451 | + | 0.947939i | \(0.603163\pi\) | |||||||
\(504\) | −11.5485 | −0.514410 | ||||||||
\(505\) | 8.36271 | 0.372136 | ||||||||
\(506\) | −4.26161 | −0.189452 | ||||||||
\(507\) | −19.4152 | −0.862259 | ||||||||
\(508\) | −5.47636 | −0.242974 | ||||||||
\(509\) | 13.2359 | 0.586672 | 0.293336 | − | 0.956009i | \(-0.405235\pi\) | ||||
0.293336 | + | 0.956009i | \(0.405235\pi\) | |||||||
\(510\) | −12.1084 | −0.536169 | ||||||||
\(511\) | −16.7661 | −0.741689 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −2.38664 | −0.105373 | ||||||||
\(514\) | −15.9746 | −0.704610 | ||||||||
\(515\) | −12.0383 | −0.530470 | ||||||||
\(516\) | −2.78265 | −0.122499 | ||||||||
\(517\) | −3.57015 | −0.157015 | ||||||||
\(518\) | −2.18172 | −0.0958591 | ||||||||
\(519\) | 34.1664 | 1.49974 | ||||||||
\(520\) | −2.78932 | −0.122320 | ||||||||
\(521\) | 34.4885 | 1.51097 | 0.755485 | − | 0.655166i | \(-0.227401\pi\) | ||||
0.755485 | + | 0.655166i | \(0.227401\pi\) | |||||||
\(522\) | 11.5808 | 0.506876 | ||||||||
\(523\) | −31.6562 | −1.38423 | −0.692114 | − | 0.721788i | \(-0.743321\pi\) | ||||
−0.692114 | + | 0.721788i | \(0.743321\pi\) | |||||||
\(524\) | 19.0650 | 0.832859 | ||||||||
\(525\) | −36.6538 | −1.59970 | ||||||||
\(526\) | −20.7078 | −0.902905 | ||||||||
\(527\) | 34.6298 | 1.50850 | ||||||||
\(528\) | 1.84733 | 0.0803948 | ||||||||
\(529\) | 13.1542 | 0.571921 | ||||||||
\(530\) | 3.97883 | 0.172829 | ||||||||
\(531\) | 5.63477 | 0.244528 | ||||||||
\(532\) | −3.51233 | −0.152279 | ||||||||
\(533\) | 25.3936 | 1.09992 | ||||||||
\(534\) | −6.40994 | −0.277385 | ||||||||
\(535\) | 7.96819 | 0.344495 | ||||||||
\(536\) | −2.98628 | −0.128988 | ||||||||
\(537\) | 14.9585 | 0.645507 | ||||||||
\(538\) | −30.4598 | −1.31321 | ||||||||
\(539\) | −1.60679 | −0.0692094 | ||||||||
\(540\) | 1.27593 | 0.0549071 | ||||||||
\(541\) | 9.22216 | 0.396492 | 0.198246 | − | 0.980152i | \(-0.436476\pi\) | ||||
0.198246 | + | 0.980152i | \(0.436476\pi\) | |||||||
\(542\) | −21.4757 | −0.922460 | ||||||||
\(543\) | 10.8374 | 0.465077 | ||||||||
\(544\) | −7.53136 | −0.322904 | ||||||||
\(545\) | 2.42527 | 0.103887 | ||||||||
\(546\) | 35.8804 | 1.53554 | ||||||||
\(547\) | −16.5514 | −0.707688 | −0.353844 | − | 0.935305i | \(-0.615126\pi\) | ||||
−0.353844 | + | 0.935305i | \(0.615126\pi\) | |||||||
\(548\) | −15.1802 | −0.648466 | ||||||||
\(549\) | −7.32473 | −0.312612 | ||||||||
\(550\) | 3.27410 | 0.139608 | ||||||||
\(551\) | 3.52215 | 0.150049 | ||||||||
\(552\) | −15.6722 | −0.667053 | ||||||||
\(553\) | −33.4015 | −1.42038 | ||||||||
\(554\) | −13.6355 | −0.579316 | ||||||||
\(555\) | 1.15223 | 0.0489096 | ||||||||
\(556\) | −6.26425 | −0.265664 | ||||||||
\(557\) | 6.47071 | 0.274173 | 0.137086 | − | 0.990559i | \(-0.456226\pi\) | ||||
0.137086 | + | 0.990559i | \(0.456226\pi\) | |||||||
\(558\) | −17.4434 | −0.738436 | ||||||||
\(559\) | 4.82772 | 0.204191 | ||||||||
\(560\) | 1.87773 | 0.0793488 | ||||||||
\(561\) | −13.9129 | −0.587404 | ||||||||
\(562\) | −6.77677 | −0.285861 | ||||||||
\(563\) | −23.4795 | −0.989541 | −0.494771 | − | 0.869024i | \(-0.664748\pi\) | ||||
−0.494771 | + | 0.869024i | \(0.664748\pi\) | |||||||
\(564\) | −13.1293 | −0.552845 | ||||||||
\(565\) | 11.5308 | 0.485104 | ||||||||
\(566\) | 5.42191 | 0.227900 | ||||||||
\(567\) | 18.2326 | 0.765697 | ||||||||
\(568\) | 11.7144 | 0.491527 | ||||||||
\(569\) | −21.4300 | −0.898392 | −0.449196 | − | 0.893433i | \(-0.648290\pi\) | ||||
−0.449196 | + | 0.893433i | \(0.648290\pi\) | |||||||
\(570\) | 1.85497 | 0.0776963 | ||||||||
\(571\) | 3.52308 | 0.147437 | 0.0737183 | − | 0.997279i | \(-0.476513\pi\) | ||||
0.0737183 | + | 0.997279i | \(0.476513\pi\) | |||||||
\(572\) | −3.20501 | −0.134008 | ||||||||
\(573\) | 26.6945 | 1.11518 | ||||||||
\(574\) | −17.0947 | −0.713518 | ||||||||
\(575\) | −27.7764 | −1.15836 | ||||||||
\(576\) | 3.79362 | 0.158067 | ||||||||
\(577\) | −37.5094 | −1.56154 | −0.780769 | − | 0.624820i | \(-0.785173\pi\) | ||||
−0.780769 | + | 0.624820i | \(0.785173\pi\) | |||||||
\(578\) | 39.7213 | 1.65219 | ||||||||
\(579\) | 4.12162 | 0.171289 | ||||||||
\(580\) | −1.88298 | −0.0781866 | ||||||||
\(581\) | 4.91690 | 0.203987 | ||||||||
\(582\) | −32.6855 | −1.35486 | ||||||||
\(583\) | 4.57180 | 0.189345 | ||||||||
\(584\) | 5.50758 | 0.227905 | ||||||||
\(585\) | −10.5816 | −0.437495 | ||||||||
\(586\) | 2.48853 | 0.102800 | ||||||||
\(587\) | −0.295064 | −0.0121786 | −0.00608929 | − | 0.999981i | \(-0.501938\pi\) | ||||
−0.00608929 | + | 0.999981i | \(0.501938\pi\) | |||||||
\(588\) | −5.90903 | −0.243684 | ||||||||
\(589\) | −5.30519 | −0.218596 | ||||||||
\(590\) | −0.916189 | −0.0377189 | ||||||||
\(591\) | −1.21298 | −0.0498953 | ||||||||
\(592\) | 0.716683 | 0.0294555 | ||||||||
\(593\) | −19.9916 | −0.820956 | −0.410478 | − | 0.911870i | \(-0.634638\pi\) | ||||
−0.410478 | + | 0.911870i | \(0.634638\pi\) | |||||||
\(594\) | 1.46608 | 0.0601539 | ||||||||
\(595\) | −14.1419 | −0.579761 | ||||||||
\(596\) | 14.4738 | 0.592872 | ||||||||
\(597\) | −2.03479 | −0.0832784 | ||||||||
\(598\) | 27.1903 | 1.11189 | ||||||||
\(599\) | −5.06602 | −0.206992 | −0.103496 | − | 0.994630i | \(-0.533003\pi\) | ||||
−0.103496 | + | 0.994630i | \(0.533003\pi\) | |||||||
\(600\) | 12.0406 | 0.491555 | ||||||||
\(601\) | 33.4515 | 1.36451 | 0.682257 | − | 0.731113i | \(-0.260999\pi\) | ||||
0.682257 | + | 0.731113i | \(0.260999\pi\) | |||||||
\(602\) | −3.24996 | −0.132459 | ||||||||
\(603\) | −11.3288 | −0.461345 | ||||||||
\(604\) | −0.119120 | −0.00484691 | ||||||||
\(605\) | 6.47524 | 0.263256 | ||||||||
\(606\) | 35.3374 | 1.43548 | ||||||||
\(607\) | 41.9650 | 1.70331 | 0.851654 | − | 0.524105i | \(-0.175600\pi\) | ||||
0.851654 | + | 0.524105i | \(0.175600\pi\) | |||||||
\(608\) | 1.15378 | 0.0467921 | ||||||||
\(609\) | 24.2217 | 0.981514 | ||||||||
\(610\) | 1.19097 | 0.0482209 | ||||||||
\(611\) | 22.7786 | 0.921524 | ||||||||
\(612\) | −28.5711 | −1.15492 | ||||||||
\(613\) | −47.6468 | −1.92444 | −0.962219 | − | 0.272278i | \(-0.912223\pi\) | ||||
−0.962219 | + | 0.272278i | \(0.912223\pi\) | |||||||
\(614\) | −14.6098 | −0.589605 | ||||||||
\(615\) | 9.02824 | 0.364054 | ||||||||
\(616\) | 2.15757 | 0.0869311 | ||||||||
\(617\) | 12.0943 | 0.486897 | 0.243449 | − | 0.969914i | \(-0.421721\pi\) | ||||
0.243449 | + | 0.969914i | \(0.421721\pi\) | |||||||
\(618\) | −50.8689 | −2.04625 | ||||||||
\(619\) | 13.4894 | 0.542185 | 0.271093 | − | 0.962553i | \(-0.412615\pi\) | ||||
0.271093 | + | 0.962553i | \(0.412615\pi\) | |||||||
\(620\) | 2.83622 | 0.113905 | ||||||||
\(621\) | −12.4378 | −0.499110 | ||||||||
\(622\) | −11.7922 | −0.472826 | ||||||||
\(623\) | −7.48643 | −0.299937 | ||||||||
\(624\) | −11.7865 | −0.471838 | ||||||||
\(625\) | 19.4376 | 0.777506 | ||||||||
\(626\) | −5.04499 | −0.201639 | ||||||||
\(627\) | 2.13142 | 0.0851208 | ||||||||
\(628\) | 15.5116 | 0.618978 | ||||||||
\(629\) | −5.39759 | −0.215216 | ||||||||
\(630\) | 7.12341 | 0.283803 | ||||||||
\(631\) | 5.65521 | 0.225130 | 0.112565 | − | 0.993644i | \(-0.464093\pi\) | ||||
0.112565 | + | 0.993644i | \(0.464093\pi\) | |||||||
\(632\) | 10.9722 | 0.436452 | ||||||||
\(633\) | 62.7959 | 2.49591 | ||||||||
\(634\) | −11.4506 | −0.454762 | ||||||||
\(635\) | 3.37797 | 0.134050 | ||||||||
\(636\) | 16.8129 | 0.666676 | ||||||||
\(637\) | 10.2518 | 0.406191 | ||||||||
\(638\) | −2.16360 | −0.0856579 | ||||||||
\(639\) | 44.4401 | 1.75802 | ||||||||
\(640\) | −0.616826 | −0.0243822 | ||||||||
\(641\) | 16.8022 | 0.663646 | 0.331823 | − | 0.943342i | \(-0.392336\pi\) | ||||
0.331823 | + | 0.943342i | \(0.392336\pi\) | |||||||
\(642\) | 33.6703 | 1.32886 | ||||||||
\(643\) | −7.13022 | −0.281188 | −0.140594 | − | 0.990067i | \(-0.544901\pi\) | ||||
−0.140594 | + | 0.990067i | \(0.544901\pi\) | |||||||
\(644\) | −18.3042 | −0.721286 | ||||||||
\(645\) | 1.71641 | 0.0675835 | ||||||||
\(646\) | −8.68956 | −0.341886 | ||||||||
\(647\) | −1.18914 | −0.0467498 | −0.0233749 | − | 0.999727i | \(-0.507441\pi\) | ||||
−0.0233749 | + | 0.999727i | \(0.507441\pi\) | |||||||
\(648\) | −5.98931 | −0.235282 | ||||||||
\(649\) | −1.05273 | −0.0413232 | ||||||||
\(650\) | −20.8897 | −0.819361 | ||||||||
\(651\) | −36.4836 | −1.42991 | ||||||||
\(652\) | −15.0880 | −0.590890 | ||||||||
\(653\) | 26.7321 | 1.04611 | 0.523054 | − | 0.852299i | \(-0.324793\pi\) | ||||
0.523054 | + | 0.852299i | \(0.324793\pi\) | |||||||
\(654\) | 10.2482 | 0.400736 | ||||||||
\(655\) | −11.7598 | −0.459494 | ||||||||
\(656\) | 5.61551 | 0.219249 | ||||||||
\(657\) | 20.8937 | 0.815140 | ||||||||
\(658\) | −15.3343 | −0.597793 | ||||||||
\(659\) | −19.3339 | −0.753141 | −0.376570 | − | 0.926388i | \(-0.622897\pi\) | ||||
−0.376570 | + | 0.926388i | \(0.622897\pi\) | |||||||
\(660\) | −1.13948 | −0.0443543 | ||||||||
\(661\) | 43.1667 | 1.67899 | 0.839495 | − | 0.543368i | \(-0.182851\pi\) | ||||
0.839495 | + | 0.543368i | \(0.182851\pi\) | |||||||
\(662\) | −23.9042 | −0.929064 | ||||||||
\(663\) | 88.7684 | 3.44748 | ||||||||
\(664\) | −1.61518 | −0.0626810 | ||||||||
\(665\) | 2.16650 | 0.0840133 | ||||||||
\(666\) | 2.71882 | 0.105352 | ||||||||
\(667\) | 18.3553 | 0.710722 | ||||||||
\(668\) | 14.4544 | 0.559257 | ||||||||
\(669\) | 49.3783 | 1.90907 | ||||||||
\(670\) | 1.84202 | 0.0711634 | ||||||||
\(671\) | 1.36846 | 0.0528288 | ||||||||
\(672\) | 7.93454 | 0.306082 | ||||||||
\(673\) | −41.2219 | −1.58899 | −0.794493 | − | 0.607273i | \(-0.792264\pi\) | ||||
−0.794493 | + | 0.607273i | \(0.792264\pi\) | |||||||
\(674\) | −17.9843 | −0.692729 | ||||||||
\(675\) | 9.55564 | 0.367797 | ||||||||
\(676\) | 7.44888 | 0.286496 | ||||||||
\(677\) | 3.56036 | 0.136836 | 0.0684179 | − | 0.997657i | \(-0.478205\pi\) | ||||
0.0684179 | + | 0.997657i | \(0.478205\pi\) | |||||||
\(678\) | 48.7244 | 1.87125 | ||||||||
\(679\) | −38.1747 | −1.46501 | ||||||||
\(680\) | 4.64554 | 0.178148 | ||||||||
\(681\) | 55.4476 | 2.12476 | ||||||||
\(682\) | 3.25890 | 0.124790 | ||||||||
\(683\) | 33.8031 | 1.29344 | 0.646720 | − | 0.762727i | \(-0.276140\pi\) | ||||
0.646720 | + | 0.762727i | \(0.276140\pi\) | |||||||
\(684\) | 4.37702 | 0.167359 | ||||||||
\(685\) | 9.36354 | 0.357763 | ||||||||
\(686\) | 14.4079 | 0.550097 | ||||||||
\(687\) | −24.6700 | −0.941220 | ||||||||
\(688\) | 1.06760 | 0.0407017 | ||||||||
\(689\) | −29.1694 | −1.11127 | ||||||||
\(690\) | 9.66702 | 0.368017 | ||||||||
\(691\) | 30.5921 | 1.16378 | 0.581890 | − | 0.813268i | \(-0.302313\pi\) | ||||
0.581890 | + | 0.813268i | \(0.302313\pi\) | |||||||
\(692\) | −13.1084 | −0.498305 | ||||||||
\(693\) | 8.18501 | 0.310923 | ||||||||
\(694\) | 17.4068 | 0.660754 | ||||||||
\(695\) | 3.86396 | 0.146568 | ||||||||
\(696\) | −7.95672 | −0.301599 | ||||||||
\(697\) | −42.2924 | −1.60194 | ||||||||
\(698\) | −29.2073 | −1.10551 | ||||||||
\(699\) | 19.3986 | 0.733721 | ||||||||
\(700\) | 14.0627 | 0.531520 | ||||||||
\(701\) | −34.9799 | −1.32117 | −0.660587 | − | 0.750750i | \(-0.729693\pi\) | ||||
−0.660587 | + | 0.750750i | \(0.729693\pi\) | |||||||
\(702\) | −9.35400 | −0.353044 | ||||||||
\(703\) | 0.826897 | 0.0311870 | ||||||||
\(704\) | −0.708752 | −0.0267121 | ||||||||
\(705\) | 8.09853 | 0.305008 | ||||||||
\(706\) | −18.7365 | −0.705157 | ||||||||
\(707\) | 41.2720 | 1.55219 | ||||||||
\(708\) | −3.87144 | −0.145498 | ||||||||
\(709\) | 13.4455 | 0.504955 | 0.252477 | − | 0.967603i | \(-0.418755\pi\) | ||||
0.252477 | + | 0.967603i | \(0.418755\pi\) | |||||||
\(710\) | −7.22578 | −0.271179 | ||||||||
\(711\) | 41.6245 | 1.56104 | ||||||||
\(712\) | 2.45925 | 0.0921644 | ||||||||
\(713\) | −27.6475 | −1.03541 | ||||||||
\(714\) | −59.7579 | −2.23638 | ||||||||
\(715\) | 1.97693 | 0.0739331 | ||||||||
\(716\) | −5.73901 | −0.214477 | ||||||||
\(717\) | −62.3912 | −2.33004 | ||||||||
\(718\) | 26.8376 | 1.00157 | ||||||||
\(719\) | −21.6499 | −0.807403 | −0.403702 | − | 0.914891i | \(-0.632277\pi\) | ||||
−0.403702 | + | 0.914891i | \(0.632277\pi\) | |||||||
\(720\) | −2.34000 | −0.0872068 | ||||||||
\(721\) | −59.4118 | −2.21261 | ||||||||
\(722\) | −17.6688 | −0.657564 | ||||||||
\(723\) | 19.1535 | 0.712327 | ||||||||
\(724\) | −4.15790 | −0.154527 | ||||||||
\(725\) | −14.1020 | −0.523735 | ||||||||
\(726\) | 27.3617 | 1.01549 | ||||||||
\(727\) | −30.9286 | −1.14708 | −0.573540 | − | 0.819178i | \(-0.694430\pi\) | ||||
−0.573540 | + | 0.819178i | \(0.694430\pi\) | |||||||
\(728\) | −13.7659 | −0.510200 | ||||||||
\(729\) | −38.8958 | −1.44059 | ||||||||
\(730\) | −3.39722 | −0.125737 | ||||||||
\(731\) | −8.04045 | −0.297387 | ||||||||
\(732\) | 5.03255 | 0.186008 | ||||||||
\(733\) | 2.35799 | 0.0870945 | 0.0435472 | − | 0.999051i | \(-0.486134\pi\) | ||||
0.0435472 | + | 0.999051i | \(0.486134\pi\) | |||||||
\(734\) | 17.6152 | 0.650188 | ||||||||
\(735\) | 3.64484 | 0.134442 | ||||||||
\(736\) | 6.01283 | 0.221636 | ||||||||
\(737\) | 2.11653 | 0.0779635 | ||||||||
\(738\) | 21.3031 | 0.784179 | ||||||||
\(739\) | 6.06474 | 0.223095 | 0.111548 | − | 0.993759i | \(-0.464419\pi\) | ||||
0.111548 | + | 0.993759i | \(0.464419\pi\) | |||||||
\(740\) | −0.442069 | −0.0162508 | ||||||||
\(741\) | −13.5991 | −0.499575 | ||||||||
\(742\) | 19.6365 | 0.720878 | ||||||||
\(743\) | −15.9695 | −0.585862 | −0.292931 | − | 0.956134i | \(-0.594631\pi\) | ||||
−0.292931 | + | 0.956134i | \(0.594631\pi\) | |||||||
\(744\) | 11.9847 | 0.439380 | ||||||||
\(745\) | −8.92785 | −0.327091 | ||||||||
\(746\) | 37.0947 | 1.35813 | ||||||||
\(747\) | −6.12736 | −0.224188 | ||||||||
\(748\) | 5.33786 | 0.195172 | ||||||||
\(749\) | 39.3249 | 1.43690 | ||||||||
\(750\) | −15.4656 | −0.564724 | ||||||||
\(751\) | 10.5346 | 0.384412 | 0.192206 | − | 0.981355i | \(-0.438436\pi\) | ||||
0.192206 | + | 0.981355i | \(0.438436\pi\) | |||||||
\(752\) | 5.03724 | 0.183689 | ||||||||
\(753\) | −60.1965 | −2.19368 | ||||||||
\(754\) | 13.8044 | 0.502727 | ||||||||
\(755\) | 0.0734761 | 0.00267407 | ||||||||
\(756\) | 6.29700 | 0.229020 | ||||||||
\(757\) | −16.0653 | −0.583904 | −0.291952 | − | 0.956433i | \(-0.594305\pi\) | ||||
−0.291952 | + | 0.956433i | \(0.594305\pi\) | |||||||
\(758\) | 11.6444 | 0.422942 | ||||||||
\(759\) | 11.1077 | 0.403184 | ||||||||
\(760\) | −0.711684 | −0.0258155 | ||||||||
\(761\) | −4.11506 | −0.149171 | −0.0745853 | − | 0.997215i | \(-0.523763\pi\) | ||||
−0.0745853 | + | 0.997215i | \(0.523763\pi\) | |||||||
\(762\) | 14.2739 | 0.517089 | ||||||||
\(763\) | 11.9693 | 0.433317 | ||||||||
\(764\) | −10.2417 | −0.370531 | ||||||||
\(765\) | 17.6234 | 0.637175 | ||||||||
\(766\) | 7.91835 | 0.286102 | ||||||||
\(767\) | 6.71672 | 0.242527 | ||||||||
\(768\) | −2.60646 | −0.0940524 | ||||||||
\(769\) | −30.3888 | −1.09585 | −0.547924 | − | 0.836528i | \(-0.684582\pi\) | ||||
−0.547924 | + | 0.836528i | \(0.684582\pi\) | |||||||
\(770\) | −1.33085 | −0.0479604 | ||||||||
\(771\) | 41.6372 | 1.49953 | ||||||||
\(772\) | −1.58131 | −0.0569127 | ||||||||
\(773\) | 24.3087 | 0.874324 | 0.437162 | − | 0.899383i | \(-0.355984\pi\) | ||||
0.437162 | + | 0.899383i | \(0.355984\pi\) | |||||||
\(774\) | 4.05006 | 0.145576 | ||||||||
\(775\) | 21.2409 | 0.762997 | ||||||||
\(776\) | 12.5402 | 0.450167 | ||||||||
\(777\) | 5.68655 | 0.204004 | ||||||||
\(778\) | 22.7545 | 0.815788 | ||||||||
\(779\) | 6.47909 | 0.232137 | ||||||||
\(780\) | 7.27023 | 0.260316 | ||||||||
\(781\) | −8.30263 | −0.297092 | ||||||||
\(782\) | −45.2848 | −1.61938 | ||||||||
\(783\) | −6.31460 | −0.225665 | ||||||||
\(784\) | 2.26707 | 0.0809669 | ||||||||
\(785\) | −9.56794 | −0.341494 | ||||||||
\(786\) | −49.6922 | −1.77246 | ||||||||
\(787\) | −5.87991 | −0.209596 | −0.104798 | − | 0.994494i | \(-0.533420\pi\) | ||||
−0.104798 | + | 0.994494i | \(0.533420\pi\) | |||||||
\(788\) | 0.465375 | 0.0165783 | ||||||||
\(789\) | 53.9741 | 1.92153 | ||||||||
\(790\) | −6.76796 | −0.240793 | ||||||||
\(791\) | 56.9072 | 2.02339 | ||||||||
\(792\) | −2.68873 | −0.0955400 | ||||||||
\(793\) | −8.73117 | −0.310053 | ||||||||
\(794\) | −20.7737 | −0.737232 | ||||||||
\(795\) | −10.3707 | −0.367809 | ||||||||
\(796\) | 0.780673 | 0.0276702 | ||||||||
\(797\) | 21.1411 | 0.748857 | 0.374428 | − | 0.927256i | \(-0.377839\pi\) | ||||
0.374428 | + | 0.927256i | \(0.377839\pi\) | |||||||
\(798\) | 9.15475 | 0.324075 | ||||||||
\(799\) | −37.9372 | −1.34212 | ||||||||
\(800\) | −4.61953 | −0.163325 | ||||||||
\(801\) | 9.32947 | 0.329641 | ||||||||
\(802\) | −23.2179 | −0.819854 | ||||||||
\(803\) | −3.90351 | −0.137752 | ||||||||
\(804\) | 7.78362 | 0.274507 | ||||||||
\(805\) | 11.2905 | 0.397938 | ||||||||
\(806\) | −20.7927 | −0.732392 | ||||||||
\(807\) | 79.3921 | 2.79473 | ||||||||
\(808\) | −13.5576 | −0.476956 | ||||||||
\(809\) | −30.7131 | −1.07982 | −0.539908 | − | 0.841724i | \(-0.681541\pi\) | ||||
−0.539908 | + | 0.841724i | \(0.681541\pi\) | |||||||
\(810\) | 3.69437 | 0.129807 | ||||||||
\(811\) | 27.2339 | 0.956311 | 0.478156 | − | 0.878275i | \(-0.341305\pi\) | ||||
0.478156 | + | 0.878275i | \(0.341305\pi\) | |||||||
\(812\) | −9.29297 | −0.326119 | ||||||||
\(813\) | 55.9755 | 1.96315 | ||||||||
\(814\) | −0.507951 | −0.0178037 | ||||||||
\(815\) | 9.30665 | 0.325998 | ||||||||
\(816\) | 19.6302 | 0.687193 | ||||||||
\(817\) | 1.23178 | 0.0430944 | ||||||||
\(818\) | −11.9253 | −0.416959 | ||||||||
\(819\) | −52.2228 | −1.82481 | ||||||||
\(820\) | −3.46380 | −0.120961 | ||||||||
\(821\) | −35.8648 | −1.25169 | −0.625845 | − | 0.779947i | \(-0.715246\pi\) | ||||
−0.625845 | + | 0.779947i | \(0.715246\pi\) | |||||||
\(822\) | 39.5665 | 1.38004 | ||||||||
\(823\) | −1.25030 | −0.0435827 | −0.0217913 | − | 0.999763i | \(-0.506937\pi\) | ||||
−0.0217913 | + | 0.999763i | \(0.506937\pi\) | |||||||
\(824\) | 19.5165 | 0.679889 | ||||||||
\(825\) | −8.53380 | −0.297109 | ||||||||
\(826\) | −4.52161 | −0.157327 | ||||||||
\(827\) | −3.16554 | −0.110077 | −0.0550383 | − | 0.998484i | \(-0.517528\pi\) | ||||
−0.0550383 | + | 0.998484i | \(0.517528\pi\) | |||||||
\(828\) | 22.8104 | 0.792716 | ||||||||
\(829\) | 35.8011 | 1.24342 | 0.621712 | − | 0.783246i | \(-0.286438\pi\) | ||||
0.621712 | + | 0.783246i | \(0.286438\pi\) | |||||||
\(830\) | 0.996283 | 0.0345815 | ||||||||
\(831\) | 35.5403 | 1.23288 | ||||||||
\(832\) | 4.52204 | 0.156774 | ||||||||
\(833\) | −17.0741 | −0.591584 | ||||||||
\(834\) | 16.3275 | 0.565375 | ||||||||
\(835\) | −8.91585 | −0.308546 | ||||||||
\(836\) | −0.817747 | −0.0282824 | ||||||||
\(837\) | 9.51128 | 0.328758 | ||||||||
\(838\) | 27.7954 | 0.960177 | ||||||||
\(839\) | 56.8969 | 1.96430 | 0.982150 | − | 0.188101i | \(-0.0602334\pi\) | ||||
0.982150 | + | 0.188101i | \(0.0602334\pi\) | |||||||
\(840\) | −4.89423 | −0.168867 | ||||||||
\(841\) | −19.6811 | −0.678657 | ||||||||
\(842\) | −34.8715 | −1.20175 | ||||||||
\(843\) | 17.6634 | 0.608359 | ||||||||
\(844\) | −24.0924 | −0.829296 | ||||||||
\(845\) | −4.59467 | −0.158061 | ||||||||
\(846\) | 19.1094 | 0.656994 | ||||||||
\(847\) | 31.9569 | 1.09805 | ||||||||
\(848\) | −6.45049 | −0.221511 | ||||||||
\(849\) | −14.1320 | −0.485008 | ||||||||
\(850\) | 34.7913 | 1.19333 | ||||||||
\(851\) | 4.30930 | 0.147721 | ||||||||
\(852\) | −30.5332 | −1.04605 | ||||||||
\(853\) | 44.9664 | 1.53962 | 0.769810 | − | 0.638273i | \(-0.220351\pi\) | ||||
0.769810 | + | 0.638273i | \(0.220351\pi\) | |||||||
\(854\) | 5.87772 | 0.201131 | ||||||||
\(855\) | −2.69986 | −0.0923332 | ||||||||
\(856\) | −12.9180 | −0.441530 | ||||||||
\(857\) | 16.0390 | 0.547880 | 0.273940 | − | 0.961747i | \(-0.411673\pi\) | ||||
0.273940 | + | 0.961747i | \(0.411673\pi\) | |||||||
\(858\) | 8.35372 | 0.285191 | ||||||||
\(859\) | −50.5465 | −1.72462 | −0.862311 | − | 0.506378i | \(-0.830984\pi\) | ||||
−0.862311 | + | 0.506378i | \(0.830984\pi\) | |||||||
\(860\) | −0.658522 | −0.0224554 | ||||||||
\(861\) | 44.5565 | 1.51848 | ||||||||
\(862\) | −14.4154 | −0.490990 | ||||||||
\(863\) | −22.6391 | −0.770645 | −0.385322 | − | 0.922782i | \(-0.625910\pi\) | ||||
−0.385322 | + | 0.922782i | \(0.625910\pi\) | |||||||
\(864\) | −2.06853 | −0.0703729 | ||||||||
\(865\) | 8.08558 | 0.274918 | ||||||||
\(866\) | −13.7117 | −0.465941 | ||||||||
\(867\) | −103.532 | −3.51613 | ||||||||
\(868\) | 13.9974 | 0.475103 | ||||||||
\(869\) | −7.77659 | −0.263803 | ||||||||
\(870\) | 4.90791 | 0.166394 | ||||||||
\(871\) | −13.5041 | −0.457569 | ||||||||
\(872\) | −3.93185 | −0.133149 | ||||||||
\(873\) | 47.5727 | 1.61009 | ||||||||
\(874\) | 6.93751 | 0.234665 | ||||||||
\(875\) | −18.0629 | −0.610638 | ||||||||
\(876\) | −14.3553 | −0.485020 | ||||||||
\(877\) | −9.68447 | −0.327021 | −0.163511 | − | 0.986542i | \(-0.552282\pi\) | ||||
−0.163511 | + | 0.986542i | \(0.552282\pi\) | |||||||
\(878\) | 14.5141 | 0.489827 | ||||||||
\(879\) | −6.48625 | −0.218776 | ||||||||
\(880\) | 0.437177 | 0.0147372 | ||||||||
\(881\) | −3.67703 | −0.123882 | −0.0619411 | − | 0.998080i | \(-0.519729\pi\) | ||||
−0.0619411 | + | 0.998080i | \(0.519729\pi\) | |||||||
\(882\) | 8.60041 | 0.289591 | ||||||||
\(883\) | 6.80588 | 0.229036 | 0.114518 | − | 0.993421i | \(-0.463468\pi\) | ||||
0.114518 | + | 0.993421i | \(0.463468\pi\) | |||||||
\(884\) | −34.0571 | −1.14546 | ||||||||
\(885\) | 2.38801 | 0.0802720 | ||||||||
\(886\) | −34.0471 | −1.14383 | ||||||||
\(887\) | 12.8262 | 0.430661 | 0.215331 | − | 0.976541i | \(-0.430917\pi\) | ||||
0.215331 | + | 0.976541i | \(0.430917\pi\) | |||||||
\(888\) | −1.86800 | −0.0626861 | ||||||||
\(889\) | 16.6711 | 0.559130 | ||||||||
\(890\) | −1.51693 | −0.0508477 | ||||||||
\(891\) | 4.24494 | 0.142211 | ||||||||
\(892\) | −18.9446 | −0.634312 | ||||||||
\(893\) | 5.81189 | 0.194487 | ||||||||
\(894\) | −37.7255 | −1.26173 | ||||||||
\(895\) | 3.53997 | 0.118328 | ||||||||
\(896\) | −3.04419 | −0.101699 | ||||||||
\(897\) | −70.8704 | −2.36629 | ||||||||
\(898\) | 14.4308 | 0.481562 | ||||||||
\(899\) | −14.0365 | −0.468144 | ||||||||
\(900\) | −17.5247 | −0.584157 | ||||||||
\(901\) | 48.5809 | 1.61847 | ||||||||
\(902\) | −3.98001 | −0.132520 | ||||||||
\(903\) | 8.47089 | 0.281894 | ||||||||
\(904\) | −18.6937 | −0.621744 | ||||||||
\(905\) | 2.56470 | 0.0852536 | ||||||||
\(906\) | 0.310480 | 0.0103150 | ||||||||
\(907\) | −3.84368 | −0.127627 | −0.0638136 | − | 0.997962i | \(-0.520326\pi\) | ||||
−0.0638136 | + | 0.997962i | \(0.520326\pi\) | |||||||
\(908\) | −21.2732 | −0.705975 | ||||||||
\(909\) | −51.4325 | −1.70591 | ||||||||
\(910\) | 8.49120 | 0.281480 | ||||||||
\(911\) | 29.0050 | 0.960979 | 0.480490 | − | 0.877000i | \(-0.340459\pi\) | ||||
0.480490 | + | 0.877000i | \(0.340459\pi\) | |||||||
\(912\) | −3.00729 | −0.0995813 | ||||||||
\(913\) | 1.14476 | 0.0378860 | ||||||||
\(914\) | −17.7909 | −0.588470 | ||||||||
\(915\) | −3.10421 | −0.102622 | ||||||||
\(916\) | 9.46496 | 0.312731 | ||||||||
\(917\) | −58.0375 | −1.91657 | ||||||||
\(918\) | 15.5789 | 0.514179 | ||||||||
\(919\) | 38.3305 | 1.26441 | 0.632204 | − | 0.774802i | \(-0.282151\pi\) | ||||
0.632204 | + | 0.774802i | \(0.282151\pi\) | |||||||
\(920\) | −3.70887 | −0.122278 | ||||||||
\(921\) | 38.0799 | 1.25478 | ||||||||
\(922\) | 27.0926 | 0.892249 | ||||||||
\(923\) | 52.9732 | 1.74364 | ||||||||
\(924\) | −5.62362 | −0.185004 | ||||||||
\(925\) | −3.31074 | −0.108856 | ||||||||
\(926\) | −32.5408 | −1.06936 | ||||||||
\(927\) | 74.0381 | 2.43173 | ||||||||
\(928\) | 3.05269 | 0.100210 | ||||||||
\(929\) | 4.34903 | 0.142687 | 0.0713435 | − | 0.997452i | \(-0.477271\pi\) | ||||
0.0713435 | + | 0.997452i | \(0.477271\pi\) | |||||||
\(930\) | −7.39247 | −0.242409 | ||||||||
\(931\) | 2.61571 | 0.0857265 | ||||||||
\(932\) | −7.44251 | −0.243787 | ||||||||
\(933\) | 30.7360 | 1.00625 | ||||||||
\(934\) | −4.16093 | −0.136150 | ||||||||
\(935\) | −3.29253 | −0.107677 | ||||||||
\(936\) | 17.1549 | 0.560726 | ||||||||
\(937\) | 10.1199 | 0.330602 | 0.165301 | − | 0.986243i | \(-0.447140\pi\) | ||||
0.165301 | + | 0.986243i | \(0.447140\pi\) | |||||||
\(938\) | 9.09080 | 0.296825 | ||||||||
\(939\) | 13.1496 | 0.429120 | ||||||||
\(940\) | −3.10710 | −0.101342 | ||||||||
\(941\) | −7.66545 | −0.249887 | −0.124943 | − | 0.992164i | \(-0.539875\pi\) | ||||
−0.124943 | + | 0.992164i | \(0.539875\pi\) | |||||||
\(942\) | −40.4302 | −1.31729 | ||||||||
\(943\) | 33.7651 | 1.09954 | ||||||||
\(944\) | 1.48533 | 0.0483433 | ||||||||
\(945\) | −3.88416 | −0.126352 | ||||||||
\(946\) | −0.756661 | −0.0246012 | ||||||||
\(947\) | −17.1425 | −0.557056 | −0.278528 | − | 0.960428i | \(-0.589846\pi\) | ||||
−0.278528 | + | 0.960428i | \(0.589846\pi\) | |||||||
\(948\) | −28.5986 | −0.928841 | ||||||||
\(949\) | 24.9055 | 0.808468 | ||||||||
\(950\) | −5.32993 | −0.172926 | ||||||||
\(951\) | 29.8456 | 0.967809 | ||||||||
\(952\) | 22.9269 | 0.743064 | ||||||||
\(953\) | 1.31656 | 0.0426477 | 0.0213239 | − | 0.999773i | \(-0.493212\pi\) | ||||
0.0213239 | + | 0.999773i | \(0.493212\pi\) | |||||||
\(954\) | −24.4707 | −0.792268 | ||||||||
\(955\) | 6.31734 | 0.204424 | ||||||||
\(956\) | 23.9371 | 0.774183 | ||||||||
\(957\) | 5.63934 | 0.182294 | ||||||||
\(958\) | −29.7519 | −0.961239 | ||||||||
\(959\) | 46.2114 | 1.49224 | ||||||||
\(960\) | 1.60773 | 0.0518893 | ||||||||
\(961\) | −9.85768 | −0.317990 | ||||||||
\(962\) | 3.24087 | 0.104490 | ||||||||
\(963\) | −49.0061 | −1.57920 | ||||||||
\(964\) | −7.34849 | −0.236679 | ||||||||
\(965\) | 0.975396 | 0.0313991 | ||||||||
\(966\) | 47.7091 | 1.53501 | ||||||||
\(967\) | 60.6103 | 1.94910 | 0.974549 | − | 0.224176i | \(-0.0719690\pi\) | ||||
0.974549 | + | 0.224176i | \(0.0719690\pi\) | |||||||
\(968\) | −10.4977 | −0.337408 | ||||||||
\(969\) | 22.6490 | 0.727589 | ||||||||
\(970\) | −7.73513 | −0.248360 | ||||||||
\(971\) | −41.5176 | −1.33236 | −0.666182 | − | 0.745789i | \(-0.732073\pi\) | ||||
−0.666182 | + | 0.745789i | \(0.732073\pi\) | |||||||
\(972\) | 21.8165 | 0.699764 | ||||||||
\(973\) | 19.0696 | 0.611342 | ||||||||
\(974\) | 31.3125 | 1.00332 | ||||||||
\(975\) | 54.4481 | 1.74373 | ||||||||
\(976\) | −1.93080 | −0.0618035 | ||||||||
\(977\) | −3.73681 | −0.119551 | −0.0597755 | − | 0.998212i | \(-0.519038\pi\) | ||||
−0.0597755 | + | 0.998212i | \(0.519038\pi\) | |||||||
\(978\) | 39.3261 | 1.25751 | ||||||||
\(979\) | −1.74300 | −0.0557065 | ||||||||
\(980\) | −1.39839 | −0.0446699 | ||||||||
\(981\) | −14.9159 | −0.476229 | ||||||||
\(982\) | 2.57433 | 0.0821501 | ||||||||
\(983\) | 43.9104 | 1.40053 | 0.700263 | − | 0.713885i | \(-0.253066\pi\) | ||||
0.700263 | + | 0.713885i | \(0.253066\pi\) | |||||||
\(984\) | −14.6366 | −0.466598 | ||||||||
\(985\) | −0.287056 | −0.00914635 | ||||||||
\(986\) | −22.9909 | −0.732180 | ||||||||
\(987\) | 39.9682 | 1.27220 | ||||||||
\(988\) | 5.21746 | 0.165990 | ||||||||
\(989\) | 6.41928 | 0.204121 | ||||||||
\(990\) | 1.65848 | 0.0527100 | ||||||||
\(991\) | −22.1178 | −0.702595 | −0.351298 | − | 0.936264i | \(-0.614259\pi\) | ||||
−0.351298 | + | 0.936264i | \(0.614259\pi\) | |||||||
\(992\) | −4.59808 | −0.145989 | ||||||||
\(993\) | 62.3053 | 1.97720 | ||||||||
\(994\) | −35.6610 | −1.13110 | ||||||||
\(995\) | −0.481539 | −0.0152658 | ||||||||
\(996\) | 4.20989 | 0.133395 | ||||||||
\(997\) | 13.8301 | 0.438004 | 0.219002 | − | 0.975724i | \(-0.429720\pi\) | ||||
0.219002 | + | 0.975724i | \(0.429720\pi\) | |||||||
\(998\) | −31.6113 | −1.00064 | ||||||||
\(999\) | −1.48248 | −0.0469037 |
(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 | 8042.2.a.a.1.7 | ✓ | 67 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8042.2.a.a.1.7 | ✓ | 67 | 1.1 | even | 1 | trivial |