Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8043,2,Mod(1,8043)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8043, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8043.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8043 = 3 \cdot 7 \cdot 383 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8043.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: | \(64.2236783457\) |
Analytic rank: | \(0\) |
Dimension: | \(52\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 8043.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.10272 | −0.779740 | −0.389870 | − | 0.920870i | \(-0.627480\pi\) | ||||
−0.389870 | + | 0.920870i | \(0.627480\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −0.784010 | −0.392005 | ||||||||
\(5\) | 0.760743 | 0.340215 | 0.170107 | − | 0.985426i | \(-0.445589\pi\) | ||||
0.170107 | + | 0.985426i | \(0.445589\pi\) | |||||||
\(6\) | 1.10272 | 0.450183 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 3.06998 | 1.08540 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.838886 | −0.265279 | ||||||||
\(11\) | 0.597329 | 0.180101 | 0.0900507 | − | 0.995937i | \(-0.471297\pi\) | ||||
0.0900507 | + | 0.995937i | \(0.471297\pi\) | |||||||
\(12\) | 0.784010 | 0.226324 | ||||||||
\(13\) | −4.75703 | −1.31936 | −0.659681 | − | 0.751546i | \(-0.729309\pi\) | ||||
−0.659681 | + | 0.751546i | \(0.729309\pi\) | |||||||
\(14\) | −1.10272 | −0.294714 | ||||||||
\(15\) | −0.760743 | −0.196423 | ||||||||
\(16\) | −1.81731 | −0.454327 | ||||||||
\(17\) | 1.90750 | 0.462637 | 0.231319 | − | 0.972878i | \(-0.425696\pi\) | ||||
0.231319 | + | 0.972878i | \(0.425696\pi\) | |||||||
\(18\) | −1.10272 | −0.259913 | ||||||||
\(19\) | −5.87579 | −1.34800 | −0.673999 | − | 0.738732i | \(-0.735425\pi\) | ||||
−0.673999 | + | 0.738732i | \(0.735425\pi\) | |||||||
\(20\) | −0.596430 | −0.133366 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | −0.658686 | −0.140432 | ||||||||
\(23\) | −7.97969 | −1.66388 | −0.831940 | − | 0.554866i | \(-0.812770\pi\) | ||||
−0.831940 | + | 0.554866i | \(0.812770\pi\) | |||||||
\(24\) | −3.06998 | −0.626657 | ||||||||
\(25\) | −4.42127 | −0.884254 | ||||||||
\(26\) | 5.24567 | 1.02876 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −0.784010 | −0.148164 | ||||||||
\(29\) | 3.85644 | 0.716123 | 0.358061 | − | 0.933698i | \(-0.383438\pi\) | ||||
0.358061 | + | 0.933698i | \(0.383438\pi\) | |||||||
\(30\) | 0.838886 | 0.153159 | ||||||||
\(31\) | −4.54227 | −0.815816 | −0.407908 | − | 0.913023i | \(-0.633742\pi\) | ||||
−0.407908 | + | 0.913023i | \(0.633742\pi\) | |||||||
\(32\) | −4.13598 | −0.731145 | ||||||||
\(33\) | −0.597329 | −0.103982 | ||||||||
\(34\) | −2.10344 | −0.360737 | ||||||||
\(35\) | 0.760743 | 0.128589 | ||||||||
\(36\) | −0.784010 | −0.130668 | ||||||||
\(37\) | −4.13929 | −0.680494 | −0.340247 | − | 0.940336i | \(-0.610511\pi\) | ||||
−0.340247 | + | 0.940336i | \(0.610511\pi\) | |||||||
\(38\) | 6.47935 | 1.05109 | ||||||||
\(39\) | 4.75703 | 0.761734 | ||||||||
\(40\) | 2.33547 | 0.369270 | ||||||||
\(41\) | 9.73395 | 1.52019 | 0.760093 | − | 0.649814i | \(-0.225153\pi\) | ||||
0.760093 | + | 0.649814i | \(0.225153\pi\) | |||||||
\(42\) | 1.10272 | 0.170153 | ||||||||
\(43\) | −10.9381 | −1.66804 | −0.834022 | − | 0.551731i | \(-0.813967\pi\) | ||||
−0.834022 | + | 0.551731i | \(0.813967\pi\) | |||||||
\(44\) | −0.468312 | −0.0706006 | ||||||||
\(45\) | 0.760743 | 0.113405 | ||||||||
\(46\) | 8.79936 | 1.29739 | ||||||||
\(47\) | −5.17145 | −0.754333 | −0.377167 | − | 0.926145i | \(-0.623102\pi\) | ||||
−0.377167 | + | 0.926145i | \(0.623102\pi\) | |||||||
\(48\) | 1.81731 | 0.262306 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 4.87542 | 0.689489 | ||||||||
\(51\) | −1.90750 | −0.267104 | ||||||||
\(52\) | 3.72956 | 0.517196 | ||||||||
\(53\) | 14.0161 | 1.92526 | 0.962628 | − | 0.270829i | \(-0.0872978\pi\) | ||||
0.962628 | + | 0.270829i | \(0.0872978\pi\) | |||||||
\(54\) | 1.10272 | 0.150061 | ||||||||
\(55\) | 0.454414 | 0.0612731 | ||||||||
\(56\) | 3.06998 | 0.410244 | ||||||||
\(57\) | 5.87579 | 0.778267 | ||||||||
\(58\) | −4.25257 | −0.558390 | ||||||||
\(59\) | −7.09175 | −0.923268 | −0.461634 | − | 0.887071i | \(-0.652737\pi\) | ||||
−0.461634 | + | 0.887071i | \(0.652737\pi\) | |||||||
\(60\) | 0.596430 | 0.0769988 | ||||||||
\(61\) | −4.13631 | −0.529600 | −0.264800 | − | 0.964303i | \(-0.585306\pi\) | ||||
−0.264800 | + | 0.964303i | \(0.585306\pi\) | |||||||
\(62\) | 5.00885 | 0.636125 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 8.19545 | 1.02443 | ||||||||
\(65\) | −3.61888 | −0.448866 | ||||||||
\(66\) | 0.658686 | 0.0810787 | ||||||||
\(67\) | 1.80164 | 0.220105 | 0.110052 | − | 0.993926i | \(-0.464898\pi\) | ||||
0.110052 | + | 0.993926i | \(0.464898\pi\) | |||||||
\(68\) | −1.49550 | −0.181356 | ||||||||
\(69\) | 7.97969 | 0.960642 | ||||||||
\(70\) | −0.838886 | −0.100266 | ||||||||
\(71\) | −15.7873 | −1.87361 | −0.936805 | − | 0.349852i | \(-0.886232\pi\) | ||||
−0.936805 | + | 0.349852i | \(0.886232\pi\) | |||||||
\(72\) | 3.06998 | 0.361801 | ||||||||
\(73\) | 6.46981 | 0.757234 | 0.378617 | − | 0.925553i | \(-0.376400\pi\) | ||||
0.378617 | + | 0.925553i | \(0.376400\pi\) | |||||||
\(74\) | 4.56447 | 0.530609 | ||||||||
\(75\) | 4.42127 | 0.510524 | ||||||||
\(76\) | 4.60668 | 0.528422 | ||||||||
\(77\) | 0.597329 | 0.0680719 | ||||||||
\(78\) | −5.24567 | −0.593955 | ||||||||
\(79\) | −2.06675 | −0.232528 | −0.116264 | − | 0.993218i | \(-0.537092\pi\) | ||||
−0.116264 | + | 0.993218i | \(0.537092\pi\) | |||||||
\(80\) | −1.38251 | −0.154569 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −10.7338 | −1.18535 | ||||||||
\(83\) | 10.4388 | 1.14581 | 0.572906 | − | 0.819621i | \(-0.305816\pi\) | ||||
0.572906 | + | 0.819621i | \(0.305816\pi\) | |||||||
\(84\) | 0.784010 | 0.0855425 | ||||||||
\(85\) | 1.45112 | 0.157396 | ||||||||
\(86\) | 12.0617 | 1.30064 | ||||||||
\(87\) | −3.85644 | −0.413454 | ||||||||
\(88\) | 1.83379 | 0.195483 | ||||||||
\(89\) | 5.04949 | 0.535245 | 0.267623 | − | 0.963524i | \(-0.413762\pi\) | ||||
0.267623 | + | 0.963524i | \(0.413762\pi\) | |||||||
\(90\) | −0.838886 | −0.0884264 | ||||||||
\(91\) | −4.75703 | −0.498672 | ||||||||
\(92\) | 6.25615 | 0.652249 | ||||||||
\(93\) | 4.54227 | 0.471012 | ||||||||
\(94\) | 5.70266 | 0.588184 | ||||||||
\(95\) | −4.46997 | −0.458609 | ||||||||
\(96\) | 4.13598 | 0.422127 | ||||||||
\(97\) | 12.8199 | 1.30167 | 0.650833 | − | 0.759221i | \(-0.274420\pi\) | ||||
0.650833 | + | 0.759221i | \(0.274420\pi\) | |||||||
\(98\) | −1.10272 | −0.111391 | ||||||||
\(99\) | 0.597329 | 0.0600338 | ||||||||
\(100\) | 3.46632 | 0.346632 | ||||||||
\(101\) | 12.3187 | 1.22575 | 0.612877 | − | 0.790178i | \(-0.290012\pi\) | ||||
0.612877 | + | 0.790178i | \(0.290012\pi\) | |||||||
\(102\) | 2.10344 | 0.208272 | ||||||||
\(103\) | 8.63579 | 0.850909 | 0.425455 | − | 0.904980i | \(-0.360114\pi\) | ||||
0.425455 | + | 0.904980i | \(0.360114\pi\) | |||||||
\(104\) | −14.6040 | −1.43204 | ||||||||
\(105\) | −0.760743 | −0.0742409 | ||||||||
\(106\) | −15.4558 | −1.50120 | ||||||||
\(107\) | 12.0518 | 1.16509 | 0.582544 | − | 0.812799i | \(-0.302057\pi\) | ||||
0.582544 | + | 0.812799i | \(0.302057\pi\) | |||||||
\(108\) | 0.784010 | 0.0754414 | ||||||||
\(109\) | 13.3643 | 1.28006 | 0.640032 | − | 0.768349i | \(-0.278921\pi\) | ||||
0.640032 | + | 0.768349i | \(0.278921\pi\) | |||||||
\(110\) | −0.501091 | −0.0477772 | ||||||||
\(111\) | 4.13929 | 0.392884 | ||||||||
\(112\) | −1.81731 | −0.171720 | ||||||||
\(113\) | −17.2347 | −1.62131 | −0.810653 | − | 0.585527i | \(-0.800887\pi\) | ||||
−0.810653 | + | 0.585527i | \(0.800887\pi\) | |||||||
\(114\) | −6.47935 | −0.606847 | ||||||||
\(115\) | −6.07049 | −0.566076 | ||||||||
\(116\) | −3.02349 | −0.280724 | ||||||||
\(117\) | −4.75703 | −0.439787 | ||||||||
\(118\) | 7.82021 | 0.719909 | ||||||||
\(119\) | 1.90750 | 0.174861 | ||||||||
\(120\) | −2.33547 | −0.213198 | ||||||||
\(121\) | −10.6432 | −0.967563 | ||||||||
\(122\) | 4.56119 | 0.412951 | ||||||||
\(123\) | −9.73395 | −0.877680 | ||||||||
\(124\) | 3.56118 | 0.319804 | ||||||||
\(125\) | −7.16717 | −0.641051 | ||||||||
\(126\) | −1.10272 | −0.0982381 | ||||||||
\(127\) | −10.0255 | −0.889616 | −0.444808 | − | 0.895626i | \(-0.646728\pi\) | ||||
−0.444808 | + | 0.895626i | \(0.646728\pi\) | |||||||
\(128\) | −0.765317 | −0.0676451 | ||||||||
\(129\) | 10.9381 | 0.963046 | ||||||||
\(130\) | 3.99060 | 0.349999 | ||||||||
\(131\) | 2.29268 | 0.200313 | 0.100156 | − | 0.994972i | \(-0.468066\pi\) | ||||
0.100156 | + | 0.994972i | \(0.468066\pi\) | |||||||
\(132\) | 0.468312 | 0.0407613 | ||||||||
\(133\) | −5.87579 | −0.509496 | ||||||||
\(134\) | −1.98670 | −0.171625 | ||||||||
\(135\) | −0.760743 | −0.0654743 | ||||||||
\(136\) | 5.85600 | 0.502148 | ||||||||
\(137\) | 14.5342 | 1.24174 | 0.620872 | − | 0.783912i | \(-0.286779\pi\) | ||||
0.620872 | + | 0.783912i | \(0.286779\pi\) | |||||||
\(138\) | −8.79936 | −0.749051 | ||||||||
\(139\) | −16.4202 | −1.39274 | −0.696371 | − | 0.717682i | \(-0.745203\pi\) | ||||
−0.696371 | + | 0.717682i | \(0.745203\pi\) | |||||||
\(140\) | −0.596430 | −0.0504075 | ||||||||
\(141\) | 5.17145 | 0.435514 | ||||||||
\(142\) | 17.4090 | 1.46093 | ||||||||
\(143\) | −2.84151 | −0.237619 | ||||||||
\(144\) | −1.81731 | −0.151442 | ||||||||
\(145\) | 2.93376 | 0.243635 | ||||||||
\(146\) | −7.13439 | −0.590446 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 3.24524 | 0.266757 | ||||||||
\(149\) | 17.8458 | 1.46198 | 0.730991 | − | 0.682387i | \(-0.239058\pi\) | ||||
0.730991 | + | 0.682387i | \(0.239058\pi\) | |||||||
\(150\) | −4.87542 | −0.398076 | ||||||||
\(151\) | −7.76863 | −0.632202 | −0.316101 | − | 0.948726i | \(-0.602374\pi\) | ||||
−0.316101 | + | 0.948726i | \(0.602374\pi\) | |||||||
\(152\) | −18.0386 | −1.46312 | ||||||||
\(153\) | 1.90750 | 0.154212 | ||||||||
\(154\) | −0.658686 | −0.0530784 | ||||||||
\(155\) | −3.45550 | −0.277553 | ||||||||
\(156\) | −3.72956 | −0.298603 | ||||||||
\(157\) | 7.79929 | 0.622451 | 0.311226 | − | 0.950336i | \(-0.399261\pi\) | ||||
0.311226 | + | 0.950336i | \(0.399261\pi\) | |||||||
\(158\) | 2.27905 | 0.181312 | ||||||||
\(159\) | −14.0161 | −1.11155 | ||||||||
\(160\) | −3.14642 | −0.248746 | ||||||||
\(161\) | −7.97969 | −0.628887 | ||||||||
\(162\) | −1.10272 | −0.0866378 | ||||||||
\(163\) | 18.1935 | 1.42503 | 0.712514 | − | 0.701658i | \(-0.247556\pi\) | ||||
0.712514 | + | 0.701658i | \(0.247556\pi\) | |||||||
\(164\) | −7.63151 | −0.595921 | ||||||||
\(165\) | −0.454414 | −0.0353761 | ||||||||
\(166\) | −11.5111 | −0.893436 | ||||||||
\(167\) | −15.8635 | −1.22755 | −0.613776 | − | 0.789480i | \(-0.710350\pi\) | ||||
−0.613776 | + | 0.789480i | \(0.710350\pi\) | |||||||
\(168\) | −3.06998 | −0.236854 | ||||||||
\(169\) | 9.62931 | 0.740716 | ||||||||
\(170\) | −1.60018 | −0.122728 | ||||||||
\(171\) | −5.87579 | −0.449333 | ||||||||
\(172\) | 8.57557 | 0.653881 | ||||||||
\(173\) | −21.0753 | −1.60232 | −0.801162 | − | 0.598447i | \(-0.795785\pi\) | ||||
−0.801162 | + | 0.598447i | \(0.795785\pi\) | |||||||
\(174\) | 4.25257 | 0.322387 | ||||||||
\(175\) | −4.42127 | −0.334217 | ||||||||
\(176\) | −1.08553 | −0.0818250 | ||||||||
\(177\) | 7.09175 | 0.533049 | ||||||||
\(178\) | −5.56818 | −0.417352 | ||||||||
\(179\) | 0.843371 | 0.0630365 | 0.0315182 | − | 0.999503i | \(-0.489966\pi\) | ||||
0.0315182 | + | 0.999503i | \(0.489966\pi\) | |||||||
\(180\) | −0.596430 | −0.0444553 | ||||||||
\(181\) | −5.23412 | −0.389049 | −0.194525 | − | 0.980898i | \(-0.562316\pi\) | ||||
−0.194525 | + | 0.980898i | \(0.562316\pi\) | |||||||
\(182\) | 5.24567 | 0.388835 | ||||||||
\(183\) | 4.13631 | 0.305765 | ||||||||
\(184\) | −24.4975 | −1.80598 | ||||||||
\(185\) | −3.14893 | −0.231514 | ||||||||
\(186\) | −5.00885 | −0.367267 | ||||||||
\(187\) | 1.13941 | 0.0833217 | ||||||||
\(188\) | 4.05446 | 0.295702 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 4.92912 | 0.357596 | ||||||||
\(191\) | 20.0268 | 1.44909 | 0.724544 | − | 0.689229i | \(-0.242051\pi\) | ||||
0.724544 | + | 0.689229i | \(0.242051\pi\) | |||||||
\(192\) | −8.19545 | −0.591455 | ||||||||
\(193\) | 1.87046 | 0.134638 | 0.0673192 | − | 0.997731i | \(-0.478555\pi\) | ||||
0.0673192 | + | 0.997731i | \(0.478555\pi\) | |||||||
\(194\) | −14.1368 | −1.01496 | ||||||||
\(195\) | 3.61888 | 0.259153 | ||||||||
\(196\) | −0.784010 | −0.0560007 | ||||||||
\(197\) | −8.97502 | −0.639444 | −0.319722 | − | 0.947511i | \(-0.603589\pi\) | ||||
−0.319722 | + | 0.947511i | \(0.603589\pi\) | |||||||
\(198\) | −0.658686 | −0.0468108 | ||||||||
\(199\) | −0.936829 | −0.0664100 | −0.0332050 | − | 0.999449i | \(-0.510571\pi\) | ||||
−0.0332050 | + | 0.999449i | \(0.510571\pi\) | |||||||
\(200\) | −13.5732 | −0.959771 | ||||||||
\(201\) | −1.80164 | −0.127078 | ||||||||
\(202\) | −13.5840 | −0.955770 | ||||||||
\(203\) | 3.85644 | 0.270669 | ||||||||
\(204\) | 1.49550 | 0.104706 | ||||||||
\(205\) | 7.40503 | 0.517190 | ||||||||
\(206\) | −9.52285 | −0.663488 | ||||||||
\(207\) | −7.97969 | −0.554627 | ||||||||
\(208\) | 8.64499 | 0.599422 | ||||||||
\(209\) | −3.50978 | −0.242777 | ||||||||
\(210\) | 0.838886 | 0.0578886 | ||||||||
\(211\) | −22.8895 | −1.57578 | −0.787890 | − | 0.615815i | \(-0.788827\pi\) | ||||
−0.787890 | + | 0.615815i | \(0.788827\pi\) | |||||||
\(212\) | −10.9887 | −0.754709 | ||||||||
\(213\) | 15.7873 | 1.08173 | ||||||||
\(214\) | −13.2897 | −0.908466 | ||||||||
\(215\) | −8.32108 | −0.567493 | ||||||||
\(216\) | −3.06998 | −0.208886 | ||||||||
\(217\) | −4.54227 | −0.308349 | ||||||||
\(218\) | −14.7370 | −0.998117 | ||||||||
\(219\) | −6.46981 | −0.437189 | ||||||||
\(220\) | −0.356265 | −0.0240194 | ||||||||
\(221\) | −9.07404 | −0.610386 | ||||||||
\(222\) | −4.56447 | −0.306347 | ||||||||
\(223\) | 27.8810 | 1.86705 | 0.933526 | − | 0.358511i | \(-0.116715\pi\) | ||||
0.933526 | + | 0.358511i | \(0.116715\pi\) | |||||||
\(224\) | −4.13598 | −0.276347 | ||||||||
\(225\) | −4.42127 | −0.294751 | ||||||||
\(226\) | 19.0051 | 1.26420 | ||||||||
\(227\) | −5.06112 | −0.335918 | −0.167959 | − | 0.985794i | \(-0.553718\pi\) | ||||
−0.167959 | + | 0.985794i | \(0.553718\pi\) | |||||||
\(228\) | −4.60668 | −0.305085 | ||||||||
\(229\) | −18.5129 | −1.22337 | −0.611683 | − | 0.791103i | \(-0.709507\pi\) | ||||
−0.611683 | + | 0.791103i | \(0.709507\pi\) | |||||||
\(230\) | 6.69405 | 0.441393 | ||||||||
\(231\) | −0.597329 | −0.0393014 | ||||||||
\(232\) | 11.8392 | 0.777281 | ||||||||
\(233\) | −5.29665 | −0.346995 | −0.173497 | − | 0.984834i | \(-0.555507\pi\) | ||||
−0.173497 | + | 0.984834i | \(0.555507\pi\) | |||||||
\(234\) | 5.24567 | 0.342920 | ||||||||
\(235\) | −3.93414 | −0.256635 | ||||||||
\(236\) | 5.56000 | 0.361925 | ||||||||
\(237\) | 2.06675 | 0.134250 | ||||||||
\(238\) | −2.10344 | −0.136346 | ||||||||
\(239\) | 25.2222 | 1.63149 | 0.815744 | − | 0.578413i | \(-0.196328\pi\) | ||||
0.815744 | + | 0.578413i | \(0.196328\pi\) | |||||||
\(240\) | 1.38251 | 0.0892404 | ||||||||
\(241\) | 27.6212 | 1.77924 | 0.889618 | − | 0.456706i | \(-0.150971\pi\) | ||||
0.889618 | + | 0.456706i | \(0.150971\pi\) | |||||||
\(242\) | 11.7365 | 0.754448 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 3.24291 | 0.207606 | ||||||||
\(245\) | 0.760743 | 0.0486021 | ||||||||
\(246\) | 10.7338 | 0.684363 | ||||||||
\(247\) | 27.9513 | 1.77850 | ||||||||
\(248\) | −13.9447 | −0.885489 | ||||||||
\(249\) | −10.4388 | −0.661535 | ||||||||
\(250\) | 7.90337 | 0.499853 | ||||||||
\(251\) | −7.27590 | −0.459251 | −0.229625 | − | 0.973279i | \(-0.573750\pi\) | ||||
−0.229625 | + | 0.973279i | \(0.573750\pi\) | |||||||
\(252\) | −0.784010 | −0.0493880 | ||||||||
\(253\) | −4.76650 | −0.299667 | ||||||||
\(254\) | 11.0553 | 0.693669 | ||||||||
\(255\) | −1.45112 | −0.0908726 | ||||||||
\(256\) | −15.5470 | −0.971685 | ||||||||
\(257\) | 21.9250 | 1.36764 | 0.683821 | − | 0.729649i | \(-0.260317\pi\) | ||||
0.683821 | + | 0.729649i | \(0.260317\pi\) | |||||||
\(258\) | −12.0617 | −0.750926 | ||||||||
\(259\) | −4.13929 | −0.257203 | ||||||||
\(260\) | 2.83723 | 0.175958 | ||||||||
\(261\) | 3.85644 | 0.238708 | ||||||||
\(262\) | −2.52819 | −0.156192 | ||||||||
\(263\) | 16.9826 | 1.04719 | 0.523595 | − | 0.851967i | \(-0.324591\pi\) | ||||
0.523595 | + | 0.851967i | \(0.324591\pi\) | |||||||
\(264\) | −1.83379 | −0.112862 | ||||||||
\(265\) | 10.6626 | 0.655000 | ||||||||
\(266\) | 6.47935 | 0.397274 | ||||||||
\(267\) | −5.04949 | −0.309024 | ||||||||
\(268\) | −1.41250 | −0.0862822 | ||||||||
\(269\) | −27.0483 | −1.64916 | −0.824581 | − | 0.565744i | \(-0.808589\pi\) | ||||
−0.824581 | + | 0.565744i | \(0.808589\pi\) | |||||||
\(270\) | 0.838886 | 0.0510530 | ||||||||
\(271\) | 8.39077 | 0.509703 | 0.254851 | − | 0.966980i | \(-0.417973\pi\) | ||||
0.254851 | + | 0.966980i | \(0.417973\pi\) | |||||||
\(272\) | −3.46652 | −0.210189 | ||||||||
\(273\) | 4.75703 | 0.287908 | ||||||||
\(274\) | −16.0272 | −0.968237 | ||||||||
\(275\) | −2.64095 | −0.159255 | ||||||||
\(276\) | −6.25615 | −0.376576 | ||||||||
\(277\) | 18.3355 | 1.10167 | 0.550836 | − | 0.834614i | \(-0.314309\pi\) | ||||
0.550836 | + | 0.834614i | \(0.314309\pi\) | |||||||
\(278\) | 18.1069 | 1.08598 | ||||||||
\(279\) | −4.54227 | −0.271939 | ||||||||
\(280\) | 2.33547 | 0.139571 | ||||||||
\(281\) | −21.9017 | −1.30655 | −0.653273 | − | 0.757123i | \(-0.726605\pi\) | ||||
−0.653273 | + | 0.757123i | \(0.726605\pi\) | |||||||
\(282\) | −5.70266 | −0.339588 | ||||||||
\(283\) | 2.35374 | 0.139915 | 0.0699577 | − | 0.997550i | \(-0.477714\pi\) | ||||
0.0699577 | + | 0.997550i | \(0.477714\pi\) | |||||||
\(284\) | 12.3774 | 0.734464 | ||||||||
\(285\) | 4.46997 | 0.264778 | ||||||||
\(286\) | 3.13339 | 0.185281 | ||||||||
\(287\) | 9.73395 | 0.574577 | ||||||||
\(288\) | −4.13598 | −0.243715 | ||||||||
\(289\) | −13.3614 | −0.785967 | ||||||||
\(290\) | −3.23511 | −0.189972 | ||||||||
\(291\) | −12.8199 | −0.751517 | ||||||||
\(292\) | −5.07239 | −0.296839 | ||||||||
\(293\) | −6.44889 | −0.376748 | −0.188374 | − | 0.982097i | \(-0.560322\pi\) | ||||
−0.188374 | + | 0.982097i | \(0.560322\pi\) | |||||||
\(294\) | 1.10272 | 0.0643119 | ||||||||
\(295\) | −5.39500 | −0.314109 | ||||||||
\(296\) | −12.7075 | −0.738610 | ||||||||
\(297\) | −0.597329 | −0.0346605 | ||||||||
\(298\) | −19.6789 | −1.13997 | ||||||||
\(299\) | 37.9596 | 2.19526 | ||||||||
\(300\) | −3.46632 | −0.200128 | ||||||||
\(301\) | −10.9381 | −0.630461 | ||||||||
\(302\) | 8.56662 | 0.492954 | ||||||||
\(303\) | −12.3187 | −0.707689 | ||||||||
\(304\) | 10.6781 | 0.612433 | ||||||||
\(305\) | −3.14667 | −0.180178 | ||||||||
\(306\) | −2.10344 | −0.120246 | ||||||||
\(307\) | −0.105629 | −0.00602858 | −0.00301429 | − | 0.999995i | \(-0.500959\pi\) | ||||
−0.00301429 | + | 0.999995i | \(0.500959\pi\) | |||||||
\(308\) | −0.468312 | −0.0266845 | ||||||||
\(309\) | −8.63579 | −0.491273 | ||||||||
\(310\) | 3.81045 | 0.216419 | ||||||||
\(311\) | −3.41558 | −0.193680 | −0.0968399 | − | 0.995300i | \(-0.530873\pi\) | ||||
−0.0968399 | + | 0.995300i | \(0.530873\pi\) | |||||||
\(312\) | 14.6040 | 0.826788 | ||||||||
\(313\) | −18.3685 | −1.03825 | −0.519124 | − | 0.854699i | \(-0.673742\pi\) | ||||
−0.519124 | + | 0.854699i | \(0.673742\pi\) | |||||||
\(314\) | −8.60043 | −0.485350 | ||||||||
\(315\) | 0.760743 | 0.0428630 | ||||||||
\(316\) | 1.62036 | 0.0911521 | ||||||||
\(317\) | 29.2567 | 1.64322 | 0.821610 | − | 0.570051i | \(-0.193076\pi\) | ||||
0.821610 | + | 0.570051i | \(0.193076\pi\) | |||||||
\(318\) | 15.4558 | 0.866718 | ||||||||
\(319\) | 2.30356 | 0.128975 | ||||||||
\(320\) | 6.23463 | 0.348526 | ||||||||
\(321\) | −12.0518 | −0.672664 | ||||||||
\(322\) | 8.79936 | 0.490369 | ||||||||
\(323\) | −11.2081 | −0.623635 | ||||||||
\(324\) | −0.784010 | −0.0435561 | ||||||||
\(325\) | 21.0321 | 1.16665 | ||||||||
\(326\) | −20.0624 | −1.11115 | ||||||||
\(327\) | −13.3643 | −0.739045 | ||||||||
\(328\) | 29.8830 | 1.65001 | ||||||||
\(329\) | −5.17145 | −0.285111 | ||||||||
\(330\) | 0.501091 | 0.0275842 | ||||||||
\(331\) | −0.175156 | −0.00962742 | −0.00481371 | − | 0.999988i | \(-0.501532\pi\) | ||||
−0.00481371 | + | 0.999988i | \(0.501532\pi\) | |||||||
\(332\) | −8.18416 | −0.449164 | ||||||||
\(333\) | −4.13929 | −0.226831 | ||||||||
\(334\) | 17.4930 | 0.957172 | ||||||||
\(335\) | 1.37058 | 0.0748829 | ||||||||
\(336\) | 1.81731 | 0.0991424 | ||||||||
\(337\) | −1.14949 | −0.0626167 | −0.0313084 | − | 0.999510i | \(-0.509967\pi\) | ||||
−0.0313084 | + | 0.999510i | \(0.509967\pi\) | |||||||
\(338\) | −10.6184 | −0.577566 | ||||||||
\(339\) | 17.2347 | 0.936061 | ||||||||
\(340\) | −1.13769 | −0.0617000 | ||||||||
\(341\) | −2.71323 | −0.146930 | ||||||||
\(342\) | 6.47935 | 0.350363 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −33.5798 | −1.81050 | ||||||||
\(345\) | 6.07049 | 0.326824 | ||||||||
\(346\) | 23.2401 | 1.24940 | ||||||||
\(347\) | 12.9858 | 0.697115 | 0.348557 | − | 0.937287i | \(-0.386672\pi\) | ||||
0.348557 | + | 0.937287i | \(0.386672\pi\) | |||||||
\(348\) | 3.02349 | 0.162076 | ||||||||
\(349\) | −4.50375 | −0.241080 | −0.120540 | − | 0.992708i | \(-0.538463\pi\) | ||||
−0.120540 | + | 0.992708i | \(0.538463\pi\) | |||||||
\(350\) | 4.87542 | 0.260602 | ||||||||
\(351\) | 4.75703 | 0.253911 | ||||||||
\(352\) | −2.47054 | −0.131680 | ||||||||
\(353\) | −34.4305 | −1.83255 | −0.916274 | − | 0.400551i | \(-0.868819\pi\) | ||||
−0.916274 | + | 0.400551i | \(0.868819\pi\) | |||||||
\(354\) | −7.82021 | −0.415640 | ||||||||
\(355\) | −12.0101 | −0.637430 | ||||||||
\(356\) | −3.95885 | −0.209819 | ||||||||
\(357\) | −1.90750 | −0.100956 | ||||||||
\(358\) | −0.930001 | −0.0491521 | ||||||||
\(359\) | 13.7260 | 0.724429 | 0.362215 | − | 0.932095i | \(-0.382021\pi\) | ||||
0.362215 | + | 0.932095i | \(0.382021\pi\) | |||||||
\(360\) | 2.33547 | 0.123090 | ||||||||
\(361\) | 15.5249 | 0.817101 | ||||||||
\(362\) | 5.77177 | 0.303357 | ||||||||
\(363\) | 10.6432 | 0.558623 | ||||||||
\(364\) | 3.72956 | 0.195482 | ||||||||
\(365\) | 4.92186 | 0.257622 | ||||||||
\(366\) | −4.56119 | −0.238417 | ||||||||
\(367\) | −21.1634 | −1.10472 | −0.552361 | − | 0.833605i | \(-0.686273\pi\) | ||||
−0.552361 | + | 0.833605i | \(0.686273\pi\) | |||||||
\(368\) | 14.5016 | 0.755946 | ||||||||
\(369\) | 9.73395 | 0.506729 | ||||||||
\(370\) | 3.47239 | 0.180521 | ||||||||
\(371\) | 14.0161 | 0.727678 | ||||||||
\(372\) | −3.56118 | −0.184639 | ||||||||
\(373\) | 15.9716 | 0.826976 | 0.413488 | − | 0.910510i | \(-0.364310\pi\) | ||||
0.413488 | + | 0.910510i | \(0.364310\pi\) | |||||||
\(374\) | −1.25645 | −0.0649693 | ||||||||
\(375\) | 7.16717 | 0.370111 | ||||||||
\(376\) | −15.8763 | −0.818755 | ||||||||
\(377\) | −18.3452 | −0.944825 | ||||||||
\(378\) | 1.10272 | 0.0567178 | ||||||||
\(379\) | −3.78560 | −0.194453 | −0.0972265 | − | 0.995262i | \(-0.530997\pi\) | ||||
−0.0972265 | + | 0.995262i | \(0.530997\pi\) | |||||||
\(380\) | 3.50450 | 0.179777 | ||||||||
\(381\) | 10.0255 | 0.513620 | ||||||||
\(382\) | −22.0839 | −1.12991 | ||||||||
\(383\) | −1.00000 | −0.0510976 | ||||||||
\(384\) | 0.765317 | 0.0390549 | ||||||||
\(385\) | 0.454414 | 0.0231591 | ||||||||
\(386\) | −2.06259 | −0.104983 | ||||||||
\(387\) | −10.9381 | −0.556015 | ||||||||
\(388\) | −10.0509 | −0.510259 | ||||||||
\(389\) | 28.6332 | 1.45176 | 0.725881 | − | 0.687820i | \(-0.241432\pi\) | ||||
0.725881 | + | 0.687820i | \(0.241432\pi\) | |||||||
\(390\) | −3.99060 | −0.202072 | ||||||||
\(391\) | −15.2213 | −0.769773 | ||||||||
\(392\) | 3.06998 | 0.155057 | ||||||||
\(393\) | −2.29268 | −0.115651 | ||||||||
\(394\) | 9.89693 | 0.498600 | ||||||||
\(395\) | −1.57227 | −0.0791094 | ||||||||
\(396\) | −0.468312 | −0.0235335 | ||||||||
\(397\) | 3.98827 | 0.200165 | 0.100083 | − | 0.994979i | \(-0.468089\pi\) | ||||
0.100083 | + | 0.994979i | \(0.468089\pi\) | |||||||
\(398\) | 1.03306 | 0.0517826 | ||||||||
\(399\) | 5.87579 | 0.294157 | ||||||||
\(400\) | 8.03482 | 0.401741 | ||||||||
\(401\) | −17.4610 | −0.871961 | −0.435980 | − | 0.899956i | \(-0.643598\pi\) | ||||
−0.435980 | + | 0.899956i | \(0.643598\pi\) | |||||||
\(402\) | 1.98670 | 0.0990875 | ||||||||
\(403\) | 21.6077 | 1.07636 | ||||||||
\(404\) | −9.65796 | −0.480501 | ||||||||
\(405\) | 0.760743 | 0.0378016 | ||||||||
\(406\) | −4.25257 | −0.211052 | ||||||||
\(407\) | −2.47251 | −0.122558 | ||||||||
\(408\) | −5.85600 | −0.289915 | ||||||||
\(409\) | 31.4462 | 1.55491 | 0.777457 | − | 0.628937i | \(-0.216509\pi\) | ||||
0.777457 | + | 0.628937i | \(0.216509\pi\) | |||||||
\(410\) | −8.16567 | −0.403274 | ||||||||
\(411\) | −14.5342 | −0.716921 | ||||||||
\(412\) | −6.77054 | −0.333561 | ||||||||
\(413\) | −7.09175 | −0.348962 | ||||||||
\(414\) | 8.79936 | 0.432465 | ||||||||
\(415\) | 7.94128 | 0.389822 | ||||||||
\(416\) | 19.6750 | 0.964645 | ||||||||
\(417\) | 16.4202 | 0.804100 | ||||||||
\(418\) | 3.87030 | 0.189303 | ||||||||
\(419\) | 25.9974 | 1.27006 | 0.635028 | − | 0.772489i | \(-0.280988\pi\) | ||||
0.635028 | + | 0.772489i | \(0.280988\pi\) | |||||||
\(420\) | 0.596430 | 0.0291028 | ||||||||
\(421\) | 33.0449 | 1.61051 | 0.805256 | − | 0.592927i | \(-0.202028\pi\) | ||||
0.805256 | + | 0.592927i | \(0.202028\pi\) | |||||||
\(422\) | 25.2407 | 1.22870 | ||||||||
\(423\) | −5.17145 | −0.251444 | ||||||||
\(424\) | 43.0291 | 2.08968 | ||||||||
\(425\) | −8.43359 | −0.409089 | ||||||||
\(426\) | −17.4090 | −0.843468 | ||||||||
\(427\) | −4.13631 | −0.200170 | ||||||||
\(428\) | −9.44870 | −0.456720 | ||||||||
\(429\) | 2.84151 | 0.137189 | ||||||||
\(430\) | 9.17582 | 0.442497 | ||||||||
\(431\) | 35.1244 | 1.69188 | 0.845942 | − | 0.533274i | \(-0.179039\pi\) | ||||
0.845942 | + | 0.533274i | \(0.179039\pi\) | |||||||
\(432\) | 1.81731 | 0.0874354 | ||||||||
\(433\) | −14.3613 | −0.690162 | −0.345081 | − | 0.938573i | \(-0.612149\pi\) | ||||
−0.345081 | + | 0.938573i | \(0.612149\pi\) | |||||||
\(434\) | 5.00885 | 0.240433 | ||||||||
\(435\) | −2.93376 | −0.140663 | ||||||||
\(436\) | −10.4777 | −0.501791 | ||||||||
\(437\) | 46.8870 | 2.24291 | ||||||||
\(438\) | 7.13439 | 0.340894 | ||||||||
\(439\) | −10.5230 | −0.502233 | −0.251117 | − | 0.967957i | \(-0.580798\pi\) | ||||
−0.251117 | + | 0.967957i | \(0.580798\pi\) | |||||||
\(440\) | 1.39504 | 0.0665060 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 10.0061 | 0.475943 | ||||||||
\(443\) | −19.5076 | −0.926833 | −0.463417 | − | 0.886141i | \(-0.653377\pi\) | ||||
−0.463417 | + | 0.886141i | \(0.653377\pi\) | |||||||
\(444\) | −3.24524 | −0.154012 | ||||||||
\(445\) | 3.84137 | 0.182098 | ||||||||
\(446\) | −30.7449 | −1.45582 | ||||||||
\(447\) | −17.8458 | −0.844076 | ||||||||
\(448\) | 8.19545 | 0.387198 | ||||||||
\(449\) | 15.8730 | 0.749095 | 0.374547 | − | 0.927208i | \(-0.377798\pi\) | ||||
0.374547 | + | 0.927208i | \(0.377798\pi\) | |||||||
\(450\) | 4.87542 | 0.229830 | ||||||||
\(451\) | 5.81437 | 0.273788 | ||||||||
\(452\) | 13.5122 | 0.635560 | ||||||||
\(453\) | 7.76863 | 0.365002 | ||||||||
\(454\) | 5.58099 | 0.261929 | ||||||||
\(455\) | −3.61888 | −0.169655 | ||||||||
\(456\) | 18.0386 | 0.844733 | ||||||||
\(457\) | 20.0067 | 0.935875 | 0.467938 | − | 0.883762i | \(-0.344997\pi\) | ||||
0.467938 | + | 0.883762i | \(0.344997\pi\) | |||||||
\(458\) | 20.4145 | 0.953908 | ||||||||
\(459\) | −1.90750 | −0.0890346 | ||||||||
\(460\) | 4.75932 | 0.221905 | ||||||||
\(461\) | −11.9005 | −0.554261 | −0.277130 | − | 0.960832i | \(-0.589383\pi\) | ||||
−0.277130 | + | 0.960832i | \(0.589383\pi\) | |||||||
\(462\) | 0.658686 | 0.0306449 | ||||||||
\(463\) | 22.9536 | 1.06674 | 0.533372 | − | 0.845881i | \(-0.320924\pi\) | ||||
0.533372 | + | 0.845881i | \(0.320924\pi\) | |||||||
\(464\) | −7.00834 | −0.325354 | ||||||||
\(465\) | 3.45550 | 0.160245 | ||||||||
\(466\) | 5.84072 | 0.270566 | ||||||||
\(467\) | 38.0405 | 1.76031 | 0.880153 | − | 0.474690i | \(-0.157440\pi\) | ||||
0.880153 | + | 0.474690i | \(0.157440\pi\) | |||||||
\(468\) | 3.72956 | 0.172399 | ||||||||
\(469\) | 1.80164 | 0.0831918 | ||||||||
\(470\) | 4.33826 | 0.200109 | ||||||||
\(471\) | −7.79929 | −0.359372 | ||||||||
\(472\) | −21.7716 | −1.00212 | ||||||||
\(473\) | −6.53364 | −0.300417 | ||||||||
\(474\) | −2.27905 | −0.104680 | ||||||||
\(475\) | 25.9785 | 1.19197 | ||||||||
\(476\) | −1.49550 | −0.0685462 | ||||||||
\(477\) | 14.0161 | 0.641752 | ||||||||
\(478\) | −27.8130 | −1.27214 | ||||||||
\(479\) | −19.2390 | −0.879054 | −0.439527 | − | 0.898229i | \(-0.644854\pi\) | ||||
−0.439527 | + | 0.898229i | \(0.644854\pi\) | |||||||
\(480\) | 3.14642 | 0.143614 | ||||||||
\(481\) | 19.6907 | 0.897818 | ||||||||
\(482\) | −30.4584 | −1.38734 | ||||||||
\(483\) | 7.97969 | 0.363088 | ||||||||
\(484\) | 8.34437 | 0.379290 | ||||||||
\(485\) | 9.75266 | 0.442846 | ||||||||
\(486\) | 1.10272 | 0.0500204 | ||||||||
\(487\) | −9.78468 | −0.443386 | −0.221693 | − | 0.975116i | \(-0.571158\pi\) | ||||
−0.221693 | + | 0.975116i | \(0.571158\pi\) | |||||||
\(488\) | −12.6984 | −0.574829 | ||||||||
\(489\) | −18.1935 | −0.822740 | ||||||||
\(490\) | −0.838886 | −0.0378970 | ||||||||
\(491\) | −27.6834 | −1.24934 | −0.624668 | − | 0.780891i | \(-0.714766\pi\) | ||||
−0.624668 | + | 0.780891i | \(0.714766\pi\) | |||||||
\(492\) | 7.63151 | 0.344055 | ||||||||
\(493\) | 7.35617 | 0.331305 | ||||||||
\(494\) | −30.8224 | −1.38677 | ||||||||
\(495\) | 0.454414 | 0.0204244 | ||||||||
\(496\) | 8.25471 | 0.370648 | ||||||||
\(497\) | −15.7873 | −0.708158 | ||||||||
\(498\) | 11.5111 | 0.515826 | ||||||||
\(499\) | 6.30431 | 0.282220 | 0.141110 | − | 0.989994i | \(-0.454933\pi\) | ||||
0.141110 | + | 0.989994i | \(0.454933\pi\) | |||||||
\(500\) | 5.61913 | 0.251295 | ||||||||
\(501\) | 15.8635 | 0.708728 | ||||||||
\(502\) | 8.02328 | 0.358097 | ||||||||
\(503\) | 1.27932 | 0.0570419 | 0.0285210 | − | 0.999593i | \(-0.490920\pi\) | ||||
0.0285210 | + | 0.999593i | \(0.490920\pi\) | |||||||
\(504\) | 3.06998 | 0.136748 | ||||||||
\(505\) | 9.37135 | 0.417019 | ||||||||
\(506\) | 5.25611 | 0.233663 | ||||||||
\(507\) | −9.62931 | −0.427652 | ||||||||
\(508\) | 7.86006 | 0.348734 | ||||||||
\(509\) | −12.4422 | −0.551490 | −0.275745 | − | 0.961231i | \(-0.588924\pi\) | ||||
−0.275745 | + | 0.961231i | \(0.588924\pi\) | |||||||
\(510\) | 1.60018 | 0.0708571 | ||||||||
\(511\) | 6.46981 | 0.286208 | ||||||||
\(512\) | 18.6746 | 0.825307 | ||||||||
\(513\) | 5.87579 | 0.259422 | ||||||||
\(514\) | −24.1771 | −1.06641 | ||||||||
\(515\) | 6.56961 | 0.289492 | ||||||||
\(516\) | −8.57557 | −0.377518 | ||||||||
\(517\) | −3.08906 | −0.135856 | ||||||||
\(518\) | 4.56447 | 0.200551 | ||||||||
\(519\) | 21.0753 | 0.925102 | ||||||||
\(520\) | −11.1099 | −0.487201 | ||||||||
\(521\) | −23.2942 | −1.02054 | −0.510269 | − | 0.860015i | \(-0.670454\pi\) | ||||
−0.510269 | + | 0.860015i | \(0.670454\pi\) | |||||||
\(522\) | −4.25257 | −0.186130 | ||||||||
\(523\) | 35.5096 | 1.55272 | 0.776362 | − | 0.630287i | \(-0.217063\pi\) | ||||
0.776362 | + | 0.630287i | \(0.217063\pi\) | |||||||
\(524\) | −1.79749 | −0.0785236 | ||||||||
\(525\) | 4.42127 | 0.192960 | ||||||||
\(526\) | −18.7270 | −0.816536 | ||||||||
\(527\) | −8.66440 | −0.377427 | ||||||||
\(528\) | 1.08553 | 0.0472417 | ||||||||
\(529\) | 40.6754 | 1.76850 | ||||||||
\(530\) | −11.7579 | −0.510730 | ||||||||
\(531\) | −7.09175 | −0.307756 | ||||||||
\(532\) | 4.60668 | 0.199725 | ||||||||
\(533\) | −46.3046 | −2.00568 | ||||||||
\(534\) | 5.56818 | 0.240959 | ||||||||
\(535\) | 9.16829 | 0.396380 | ||||||||
\(536\) | 5.53099 | 0.238902 | ||||||||
\(537\) | −0.843371 | −0.0363941 | ||||||||
\(538\) | 29.8266 | 1.28592 | ||||||||
\(539\) | 0.597329 | 0.0257288 | ||||||||
\(540\) | 0.596430 | 0.0256663 | ||||||||
\(541\) | −40.0860 | −1.72343 | −0.861715 | − | 0.507392i | \(-0.830610\pi\) | ||||
−0.861715 | + | 0.507392i | \(0.830610\pi\) | |||||||
\(542\) | −9.25266 | −0.397436 | ||||||||
\(543\) | 5.23412 | 0.224618 | ||||||||
\(544\) | −7.88940 | −0.338255 | ||||||||
\(545\) | 10.1668 | 0.435496 | ||||||||
\(546\) | −5.24567 | −0.224494 | ||||||||
\(547\) | 11.8844 | 0.508139 | 0.254069 | − | 0.967186i | \(-0.418231\pi\) | ||||
0.254069 | + | 0.967186i | \(0.418231\pi\) | |||||||
\(548\) | −11.3950 | −0.486769 | ||||||||
\(549\) | −4.13631 | −0.176533 | ||||||||
\(550\) | 2.91223 | 0.124178 | ||||||||
\(551\) | −22.6596 | −0.965333 | ||||||||
\(552\) | 24.4975 | 1.04268 | ||||||||
\(553\) | −2.06675 | −0.0878873 | ||||||||
\(554\) | −20.2189 | −0.859018 | ||||||||
\(555\) | 3.14893 | 0.133665 | ||||||||
\(556\) | 12.8736 | 0.545962 | ||||||||
\(557\) | 41.3572 | 1.75236 | 0.876180 | − | 0.481985i | \(-0.160084\pi\) | ||||
0.876180 | + | 0.481985i | \(0.160084\pi\) | |||||||
\(558\) | 5.00885 | 0.212042 | ||||||||
\(559\) | 52.0328 | 2.20075 | ||||||||
\(560\) | −1.38251 | −0.0584215 | ||||||||
\(561\) | −1.13941 | −0.0481058 | ||||||||
\(562\) | 24.1514 | 1.01877 | ||||||||
\(563\) | −26.3268 | −1.10954 | −0.554772 | − | 0.832002i | \(-0.687195\pi\) | ||||
−0.554772 | + | 0.832002i | \(0.687195\pi\) | |||||||
\(564\) | −4.05446 | −0.170724 | ||||||||
\(565\) | −13.1112 | −0.551592 | ||||||||
\(566\) | −2.59552 | −0.109098 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | −48.4668 | −2.03362 | ||||||||
\(569\) | 38.4293 | 1.61104 | 0.805520 | − | 0.592569i | \(-0.201886\pi\) | ||||
0.805520 | + | 0.592569i | \(0.201886\pi\) | |||||||
\(570\) | −4.92912 | −0.206458 | ||||||||
\(571\) | −0.163185 | −0.00682909 | −0.00341454 | − | 0.999994i | \(-0.501087\pi\) | ||||
−0.00341454 | + | 0.999994i | \(0.501087\pi\) | |||||||
\(572\) | 2.22777 | 0.0931478 | ||||||||
\(573\) | −20.0268 | −0.836631 | ||||||||
\(574\) | −10.7338 | −0.448021 | ||||||||
\(575\) | 35.2804 | 1.47129 | ||||||||
\(576\) | 8.19545 | 0.341477 | ||||||||
\(577\) | 34.5119 | 1.43675 | 0.718374 | − | 0.695657i | \(-0.244887\pi\) | ||||
0.718374 | + | 0.695657i | \(0.244887\pi\) | |||||||
\(578\) | 14.7339 | 0.612850 | ||||||||
\(579\) | −1.87046 | −0.0777336 | ||||||||
\(580\) | −2.30010 | −0.0955063 | ||||||||
\(581\) | 10.4388 | 0.433076 | ||||||||
\(582\) | 14.1368 | 0.585988 | ||||||||
\(583\) | 8.37220 | 0.346741 | ||||||||
\(584\) | 19.8622 | 0.821904 | ||||||||
\(585\) | −3.61888 | −0.149622 | ||||||||
\(586\) | 7.11132 | 0.293766 | ||||||||
\(587\) | −16.8268 | −0.694518 | −0.347259 | − | 0.937769i | \(-0.612887\pi\) | ||||
−0.347259 | + | 0.937769i | \(0.612887\pi\) | |||||||
\(588\) | 0.784010 | 0.0323320 | ||||||||
\(589\) | 26.6894 | 1.09972 | ||||||||
\(590\) | 5.94917 | 0.244924 | ||||||||
\(591\) | 8.97502 | 0.369183 | ||||||||
\(592\) | 7.52236 | 0.309167 | ||||||||
\(593\) | −12.8591 | −0.528059 | −0.264029 | − | 0.964515i | \(-0.585052\pi\) | ||||
−0.264029 | + | 0.964515i | \(0.585052\pi\) | |||||||
\(594\) | 0.658686 | 0.0270262 | ||||||||
\(595\) | 1.45112 | 0.0594901 | ||||||||
\(596\) | −13.9913 | −0.573104 | ||||||||
\(597\) | 0.936829 | 0.0383418 | ||||||||
\(598\) | −41.8588 | −1.71173 | ||||||||
\(599\) | 30.0650 | 1.22842 | 0.614212 | − | 0.789141i | \(-0.289474\pi\) | ||||
0.614212 | + | 0.789141i | \(0.289474\pi\) | |||||||
\(600\) | 13.5732 | 0.554124 | ||||||||
\(601\) | 21.9451 | 0.895160 | 0.447580 | − | 0.894244i | \(-0.352286\pi\) | ||||
0.447580 | + | 0.894244i | \(0.352286\pi\) | |||||||
\(602\) | 12.0617 | 0.491596 | ||||||||
\(603\) | 1.80164 | 0.0733683 | ||||||||
\(604\) | 6.09068 | 0.247826 | ||||||||
\(605\) | −8.09674 | −0.329179 | ||||||||
\(606\) | 13.5840 | 0.551814 | ||||||||
\(607\) | −1.14101 | −0.0463120 | −0.0231560 | − | 0.999732i | \(-0.507371\pi\) | ||||
−0.0231560 | + | 0.999732i | \(0.507371\pi\) | |||||||
\(608\) | 24.3022 | 0.985583 | ||||||||
\(609\) | −3.85644 | −0.156271 | ||||||||
\(610\) | 3.46989 | 0.140492 | ||||||||
\(611\) | 24.6007 | 0.995238 | ||||||||
\(612\) | −1.49550 | −0.0604520 | ||||||||
\(613\) | 34.5707 | 1.39630 | 0.698149 | − | 0.715953i | \(-0.254007\pi\) | ||||
0.698149 | + | 0.715953i | \(0.254007\pi\) | |||||||
\(614\) | 0.116479 | 0.00470073 | ||||||||
\(615\) | −7.40503 | −0.298600 | ||||||||
\(616\) | 1.83379 | 0.0738855 | ||||||||
\(617\) | −31.3212 | −1.26094 | −0.630472 | − | 0.776212i | \(-0.717139\pi\) | ||||
−0.630472 | + | 0.776212i | \(0.717139\pi\) | |||||||
\(618\) | 9.52285 | 0.383065 | ||||||||
\(619\) | 19.7289 | 0.792972 | 0.396486 | − | 0.918041i | \(-0.370230\pi\) | ||||
0.396486 | + | 0.918041i | \(0.370230\pi\) | |||||||
\(620\) | 2.70915 | 0.108802 | ||||||||
\(621\) | 7.97969 | 0.320214 | ||||||||
\(622\) | 3.76643 | 0.151020 | ||||||||
\(623\) | 5.04949 | 0.202304 | ||||||||
\(624\) | −8.64499 | −0.346077 | ||||||||
\(625\) | 16.6540 | 0.666159 | ||||||||
\(626\) | 20.2553 | 0.809564 | ||||||||
\(627\) | 3.50978 | 0.140167 | ||||||||
\(628\) | −6.11472 | −0.244004 | ||||||||
\(629\) | −7.89570 | −0.314822 | ||||||||
\(630\) | −0.838886 | −0.0334220 | ||||||||
\(631\) | 17.5508 | 0.698688 | 0.349344 | − | 0.936995i | \(-0.386404\pi\) | ||||
0.349344 | + | 0.936995i | \(0.386404\pi\) | |||||||
\(632\) | −6.34490 | −0.252387 | ||||||||
\(633\) | 22.8895 | 0.909777 | ||||||||
\(634\) | −32.2619 | −1.28128 | ||||||||
\(635\) | −7.62680 | −0.302660 | ||||||||
\(636\) | 10.9887 | 0.435732 | ||||||||
\(637\) | −4.75703 | −0.188480 | ||||||||
\(638\) | −2.54018 | −0.100567 | ||||||||
\(639\) | −15.7873 | −0.624537 | ||||||||
\(640\) | −0.582209 | −0.0230139 | ||||||||
\(641\) | −17.8880 | −0.706532 | −0.353266 | − | 0.935523i | \(-0.614929\pi\) | ||||
−0.353266 | + | 0.935523i | \(0.614929\pi\) | |||||||
\(642\) | 13.2897 | 0.524503 | ||||||||
\(643\) | −1.94088 | −0.0765408 | −0.0382704 | − | 0.999267i | \(-0.512185\pi\) | ||||
−0.0382704 | + | 0.999267i | \(0.512185\pi\) | |||||||
\(644\) | 6.25615 | 0.246527 | ||||||||
\(645\) | 8.32108 | 0.327642 | ||||||||
\(646\) | 12.3594 | 0.486273 | ||||||||
\(647\) | 4.33765 | 0.170530 | 0.0852652 | − | 0.996358i | \(-0.472826\pi\) | ||||
0.0852652 | + | 0.996358i | \(0.472826\pi\) | |||||||
\(648\) | 3.06998 | 0.120600 | ||||||||
\(649\) | −4.23611 | −0.166282 | ||||||||
\(650\) | −23.1925 | −0.909685 | ||||||||
\(651\) | 4.54227 | 0.178026 | ||||||||
\(652\) | −14.2639 | −0.558618 | ||||||||
\(653\) | −26.0061 | −1.01770 | −0.508849 | − | 0.860856i | \(-0.669929\pi\) | ||||
−0.508849 | + | 0.860856i | \(0.669929\pi\) | |||||||
\(654\) | 14.7370 | 0.576263 | ||||||||
\(655\) | 1.74414 | 0.0681493 | ||||||||
\(656\) | −17.6896 | −0.690663 | ||||||||
\(657\) | 6.46981 | 0.252411 | ||||||||
\(658\) | 5.70266 | 0.222313 | ||||||||
\(659\) | 0.167395 | 0.00652078 | 0.00326039 | − | 0.999995i | \(-0.498962\pi\) | ||||
0.00326039 | + | 0.999995i | \(0.498962\pi\) | |||||||
\(660\) | 0.356265 | 0.0138676 | ||||||||
\(661\) | −29.3022 | −1.13972 | −0.569862 | − | 0.821741i | \(-0.693003\pi\) | ||||
−0.569862 | + | 0.821741i | \(0.693003\pi\) | |||||||
\(662\) | 0.193148 | 0.00750689 | ||||||||
\(663\) | 9.07404 | 0.352407 | ||||||||
\(664\) | 32.0471 | 1.24367 | ||||||||
\(665\) | −4.46997 | −0.173338 | ||||||||
\(666\) | 4.56447 | 0.176870 | ||||||||
\(667\) | −30.7732 | −1.19154 | ||||||||
\(668\) | 12.4371 | 0.481207 | ||||||||
\(669\) | −27.8810 | −1.07794 | ||||||||
\(670\) | −1.51137 | −0.0583892 | ||||||||
\(671\) | −2.47074 | −0.0953817 | ||||||||
\(672\) | 4.13598 | 0.159549 | ||||||||
\(673\) | 0.640099 | 0.0246740 | 0.0123370 | − | 0.999924i | \(-0.496073\pi\) | ||||
0.0123370 | + | 0.999924i | \(0.496073\pi\) | |||||||
\(674\) | 1.26757 | 0.0488248 | ||||||||
\(675\) | 4.42127 | 0.170175 | ||||||||
\(676\) | −7.54947 | −0.290364 | ||||||||
\(677\) | −30.8481 | −1.18559 | −0.592794 | − | 0.805354i | \(-0.701975\pi\) | ||||
−0.592794 | + | 0.805354i | \(0.701975\pi\) | |||||||
\(678\) | −19.0051 | −0.729885 | ||||||||
\(679\) | 12.8199 | 0.491983 | ||||||||
\(680\) | 4.45491 | 0.170838 | ||||||||
\(681\) | 5.06112 | 0.193942 | ||||||||
\(682\) | 2.99193 | 0.114567 | ||||||||
\(683\) | 7.68670 | 0.294123 | 0.147062 | − | 0.989127i | \(-0.453018\pi\) | ||||
0.147062 | + | 0.989127i | \(0.453018\pi\) | |||||||
\(684\) | 4.60668 | 0.176141 | ||||||||
\(685\) | 11.0568 | 0.422459 | ||||||||
\(686\) | −1.10272 | −0.0421020 | ||||||||
\(687\) | 18.5129 | 0.706311 | ||||||||
\(688\) | 19.8779 | 0.757838 | ||||||||
\(689\) | −66.6748 | −2.54011 | ||||||||
\(690\) | −6.69405 | −0.254838 | ||||||||
\(691\) | 1.47368 | 0.0560613 | 0.0280306 | − | 0.999607i | \(-0.491076\pi\) | ||||
0.0280306 | + | 0.999607i | \(0.491076\pi\) | |||||||
\(692\) | 16.5232 | 0.628119 | ||||||||
\(693\) | 0.597329 | 0.0226906 | ||||||||
\(694\) | −14.3197 | −0.543569 | ||||||||
\(695\) | −12.4915 | −0.473831 | ||||||||
\(696\) | −11.8392 | −0.448764 | ||||||||
\(697\) | 18.5675 | 0.703295 | ||||||||
\(698\) | 4.96638 | 0.187980 | ||||||||
\(699\) | 5.29665 | 0.200338 | ||||||||
\(700\) | 3.46632 | 0.131015 | ||||||||
\(701\) | 33.5155 | 1.26586 | 0.632932 | − | 0.774207i | \(-0.281851\pi\) | ||||
0.632932 | + | 0.774207i | \(0.281851\pi\) | |||||||
\(702\) | −5.24567 | −0.197985 | ||||||||
\(703\) | 24.3216 | 0.917306 | ||||||||
\(704\) | 4.89538 | 0.184501 | ||||||||
\(705\) | 3.93414 | 0.148168 | ||||||||
\(706\) | 37.9672 | 1.42891 | ||||||||
\(707\) | 12.3187 | 0.463291 | ||||||||
\(708\) | −5.56000 | −0.208958 | ||||||||
\(709\) | −37.3801 | −1.40384 | −0.701919 | − | 0.712257i | \(-0.747673\pi\) | ||||
−0.701919 | + | 0.712257i | \(0.747673\pi\) | |||||||
\(710\) | 13.2438 | 0.497030 | ||||||||
\(711\) | −2.06675 | −0.0775093 | ||||||||
\(712\) | 15.5019 | 0.580957 | ||||||||
\(713\) | 36.2459 | 1.35742 | ||||||||
\(714\) | 2.10344 | 0.0787193 | ||||||||
\(715\) | −2.16166 | −0.0808415 | ||||||||
\(716\) | −0.661211 | −0.0247106 | ||||||||
\(717\) | −25.2222 | −0.941940 | ||||||||
\(718\) | −15.1359 | −0.564867 | ||||||||
\(719\) | 14.6873 | 0.547742 | 0.273871 | − | 0.961766i | \(-0.411696\pi\) | ||||
0.273871 | + | 0.961766i | \(0.411696\pi\) | |||||||
\(720\) | −1.38251 | −0.0515229 | ||||||||
\(721\) | 8.63579 | 0.321613 | ||||||||
\(722\) | −17.1196 | −0.637126 | ||||||||
\(723\) | −27.6212 | −1.02724 | ||||||||
\(724\) | 4.10360 | 0.152509 | ||||||||
\(725\) | −17.0504 | −0.633234 | ||||||||
\(726\) | −11.7365 | −0.435581 | ||||||||
\(727\) | −37.8324 | −1.40312 | −0.701562 | − | 0.712608i | \(-0.747514\pi\) | ||||
−0.701562 | + | 0.712608i | \(0.747514\pi\) | |||||||
\(728\) | −14.6040 | −0.541260 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −5.42743 | −0.200878 | ||||||||
\(731\) | −20.8644 | −0.771700 | ||||||||
\(732\) | −3.24291 | −0.119861 | ||||||||
\(733\) | 19.3959 | 0.716403 | 0.358202 | − | 0.933644i | \(-0.383390\pi\) | ||||
0.358202 | + | 0.933644i | \(0.383390\pi\) | |||||||
\(734\) | 23.3373 | 0.861396 | ||||||||
\(735\) | −0.760743 | −0.0280604 | ||||||||
\(736\) | 33.0038 | 1.21654 | ||||||||
\(737\) | 1.07617 | 0.0396412 | ||||||||
\(738\) | −10.7338 | −0.395117 | ||||||||
\(739\) | 33.3894 | 1.22825 | 0.614124 | − | 0.789210i | \(-0.289510\pi\) | ||||
0.614124 | + | 0.789210i | \(0.289510\pi\) | |||||||
\(740\) | 2.46879 | 0.0907547 | ||||||||
\(741\) | −27.9513 | −1.02682 | ||||||||
\(742\) | −15.4558 | −0.567400 | ||||||||
\(743\) | −18.9989 | −0.697003 | −0.348501 | − | 0.937308i | \(-0.613309\pi\) | ||||
−0.348501 | + | 0.937308i | \(0.613309\pi\) | |||||||
\(744\) | 13.9447 | 0.511237 | ||||||||
\(745\) | 13.5760 | 0.497388 | ||||||||
\(746\) | −17.6121 | −0.644826 | ||||||||
\(747\) | 10.4388 | 0.381938 | ||||||||
\(748\) | −0.893306 | −0.0326625 | ||||||||
\(749\) | 12.0518 | 0.440362 | ||||||||
\(750\) | −7.90337 | −0.288590 | ||||||||
\(751\) | 46.0114 | 1.67898 | 0.839490 | − | 0.543375i | \(-0.182854\pi\) | ||||
0.839490 | + | 0.543375i | \(0.182854\pi\) | |||||||
\(752\) | 9.39812 | 0.342714 | ||||||||
\(753\) | 7.27590 | 0.265149 | ||||||||
\(754\) | 20.2296 | 0.736718 | ||||||||
\(755\) | −5.90993 | −0.215084 | ||||||||
\(756\) | 0.784010 | 0.0285142 | ||||||||
\(757\) | −0.926254 | −0.0336653 | −0.0168326 | − | 0.999858i | \(-0.505358\pi\) | ||||
−0.0168326 | + | 0.999858i | \(0.505358\pi\) | |||||||
\(758\) | 4.17445 | 0.151623 | ||||||||
\(759\) | 4.76650 | 0.173013 | ||||||||
\(760\) | −13.7227 | −0.497775 | ||||||||
\(761\) | 12.3953 | 0.449330 | 0.224665 | − | 0.974436i | \(-0.427871\pi\) | ||||
0.224665 | + | 0.974436i | \(0.427871\pi\) | |||||||
\(762\) | −11.0553 | −0.400490 | ||||||||
\(763\) | 13.3643 | 0.483818 | ||||||||
\(764\) | −15.7012 | −0.568049 | ||||||||
\(765\) | 1.45112 | 0.0524653 | ||||||||
\(766\) | 1.10272 | 0.0398429 | ||||||||
\(767\) | 33.7357 | 1.21812 | ||||||||
\(768\) | 15.5470 | 0.561003 | ||||||||
\(769\) | −11.6725 | −0.420920 | −0.210460 | − | 0.977602i | \(-0.567496\pi\) | ||||
−0.210460 | + | 0.977602i | \(0.567496\pi\) | |||||||
\(770\) | −0.501091 | −0.0180581 | ||||||||
\(771\) | −21.9250 | −0.789609 | ||||||||
\(772\) | −1.46646 | −0.0527789 | ||||||||
\(773\) | 24.9741 | 0.898256 | 0.449128 | − | 0.893467i | \(-0.351735\pi\) | ||||
0.449128 | + | 0.893467i | \(0.351735\pi\) | |||||||
\(774\) | 12.0617 | 0.433547 | ||||||||
\(775\) | 20.0826 | 0.721389 | ||||||||
\(776\) | 39.3569 | 1.41283 | ||||||||
\(777\) | 4.13929 | 0.148496 | ||||||||
\(778\) | −31.5744 | −1.13200 | ||||||||
\(779\) | −57.1946 | −2.04921 | ||||||||
\(780\) | −2.83723 | −0.101589 | ||||||||
\(781\) | −9.43022 | −0.337440 | ||||||||
\(782\) | 16.7848 | 0.600223 | ||||||||
\(783\) | −3.85644 | −0.137818 | ||||||||
\(784\) | −1.81731 | −0.0649039 | ||||||||
\(785\) | 5.93326 | 0.211767 | ||||||||
\(786\) | 2.52819 | 0.0901775 | ||||||||
\(787\) | 17.8922 | 0.637787 | 0.318894 | − | 0.947790i | \(-0.396689\pi\) | ||||
0.318894 | + | 0.947790i | \(0.396689\pi\) | |||||||
\(788\) | 7.03650 | 0.250665 | ||||||||
\(789\) | −16.9826 | −0.604595 | ||||||||
\(790\) | 1.73377 | 0.0616848 | ||||||||
\(791\) | −17.2347 | −0.612796 | ||||||||
\(792\) | 1.83379 | 0.0651608 | ||||||||
\(793\) | 19.6765 | 0.698734 | ||||||||
\(794\) | −4.39794 | −0.156077 | ||||||||
\(795\) | −10.6626 | −0.378164 | ||||||||
\(796\) | 0.734483 | 0.0260331 | ||||||||
\(797\) | 15.1144 | 0.535378 | 0.267689 | − | 0.963505i | \(-0.413740\pi\) | ||||
0.267689 | + | 0.963505i | \(0.413740\pi\) | |||||||
\(798\) | −6.47935 | −0.229366 | ||||||||
\(799\) | −9.86455 | −0.348983 | ||||||||
\(800\) | 18.2863 | 0.646518 | ||||||||
\(801\) | 5.04949 | 0.178415 | ||||||||
\(802\) | 19.2546 | 0.679903 | ||||||||
\(803\) | 3.86460 | 0.136379 | ||||||||
\(804\) | 1.41250 | 0.0498150 | ||||||||
\(805\) | −6.07049 | −0.213957 | ||||||||
\(806\) | −23.8272 | −0.839279 | ||||||||
\(807\) | 27.0483 | 0.952144 | ||||||||
\(808\) | 37.8181 | 1.33044 | ||||||||
\(809\) | −35.2847 | −1.24054 | −0.620272 | − | 0.784386i | \(-0.712978\pi\) | ||||
−0.620272 | + | 0.784386i | \(0.712978\pi\) | |||||||
\(810\) | −0.838886 | −0.0294755 | ||||||||
\(811\) | −20.8477 | −0.732060 | −0.366030 | − | 0.930603i | \(-0.619283\pi\) | ||||
−0.366030 | + | 0.930603i | \(0.619283\pi\) | |||||||
\(812\) | −3.02349 | −0.106104 | ||||||||
\(813\) | −8.39077 | −0.294277 | ||||||||
\(814\) | 2.72649 | 0.0955634 | ||||||||
\(815\) | 13.8406 | 0.484815 | ||||||||
\(816\) | 3.46652 | 0.121353 | ||||||||
\(817\) | 64.2699 | 2.24852 | ||||||||
\(818\) | −34.6763 | −1.21243 | ||||||||
\(819\) | −4.75703 | −0.166224 | ||||||||
\(820\) | −5.80562 | −0.202741 | ||||||||
\(821\) | −37.1517 | −1.29660 | −0.648301 | − | 0.761384i | \(-0.724520\pi\) | ||||
−0.648301 | + | 0.761384i | \(0.724520\pi\) | |||||||
\(822\) | 16.0272 | 0.559012 | ||||||||
\(823\) | −43.0417 | −1.50034 | −0.750169 | − | 0.661246i | \(-0.770028\pi\) | ||||
−0.750169 | + | 0.661246i | \(0.770028\pi\) | |||||||
\(824\) | 26.5117 | 0.923579 | ||||||||
\(825\) | 2.64095 | 0.0919462 | ||||||||
\(826\) | 7.82021 | 0.272100 | ||||||||
\(827\) | 37.1593 | 1.29215 | 0.646077 | − | 0.763272i | \(-0.276408\pi\) | ||||
0.646077 | + | 0.763272i | \(0.276408\pi\) | |||||||
\(828\) | 6.25615 | 0.217416 | ||||||||
\(829\) | 19.2244 | 0.667690 | 0.333845 | − | 0.942628i | \(-0.391654\pi\) | ||||
0.333845 | + | 0.942628i | \(0.391654\pi\) | |||||||
\(830\) | −8.75701 | −0.303960 | ||||||||
\(831\) | −18.3355 | −0.636050 | ||||||||
\(832\) | −38.9860 | −1.35159 | ||||||||
\(833\) | 1.90750 | 0.0660911 | ||||||||
\(834\) | −18.1069 | −0.626989 | ||||||||
\(835\) | −12.0680 | −0.417631 | ||||||||
\(836\) | 2.75170 | 0.0951696 | ||||||||
\(837\) | 4.54227 | 0.157004 | ||||||||
\(838\) | −28.6678 | −0.990314 | ||||||||
\(839\) | 38.2179 | 1.31943 | 0.659714 | − | 0.751517i | \(-0.270678\pi\) | ||||
0.659714 | + | 0.751517i | \(0.270678\pi\) | |||||||
\(840\) | −2.33547 | −0.0805813 | ||||||||
\(841\) | −14.1279 | −0.487168 | ||||||||
\(842\) | −36.4393 | −1.25578 | ||||||||
\(843\) | 21.9017 | 0.754335 | ||||||||
\(844\) | 17.9456 | 0.617714 | ||||||||
\(845\) | 7.32543 | 0.252002 | ||||||||
\(846\) | 5.70266 | 0.196061 | ||||||||
\(847\) | −10.6432 | −0.365705 | ||||||||
\(848\) | −25.4715 | −0.874696 | ||||||||
\(849\) | −2.35374 | −0.0807802 | ||||||||
\(850\) | 9.29988 | 0.318983 | ||||||||
\(851\) | 33.0302 | 1.13226 | ||||||||
\(852\) | −12.3774 | −0.424043 | ||||||||
\(853\) | −3.38498 | −0.115899 | −0.0579497 | − | 0.998320i | \(-0.518456\pi\) | ||||
−0.0579497 | + | 0.998320i | \(0.518456\pi\) | |||||||
\(854\) | 4.56119 | 0.156081 | ||||||||
\(855\) | −4.46997 | −0.152870 | ||||||||
\(856\) | 36.9987 | 1.26459 | ||||||||
\(857\) | 28.5458 | 0.975107 | 0.487554 | − | 0.873093i | \(-0.337889\pi\) | ||||
0.487554 | + | 0.873093i | \(0.337889\pi\) | |||||||
\(858\) | −3.13339 | −0.106972 | ||||||||
\(859\) | −12.6058 | −0.430105 | −0.215053 | − | 0.976602i | \(-0.568992\pi\) | ||||
−0.215053 | + | 0.976602i | \(0.568992\pi\) | |||||||
\(860\) | 6.52381 | 0.222460 | ||||||||
\(861\) | −9.73395 | −0.331732 | ||||||||
\(862\) | −38.7324 | −1.31923 | ||||||||
\(863\) | −19.5526 | −0.665578 | −0.332789 | − | 0.943001i | \(-0.607990\pi\) | ||||
−0.332789 | + | 0.943001i | \(0.607990\pi\) | |||||||
\(864\) | 4.13598 | 0.140709 | ||||||||
\(865\) | −16.0329 | −0.545134 | ||||||||
\(866\) | 15.8365 | 0.538147 | ||||||||
\(867\) | 13.3614 | 0.453778 | ||||||||
\(868\) | 3.56118 | 0.120874 | ||||||||
\(869\) | −1.23453 | −0.0418786 | ||||||||
\(870\) | 3.23511 | 0.109681 | ||||||||
\(871\) | −8.57043 | −0.290398 | ||||||||
\(872\) | 41.0280 | 1.38938 | ||||||||
\(873\) | 12.8199 | 0.433889 | ||||||||
\(874\) | −51.7032 | −1.74889 | ||||||||
\(875\) | −7.16717 | −0.242294 | ||||||||
\(876\) | 5.07239 | 0.171380 | ||||||||
\(877\) | 7.00669 | 0.236599 | 0.118300 | − | 0.992978i | \(-0.462256\pi\) | ||||
0.118300 | + | 0.992978i | \(0.462256\pi\) | |||||||
\(878\) | 11.6039 | 0.391612 | ||||||||
\(879\) | 6.44889 | 0.217516 | ||||||||
\(880\) | −0.825811 | −0.0278381 | ||||||||
\(881\) | −24.3305 | −0.819716 | −0.409858 | − | 0.912149i | \(-0.634422\pi\) | ||||
−0.409858 | + | 0.912149i | \(0.634422\pi\) | |||||||
\(882\) | −1.10272 | −0.0371305 | ||||||||
\(883\) | −22.3996 | −0.753808 | −0.376904 | − | 0.926252i | \(-0.623011\pi\) | ||||
−0.376904 | + | 0.926252i | \(0.623011\pi\) | |||||||
\(884\) | 7.11414 | 0.239274 | ||||||||
\(885\) | 5.39500 | 0.181351 | ||||||||
\(886\) | 21.5114 | 0.722689 | ||||||||
\(887\) | −5.42126 | −0.182028 | −0.0910141 | − | 0.995850i | \(-0.529011\pi\) | ||||
−0.0910141 | + | 0.995850i | \(0.529011\pi\) | |||||||
\(888\) | 12.7075 | 0.426437 | ||||||||
\(889\) | −10.0255 | −0.336243 | ||||||||
\(890\) | −4.23595 | −0.141989 | ||||||||
\(891\) | 0.597329 | 0.0200113 | ||||||||
\(892\) | −21.8590 | −0.731893 | ||||||||
\(893\) | 30.3863 | 1.01684 | ||||||||
\(894\) | 19.6789 | 0.658160 | ||||||||
\(895\) | 0.641588 | 0.0214459 | ||||||||
\(896\) | −0.765317 | −0.0255674 | ||||||||
\(897\) | −37.9596 | −1.26743 | ||||||||
\(898\) | −17.5035 | −0.584100 | ||||||||
\(899\) | −17.5170 | −0.584224 | ||||||||
\(900\) | 3.46632 | 0.115544 | ||||||||
\(901\) | 26.7357 | 0.890695 | ||||||||
\(902\) | −6.41162 | −0.213483 | ||||||||
\(903\) | 10.9381 | 0.363997 | ||||||||
\(904\) | −52.9103 | −1.75977 | ||||||||
\(905\) | −3.98182 | −0.132360 | ||||||||
\(906\) | −8.56662 | −0.284607 | ||||||||
\(907\) | −26.4779 | −0.879184 | −0.439592 | − | 0.898198i | \(-0.644877\pi\) | ||||
−0.439592 | + | 0.898198i | \(0.644877\pi\) | |||||||
\(908\) | 3.96796 | 0.131682 | ||||||||
\(909\) | 12.3187 | 0.408585 | ||||||||
\(910\) | 3.99060 | 0.132287 | ||||||||
\(911\) | −11.0624 | −0.366513 | −0.183257 | − | 0.983065i | \(-0.558664\pi\) | ||||
−0.183257 | + | 0.983065i | \(0.558664\pi\) | |||||||
\(912\) | −10.6781 | −0.353588 | ||||||||
\(913\) | 6.23543 | 0.206362 | ||||||||
\(914\) | −22.0618 | −0.729740 | ||||||||
\(915\) | 3.14667 | 0.104026 | ||||||||
\(916\) | 14.5143 | 0.479566 | ||||||||
\(917\) | 2.29268 | 0.0757111 | ||||||||
\(918\) | 2.10344 | 0.0694239 | ||||||||
\(919\) | 56.2859 | 1.85670 | 0.928349 | − | 0.371709i | \(-0.121228\pi\) | ||||
0.928349 | + | 0.371709i | \(0.121228\pi\) | |||||||
\(920\) | −18.6363 | −0.614421 | ||||||||
\(921\) | 0.105629 | 0.00348060 | ||||||||
\(922\) | 13.1229 | 0.432179 | ||||||||
\(923\) | 75.1007 | 2.47197 | ||||||||
\(924\) | 0.468312 | 0.0154063 | ||||||||
\(925\) | 18.3009 | 0.601730 | ||||||||
\(926\) | −25.3114 | −0.831784 | ||||||||
\(927\) | 8.63579 | 0.283636 | ||||||||
\(928\) | −15.9502 | −0.523590 | ||||||||
\(929\) | −31.0098 | −1.01740 | −0.508700 | − | 0.860944i | \(-0.669874\pi\) | ||||
−0.508700 | + | 0.860944i | \(0.669874\pi\) | |||||||
\(930\) | −3.81045 | −0.124950 | ||||||||
\(931\) | −5.87579 | −0.192571 | ||||||||
\(932\) | 4.15262 | 0.136024 | ||||||||
\(933\) | 3.41558 | 0.111821 | ||||||||
\(934\) | −41.9480 | −1.37258 | ||||||||
\(935\) | 0.866796 | 0.0283473 | ||||||||
\(936\) | −14.6040 | −0.477346 | ||||||||
\(937\) | −3.19862 | −0.104494 | −0.0522472 | − | 0.998634i | \(-0.516638\pi\) | ||||
−0.0522472 | + | 0.998634i | \(0.516638\pi\) | |||||||
\(938\) | −1.98670 | −0.0648680 | ||||||||
\(939\) | 18.3685 | 0.599433 | ||||||||
\(940\) | 3.08441 | 0.100602 | ||||||||
\(941\) | 47.3661 | 1.54409 | 0.772045 | − | 0.635568i | \(-0.219234\pi\) | ||||
0.772045 | + | 0.635568i | \(0.219234\pi\) | |||||||
\(942\) | 8.60043 | 0.280217 | ||||||||
\(943\) | −77.6739 | −2.52941 | ||||||||
\(944\) | 12.8879 | 0.419466 | ||||||||
\(945\) | −0.760743 | −0.0247470 | ||||||||
\(946\) | 7.20477 | 0.234247 | ||||||||
\(947\) | 34.3134 | 1.11504 | 0.557518 | − | 0.830165i | \(-0.311754\pi\) | ||||
0.557518 | + | 0.830165i | \(0.311754\pi\) | |||||||
\(948\) | −1.62036 | −0.0526267 | ||||||||
\(949\) | −30.7771 | −0.999066 | ||||||||
\(950\) | −28.6469 | −0.929430 | ||||||||
\(951\) | −29.2567 | −0.948713 | ||||||||
\(952\) | 5.85600 | 0.189794 | ||||||||
\(953\) | −5.56951 | −0.180414 | −0.0902070 | − | 0.995923i | \(-0.528753\pi\) | ||||
−0.0902070 | + | 0.995923i | \(0.528753\pi\) | |||||||
\(954\) | −15.4558 | −0.500400 | ||||||||
\(955\) | 15.2352 | 0.493001 | ||||||||
\(956\) | −19.7744 | −0.639551 | ||||||||
\(957\) | −2.30356 | −0.0744636 | ||||||||
\(958\) | 21.2153 | 0.685434 | ||||||||
\(959\) | 14.5342 | 0.469335 | ||||||||
\(960\) | −6.23463 | −0.201222 | ||||||||
\(961\) | −10.3678 | −0.334444 | ||||||||
\(962\) | −21.7133 | −0.700065 | ||||||||
\(963\) | 12.0518 | 0.388363 | ||||||||
\(964\) | −21.6553 | −0.697469 | ||||||||
\(965\) | 1.42294 | 0.0458060 | ||||||||
\(966\) | −8.79936 | −0.283115 | ||||||||
\(967\) | 41.6661 | 1.33989 | 0.669946 | − | 0.742410i | \(-0.266317\pi\) | ||||
0.669946 | + | 0.742410i | \(0.266317\pi\) | |||||||
\(968\) | −32.6744 | −1.05020 | ||||||||
\(969\) | 11.2081 | 0.360056 | ||||||||
\(970\) | −10.7545 | −0.345305 | ||||||||
\(971\) | −40.3016 | −1.29334 | −0.646669 | − | 0.762771i | \(-0.723839\pi\) | ||||
−0.646669 | + | 0.762771i | \(0.723839\pi\) | |||||||
\(972\) | 0.784010 | 0.0251471 | ||||||||
\(973\) | −16.4202 | −0.526407 | ||||||||
\(974\) | 10.7898 | 0.345726 | ||||||||
\(975\) | −21.0321 | −0.673566 | ||||||||
\(976\) | 7.51695 | 0.240612 | ||||||||
\(977\) | −24.3168 | −0.777964 | −0.388982 | − | 0.921245i | \(-0.627173\pi\) | ||||
−0.388982 | + | 0.921245i | \(0.627173\pi\) | |||||||
\(978\) | 20.0624 | 0.641524 | ||||||||
\(979\) | 3.01621 | 0.0963985 | ||||||||
\(980\) | −0.596430 | −0.0190523 | ||||||||
\(981\) | 13.3643 | 0.426688 | ||||||||
\(982\) | 30.5271 | 0.974158 | ||||||||
\(983\) | −49.8535 | −1.59008 | −0.795040 | − | 0.606558i | \(-0.792550\pi\) | ||||
−0.795040 | + | 0.606558i | \(0.792550\pi\) | |||||||
\(984\) | −29.8830 | −0.952636 | ||||||||
\(985\) | −6.82768 | −0.217548 | ||||||||
\(986\) | −8.11179 | −0.258332 | ||||||||
\(987\) | 5.17145 | 0.164609 | ||||||||
\(988\) | −21.9141 | −0.697180 | ||||||||
\(989\) | 87.2826 | 2.77542 | ||||||||
\(990\) | −0.501091 | −0.0159257 | ||||||||
\(991\) | 14.2609 | 0.453013 | 0.226507 | − | 0.974010i | \(-0.427270\pi\) | ||||
0.226507 | + | 0.974010i | \(0.427270\pi\) | |||||||
\(992\) | 18.7867 | 0.596480 | ||||||||
\(993\) | 0.175156 | 0.00555840 | ||||||||
\(994\) | 17.4090 | 0.552179 | ||||||||
\(995\) | −0.712686 | −0.0225937 | ||||||||
\(996\) | 8.18416 | 0.259325 | ||||||||
\(997\) | 33.4217 | 1.05848 | 0.529238 | − | 0.848473i | \(-0.322478\pi\) | ||||
0.529238 | + | 0.848473i | \(0.322478\pi\) | |||||||
\(998\) | −6.95188 | −0.220058 | ||||||||
\(999\) | 4.13929 | 0.130961 |
(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 | 8043.2.a.t.1.17 | ✓ | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8043.2.a.t.1.17 | ✓ | 52 | 1.1 | even | 1 | trivial |