Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4025,2,Mod(1,4025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4025, 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("4025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4025 = 5^{2} \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4025.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: | \(32.1397868136\) |
Analytic rank: | \(1\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 3 x^{13} - 18 x^{12} + 58 x^{11} + 111 x^{10} - 414 x^{9} - 244 x^{8} + 1330 x^{7} - 27 x^{6} + \cdots - 9 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 5 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(1.31920\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.31920 | −0.932816 | −0.466408 | − | 0.884570i | \(-0.654452\pi\) | ||||
−0.466408 | + | 0.884570i | \(0.654452\pi\) | |||||||
\(3\) | −2.92477 | −1.68861 | −0.844307 | − | 0.535860i | \(-0.819988\pi\) | ||||
−0.844307 | + | 0.535860i | \(0.819988\pi\) | |||||||
\(4\) | −0.259709 | −0.129855 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 3.85835 | 1.57517 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 2.98101 | 1.05395 | ||||||||
\(9\) | 5.55425 | 1.85142 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.868311 | 0.261806 | 0.130903 | − | 0.991395i | \(-0.458212\pi\) | ||||
0.130903 | + | 0.991395i | \(0.458212\pi\) | |||||||
\(12\) | 0.759589 | 0.219275 | ||||||||
\(13\) | −6.38750 | −1.77157 | −0.885787 | − | 0.464092i | \(-0.846381\pi\) | ||||
−0.885787 | + | 0.464092i | \(0.846381\pi\) | |||||||
\(14\) | 1.31920 | 0.352571 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.41313 | −0.853283 | ||||||||
\(17\) | 1.51452 | 0.367326 | 0.183663 | − | 0.982989i | \(-0.441205\pi\) | ||||
0.183663 | + | 0.982989i | \(0.441205\pi\) | |||||||
\(18\) | −7.32717 | −1.72703 | ||||||||
\(19\) | 6.70540 | 1.53832 | 0.769162 | − | 0.639054i | \(-0.220674\pi\) | ||||
0.769162 | + | 0.639054i | \(0.220674\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.92477 | 0.638236 | ||||||||
\(22\) | −1.14548 | −0.244216 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | −8.71876 | −1.77971 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 8.42639 | 1.65255 | ||||||||
\(27\) | −7.47058 | −1.43771 | ||||||||
\(28\) | 0.259709 | 0.0490805 | ||||||||
\(29\) | −6.03716 | −1.12107 | −0.560537 | − | 0.828130i | \(-0.689405\pi\) | ||||
−0.560537 | + | 0.828130i | \(0.689405\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.00792 | −1.43826 | −0.719132 | − | 0.694873i | \(-0.755461\pi\) | ||||
−0.719132 | + | 0.694873i | \(0.755461\pi\) | |||||||
\(32\) | −1.45941 | −0.257990 | ||||||||
\(33\) | −2.53961 | −0.442089 | ||||||||
\(34\) | −1.99796 | −0.342647 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.44249 | −0.240415 | ||||||||
\(37\) | 0.642278 | 0.105590 | 0.0527949 | − | 0.998605i | \(-0.483187\pi\) | ||||
0.0527949 | + | 0.998605i | \(0.483187\pi\) | |||||||
\(38\) | −8.84576 | −1.43497 | ||||||||
\(39\) | 18.6819 | 2.99150 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.73351 | 0.426903 | 0.213451 | − | 0.976954i | \(-0.431530\pi\) | ||||
0.213451 | + | 0.976954i | \(0.431530\pi\) | |||||||
\(42\) | −3.85835 | −0.595357 | ||||||||
\(43\) | 2.06872 | 0.315477 | 0.157738 | − | 0.987481i | \(-0.449580\pi\) | ||||
0.157738 | + | 0.987481i | \(0.449580\pi\) | |||||||
\(44\) | −0.225509 | −0.0339967 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.31920 | 0.194506 | ||||||||
\(47\) | −6.47726 | −0.944806 | −0.472403 | − | 0.881383i | \(-0.656613\pi\) | ||||
−0.472403 | + | 0.881383i | \(0.656613\pi\) | |||||||
\(48\) | 9.98261 | 1.44087 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.42963 | −0.620272 | ||||||||
\(52\) | 1.65889 | 0.230047 | ||||||||
\(53\) | 0.149052 | 0.0204739 | 0.0102369 | − | 0.999948i | \(-0.496741\pi\) | ||||
0.0102369 | + | 0.999948i | \(0.496741\pi\) | |||||||
\(54\) | 9.85520 | 1.34112 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.98101 | −0.398354 | ||||||||
\(57\) | −19.6117 | −2.59763 | ||||||||
\(58\) | 7.96423 | 1.04575 | ||||||||
\(59\) | 7.34394 | 0.956100 | 0.478050 | − | 0.878333i | \(-0.341344\pi\) | ||||
0.478050 | + | 0.878333i | \(0.341344\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.26843 | 0.290442 | 0.145221 | − | 0.989399i | \(-0.453611\pi\) | ||||
0.145221 | + | 0.989399i | \(0.453611\pi\) | |||||||
\(62\) | 10.5641 | 1.34164 | ||||||||
\(63\) | −5.55425 | −0.699770 | ||||||||
\(64\) | 8.75152 | 1.09394 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.35025 | 0.412387 | ||||||||
\(67\) | 15.1477 | 1.85059 | 0.925295 | − | 0.379249i | \(-0.123818\pi\) | ||||
0.925295 | + | 0.379249i | \(0.123818\pi\) | |||||||
\(68\) | −0.393336 | −0.0476990 | ||||||||
\(69\) | 2.92477 | 0.352100 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.8820 | −1.29145 | −0.645727 | − | 0.763568i | \(-0.723446\pi\) | ||||
−0.645727 | + | 0.763568i | \(0.723446\pi\) | |||||||
\(72\) | 16.5573 | 1.95129 | ||||||||
\(73\) | −2.05467 | −0.240481 | −0.120241 | − | 0.992745i | \(-0.538367\pi\) | ||||
−0.120241 | + | 0.992745i | \(0.538367\pi\) | |||||||
\(74\) | −0.847294 | −0.0984959 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.74145 | −0.199759 | ||||||||
\(77\) | −0.868311 | −0.0989532 | ||||||||
\(78\) | −24.6452 | −2.79052 | ||||||||
\(79\) | 13.1616 | 1.48080 | 0.740399 | − | 0.672168i | \(-0.234637\pi\) | ||||
0.740399 | + | 0.672168i | \(0.234637\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.18695 | 0.576328 | ||||||||
\(82\) | −3.60605 | −0.398221 | ||||||||
\(83\) | −7.99279 | −0.877323 | −0.438661 | − | 0.898652i | \(-0.644547\pi\) | ||||
−0.438661 | + | 0.898652i | \(0.644547\pi\) | |||||||
\(84\) | −0.759589 | −0.0828780 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.72906 | −0.294282 | ||||||||
\(87\) | 17.6573 | 1.89306 | ||||||||
\(88\) | 2.58844 | 0.275929 | ||||||||
\(89\) | 8.46919 | 0.897732 | 0.448866 | − | 0.893599i | \(-0.351828\pi\) | ||||
0.448866 | + | 0.893599i | \(0.351828\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.38750 | 0.669592 | ||||||||
\(92\) | 0.259709 | 0.0270766 | ||||||||
\(93\) | 23.4213 | 2.42867 | ||||||||
\(94\) | 8.54481 | 0.881330 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 4.26844 | 0.435646 | ||||||||
\(97\) | 6.18936 | 0.628435 | 0.314217 | − | 0.949351i | \(-0.398258\pi\) | ||||
0.314217 | + | 0.949351i | \(0.398258\pi\) | |||||||
\(98\) | −1.31920 | −0.133259 | ||||||||
\(99\) | 4.82282 | 0.484711 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.31297 | 0.926675 | 0.463338 | − | 0.886182i | \(-0.346652\pi\) | ||||
0.463338 | + | 0.886182i | \(0.346652\pi\) | |||||||
\(102\) | 5.84357 | 0.578599 | ||||||||
\(103\) | −4.05608 | −0.399658 | −0.199829 | − | 0.979831i | \(-0.564039\pi\) | ||||
−0.199829 | + | 0.979831i | \(0.564039\pi\) | |||||||
\(104\) | −19.0412 | −1.86714 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.196629 | −0.0190983 | ||||||||
\(107\) | −6.80490 | −0.657855 | −0.328927 | − | 0.944355i | \(-0.606687\pi\) | ||||
−0.328927 | + | 0.944355i | \(0.606687\pi\) | |||||||
\(108\) | 1.94018 | 0.186694 | ||||||||
\(109\) | 8.75082 | 0.838177 | 0.419088 | − | 0.907945i | \(-0.362350\pi\) | ||||
0.419088 | + | 0.907945i | \(0.362350\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.87851 | −0.178301 | ||||||||
\(112\) | 3.41313 | 0.322511 | ||||||||
\(113\) | 13.1530 | 1.23733 | 0.618666 | − | 0.785654i | \(-0.287673\pi\) | ||||
0.618666 | + | 0.785654i | \(0.287673\pi\) | |||||||
\(114\) | 25.8718 | 2.42311 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.56791 | 0.145577 | ||||||||
\(117\) | −35.4778 | −3.27992 | ||||||||
\(118\) | −9.68813 | −0.891865 | ||||||||
\(119\) | −1.51452 | −0.138836 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.2460 | −0.931458 | ||||||||
\(122\) | −2.99251 | −0.270929 | ||||||||
\(123\) | −7.99488 | −0.720874 | ||||||||
\(124\) | 2.07973 | 0.186765 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 7.32717 | 0.652756 | ||||||||
\(127\) | −4.89344 | −0.434223 | −0.217111 | − | 0.976147i | \(-0.569663\pi\) | ||||
−0.217111 | + | 0.976147i | \(0.569663\pi\) | |||||||
\(128\) | −8.62619 | −0.762455 | ||||||||
\(129\) | −6.05052 | −0.532719 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.81951 | 0.158971 | 0.0794855 | − | 0.996836i | \(-0.474672\pi\) | ||||
0.0794855 | + | 0.996836i | \(0.474672\pi\) | |||||||
\(132\) | 0.659560 | 0.0574073 | ||||||||
\(133\) | −6.70540 | −0.581432 | ||||||||
\(134\) | −19.9829 | −1.72626 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.51481 | 0.387142 | ||||||||
\(137\) | 17.7257 | 1.51441 | 0.757203 | − | 0.653180i | \(-0.226565\pi\) | ||||
0.757203 | + | 0.653180i | \(0.226565\pi\) | |||||||
\(138\) | −3.85835 | −0.328445 | ||||||||
\(139\) | −7.05663 | −0.598535 | −0.299268 | − | 0.954169i | \(-0.596742\pi\) | ||||
−0.299268 | + | 0.954169i | \(0.596742\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 18.9445 | 1.59541 | ||||||||
\(142\) | 14.3555 | 1.20469 | ||||||||
\(143\) | −5.54634 | −0.463808 | ||||||||
\(144\) | −18.9574 | −1.57978 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.71053 | 0.224325 | ||||||||
\(147\) | −2.92477 | −0.241231 | ||||||||
\(148\) | −0.166806 | −0.0137113 | ||||||||
\(149\) | 11.7254 | 0.960578 | 0.480289 | − | 0.877110i | \(-0.340532\pi\) | ||||
0.480289 | + | 0.877110i | \(0.340532\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.5657 | 1.26671 | 0.633357 | − | 0.773859i | \(-0.281676\pi\) | ||||
0.633357 | + | 0.773859i | \(0.281676\pi\) | |||||||
\(152\) | 19.9889 | 1.62131 | ||||||||
\(153\) | 8.41204 | 0.680073 | ||||||||
\(154\) | 1.14548 | 0.0923051 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −4.85188 | −0.388461 | ||||||||
\(157\) | −13.2451 | −1.05708 | −0.528539 | − | 0.848909i | \(-0.677260\pi\) | ||||
−0.528539 | + | 0.848909i | \(0.677260\pi\) | |||||||
\(158\) | −17.3628 | −1.38131 | ||||||||
\(159\) | −0.435942 | −0.0345724 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.00000 | 0.0788110 | ||||||||
\(162\) | −6.84263 | −0.537608 | ||||||||
\(163\) | 14.0268 | 1.09867 | 0.549334 | − | 0.835603i | \(-0.314882\pi\) | ||||
0.549334 | + | 0.835603i | \(0.314882\pi\) | |||||||
\(164\) | −0.709918 | −0.0554353 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 10.5441 | 0.818380 | ||||||||
\(167\) | 16.0378 | 1.24104 | 0.620521 | − | 0.784190i | \(-0.286921\pi\) | ||||
0.620521 | + | 0.784190i | \(0.286921\pi\) | |||||||
\(168\) | 8.71876 | 0.672667 | ||||||||
\(169\) | 27.8002 | 2.13847 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 37.2435 | 2.84808 | ||||||||
\(172\) | −0.537266 | −0.0409662 | ||||||||
\(173\) | −9.87355 | −0.750672 | −0.375336 | − | 0.926889i | \(-0.622473\pi\) | ||||
−0.375336 | + | 0.926889i | \(0.622473\pi\) | |||||||
\(174\) | −23.2935 | −1.76588 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.96366 | −0.223394 | ||||||||
\(177\) | −21.4793 | −1.61448 | ||||||||
\(178\) | −11.1726 | −0.837419 | ||||||||
\(179\) | −18.6861 | −1.39666 | −0.698331 | − | 0.715775i | \(-0.746073\pi\) | ||||
−0.698331 | + | 0.715775i | \(0.746073\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.69198 | 0.571741 | 0.285870 | − | 0.958268i | \(-0.407717\pi\) | ||||
0.285870 | + | 0.958268i | \(0.407717\pi\) | |||||||
\(182\) | −8.42639 | −0.624606 | ||||||||
\(183\) | −6.63462 | −0.490445 | ||||||||
\(184\) | −2.98101 | −0.219763 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −30.8974 | −2.26551 | ||||||||
\(187\) | 1.31508 | 0.0961680 | ||||||||
\(188\) | 1.68221 | 0.122688 | ||||||||
\(189\) | 7.47058 | 0.543405 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −22.4874 | −1.62713 | −0.813567 | − | 0.581471i | \(-0.802477\pi\) | ||||
−0.813567 | + | 0.581471i | \(0.802477\pi\) | |||||||
\(192\) | −25.5962 | −1.84724 | ||||||||
\(193\) | 11.1608 | 0.803372 | 0.401686 | − | 0.915778i | \(-0.368424\pi\) | ||||
0.401686 | + | 0.915778i | \(0.368424\pi\) | |||||||
\(194\) | −8.16501 | −0.586214 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.259709 | −0.0185507 | ||||||||
\(197\) | 22.2357 | 1.58423 | 0.792115 | − | 0.610371i | \(-0.208980\pi\) | ||||
0.792115 | + | 0.610371i | \(0.208980\pi\) | |||||||
\(198\) | −6.36226 | −0.452146 | ||||||||
\(199\) | −2.09717 | −0.148665 | −0.0743323 | − | 0.997234i | \(-0.523683\pi\) | ||||
−0.0743323 | + | 0.997234i | \(0.523683\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −44.3035 | −3.12493 | ||||||||
\(202\) | −12.2857 | −0.864417 | ||||||||
\(203\) | 6.03716 | 0.423726 | ||||||||
\(204\) | 1.15042 | 0.0805452 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 5.35079 | 0.372807 | ||||||||
\(207\) | −5.55425 | −0.386047 | ||||||||
\(208\) | 21.8014 | 1.51165 | ||||||||
\(209\) | 5.82237 | 0.402742 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.3289 | −1.33066 | −0.665330 | − | 0.746549i | \(-0.731709\pi\) | ||||
−0.665330 | + | 0.746549i | \(0.731709\pi\) | |||||||
\(212\) | −0.0387102 | −0.00265863 | ||||||||
\(213\) | 31.8273 | 2.18077 | ||||||||
\(214\) | 8.97703 | 0.613657 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −22.2699 | −1.51527 | ||||||||
\(217\) | 8.00792 | 0.543613 | ||||||||
\(218\) | −11.5441 | −0.781864 | ||||||||
\(219\) | 6.00944 | 0.406080 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9.67402 | −0.650745 | ||||||||
\(222\) | 2.47814 | 0.166322 | ||||||||
\(223\) | −9.13897 | −0.611991 | −0.305995 | − | 0.952033i | \(-0.598989\pi\) | ||||
−0.305995 | + | 0.952033i | \(0.598989\pi\) | |||||||
\(224\) | 1.45941 | 0.0975112 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −17.3515 | −1.15420 | ||||||||
\(227\) | −10.6284 | −0.705434 | −0.352717 | − | 0.935730i | \(-0.614742\pi\) | ||||
−0.352717 | + | 0.935730i | \(0.614742\pi\) | |||||||
\(228\) | 5.09335 | 0.337315 | ||||||||
\(229\) | −18.6150 | −1.23011 | −0.615057 | − | 0.788482i | \(-0.710867\pi\) | ||||
−0.615057 | + | 0.788482i | \(0.710867\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.53961 | 0.167094 | ||||||||
\(232\) | −17.9968 | −1.18155 | ||||||||
\(233\) | −6.02705 | −0.394845 | −0.197423 | − | 0.980318i | \(-0.563257\pi\) | ||||
−0.197423 | + | 0.980318i | \(0.563257\pi\) | |||||||
\(234\) | 46.8023 | 3.05956 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.90729 | −0.124154 | ||||||||
\(237\) | −38.4947 | −2.50050 | ||||||||
\(238\) | 1.99796 | 0.129509 | ||||||||
\(239\) | 2.13377 | 0.138022 | 0.0690110 | − | 0.997616i | \(-0.478016\pi\) | ||||
0.0690110 | + | 0.997616i | \(0.478016\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.80263 | 0.116117 | 0.0580587 | − | 0.998313i | \(-0.481509\pi\) | ||||
0.0580587 | + | 0.998313i | \(0.481509\pi\) | |||||||
\(242\) | 13.5166 | 0.868879 | ||||||||
\(243\) | 7.24114 | 0.464519 | ||||||||
\(244\) | −0.589132 | −0.0377153 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 10.5468 | 0.672442 | ||||||||
\(247\) | −42.8307 | −2.72525 | ||||||||
\(248\) | −23.8717 | −1.51585 | ||||||||
\(249\) | 23.3770 | 1.48146 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −27.8767 | −1.75956 | −0.879781 | − | 0.475380i | \(-0.842311\pi\) | ||||
−0.879781 | + | 0.475380i | \(0.842311\pi\) | |||||||
\(252\) | 1.44249 | 0.0908684 | ||||||||
\(253\) | −0.868311 | −0.0545902 | ||||||||
\(254\) | 6.45543 | 0.405050 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −6.12337 | −0.382711 | ||||||||
\(257\) | 10.7703 | 0.671830 | 0.335915 | − | 0.941892i | \(-0.390954\pi\) | ||||
0.335915 | + | 0.941892i | \(0.390954\pi\) | |||||||
\(258\) | 7.98185 | 0.496928 | ||||||||
\(259\) | −0.642278 | −0.0399092 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −33.5319 | −2.07557 | ||||||||
\(262\) | −2.40029 | −0.148291 | ||||||||
\(263\) | 25.4961 | 1.57215 | 0.786077 | − | 0.618128i | \(-0.212109\pi\) | ||||
0.786077 | + | 0.618128i | \(0.212109\pi\) | |||||||
\(264\) | −7.57059 | −0.465938 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 8.84576 | 0.542369 | ||||||||
\(267\) | −24.7704 | −1.51592 | ||||||||
\(268\) | −3.93401 | −0.240308 | ||||||||
\(269\) | −0.290767 | −0.0177284 | −0.00886420 | − | 0.999961i | \(-0.502822\pi\) | ||||
−0.00886420 | + | 0.999961i | \(0.502822\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.68541 | −0.406109 | −0.203055 | − | 0.979167i | \(-0.565087\pi\) | ||||
−0.203055 | + | 0.979167i | \(0.565087\pi\) | |||||||
\(272\) | −5.16927 | −0.313433 | ||||||||
\(273\) | −18.6819 | −1.13068 | ||||||||
\(274\) | −23.3837 | −1.41266 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.759589 | −0.0457219 | ||||||||
\(277\) | 22.1955 | 1.33360 | 0.666800 | − | 0.745237i | \(-0.267664\pi\) | ||||
0.666800 | + | 0.745237i | \(0.267664\pi\) | |||||||
\(278\) | 9.30911 | 0.558323 | ||||||||
\(279\) | −44.4780 | −2.66283 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.4533 | −1.45876 | −0.729381 | − | 0.684107i | \(-0.760192\pi\) | ||||
−0.729381 | + | 0.684107i | \(0.760192\pi\) | |||||||
\(282\) | −24.9916 | −1.48823 | ||||||||
\(283\) | −27.9586 | −1.66197 | −0.830983 | − | 0.556298i | \(-0.812221\pi\) | ||||
−0.830983 | + | 0.556298i | \(0.812221\pi\) | |||||||
\(284\) | 2.82616 | 0.167701 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 7.31673 | 0.432647 | ||||||||
\(287\) | −2.73351 | −0.161354 | ||||||||
\(288\) | −8.10595 | −0.477648 | ||||||||
\(289\) | −14.7062 | −0.865072 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −18.1024 | −1.06118 | ||||||||
\(292\) | 0.533618 | 0.0312277 | ||||||||
\(293\) | −8.50236 | −0.496713 | −0.248357 | − | 0.968669i | \(-0.579890\pi\) | ||||
−0.248357 | + | 0.968669i | \(0.579890\pi\) | |||||||
\(294\) | 3.85835 | 0.225024 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.91464 | 0.111286 | ||||||||
\(297\) | −6.48679 | −0.376402 | ||||||||
\(298\) | −15.4681 | −0.896042 | ||||||||
\(299\) | 6.38750 | 0.369399 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.06872 | −0.119239 | ||||||||
\(302\) | −20.5342 | −1.18161 | ||||||||
\(303\) | −27.2383 | −1.56480 | ||||||||
\(304\) | −22.8864 | −1.31263 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −11.0972 | −0.634383 | ||||||||
\(307\) | −24.0852 | −1.37462 | −0.687309 | − | 0.726365i | \(-0.741208\pi\) | ||||
−0.687309 | + | 0.726365i | \(0.741208\pi\) | |||||||
\(308\) | 0.225509 | 0.0128495 | ||||||||
\(309\) | 11.8631 | 0.674868 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.7156 | −0.891150 | −0.445575 | − | 0.895245i | \(-0.647001\pi\) | ||||
−0.445575 | + | 0.895245i | \(0.647001\pi\) | |||||||
\(312\) | 55.6910 | 3.15288 | ||||||||
\(313\) | −12.7181 | −0.718871 | −0.359436 | − | 0.933170i | \(-0.617031\pi\) | ||||
−0.359436 | + | 0.933170i | \(0.617031\pi\) | |||||||
\(314\) | 17.4730 | 0.986059 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.41820 | −0.192289 | ||||||||
\(317\) | 22.2744 | 1.25106 | 0.625529 | − | 0.780201i | \(-0.284883\pi\) | ||||
0.625529 | + | 0.780201i | \(0.284883\pi\) | |||||||
\(318\) | 0.575095 | 0.0322497 | ||||||||
\(319\) | −5.24214 | −0.293503 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 19.9027 | 1.11086 | ||||||||
\(322\) | −1.31920 | −0.0735162 | ||||||||
\(323\) | 10.1555 | 0.565066 | ||||||||
\(324\) | −1.34710 | −0.0748389 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −18.5042 | −1.02485 | ||||||||
\(327\) | −25.5941 | −1.41536 | ||||||||
\(328\) | 8.14862 | 0.449932 | ||||||||
\(329\) | 6.47726 | 0.357103 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.897778 | −0.0493463 | −0.0246732 | − | 0.999696i | \(-0.507855\pi\) | ||||
−0.0246732 | + | 0.999696i | \(0.507855\pi\) | |||||||
\(332\) | 2.07580 | 0.113925 | ||||||||
\(333\) | 3.56737 | 0.195491 | ||||||||
\(334\) | −21.1571 | −1.15766 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −9.98261 | −0.544596 | ||||||||
\(337\) | −30.4611 | −1.65932 | −0.829662 | − | 0.558266i | \(-0.811467\pi\) | ||||
−0.829662 | + | 0.558266i | \(0.811467\pi\) | |||||||
\(338\) | −36.6740 | −1.99480 | ||||||||
\(339\) | −38.4695 | −2.08938 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.95336 | −0.376546 | ||||||||
\(342\) | −49.1316 | −2.65673 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 6.16688 | 0.332496 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 13.0252 | 0.700238 | ||||||||
\(347\) | 19.8987 | 1.06822 | 0.534109 | − | 0.845415i | \(-0.320647\pi\) | ||||
0.534109 | + | 0.845415i | \(0.320647\pi\) | |||||||
\(348\) | −4.58576 | −0.245823 | ||||||||
\(349\) | −33.7467 | −1.80642 | −0.903211 | − | 0.429198i | \(-0.858796\pi\) | ||||
−0.903211 | + | 0.429198i | \(0.858796\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 47.7184 | 2.54702 | ||||||||
\(352\) | −1.26723 | −0.0675433 | ||||||||
\(353\) | 16.0139 | 0.852335 | 0.426168 | − | 0.904644i | \(-0.359863\pi\) | ||||
0.426168 | + | 0.904644i | \(0.359863\pi\) | |||||||
\(354\) | 28.3355 | 1.50602 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −2.19953 | −0.116575 | ||||||||
\(357\) | 4.42963 | 0.234441 | ||||||||
\(358\) | 24.6507 | 1.30283 | ||||||||
\(359\) | −24.8046 | −1.30914 | −0.654569 | − | 0.756002i | \(-0.727150\pi\) | ||||
−0.654569 | + | 0.756002i | \(0.727150\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 25.9623 | 1.36644 | ||||||||
\(362\) | −10.1473 | −0.533329 | ||||||||
\(363\) | 29.9672 | 1.57287 | ||||||||
\(364\) | −1.65889 | −0.0869497 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 8.75240 | 0.457495 | ||||||||
\(367\) | −7.66912 | −0.400325 | −0.200162 | − | 0.979763i | \(-0.564147\pi\) | ||||
−0.200162 | + | 0.979763i | \(0.564147\pi\) | |||||||
\(368\) | 3.41313 | 0.177922 | ||||||||
\(369\) | 15.1826 | 0.790375 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.149052 | −0.00773839 | ||||||||
\(372\) | −6.08273 | −0.315375 | ||||||||
\(373\) | 16.1482 | 0.836124 | 0.418062 | − | 0.908418i | \(-0.362709\pi\) | ||||
0.418062 | + | 0.908418i | \(0.362709\pi\) | |||||||
\(374\) | −1.73485 | −0.0897070 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −19.3088 | −0.995775 | ||||||||
\(377\) | 38.5624 | 1.98606 | ||||||||
\(378\) | −9.85520 | −0.506897 | ||||||||
\(379\) | 28.2469 | 1.45095 | 0.725474 | − | 0.688250i | \(-0.241621\pi\) | ||||
0.725474 | + | 0.688250i | \(0.241621\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 14.3122 | 0.733235 | ||||||||
\(382\) | 29.6654 | 1.51782 | ||||||||
\(383\) | −21.3320 | −1.09001 | −0.545006 | − | 0.838432i | \(-0.683473\pi\) | ||||
−0.545006 | + | 0.838432i | \(0.683473\pi\) | |||||||
\(384\) | 25.2296 | 1.28749 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −14.7233 | −0.749398 | ||||||||
\(387\) | 11.4902 | 0.584079 | ||||||||
\(388\) | −1.60744 | −0.0816052 | ||||||||
\(389\) | 33.1646 | 1.68151 | 0.840757 | − | 0.541413i | \(-0.182110\pi\) | ||||
0.840757 | + | 0.541413i | \(0.182110\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.51452 | −0.0765927 | ||||||||
\(392\) | 2.98101 | 0.150564 | ||||||||
\(393\) | −5.32163 | −0.268441 | ||||||||
\(394\) | −29.3334 | −1.47780 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.25253 | −0.0629421 | ||||||||
\(397\) | 25.2573 | 1.26763 | 0.633813 | − | 0.773486i | \(-0.281489\pi\) | ||||
0.633813 | + | 0.773486i | \(0.281489\pi\) | |||||||
\(398\) | 2.76659 | 0.138677 | ||||||||
\(399\) | 19.6117 | 0.981813 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.85880 | 0.242637 | 0.121319 | − | 0.992614i | \(-0.461288\pi\) | ||||
0.121319 | + | 0.992614i | \(0.461288\pi\) | |||||||
\(402\) | 58.4453 | 2.91498 | ||||||||
\(403\) | 51.1506 | 2.54799 | ||||||||
\(404\) | −2.41867 | −0.120333 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7.96423 | −0.395258 | ||||||||
\(407\) | 0.557697 | 0.0276440 | ||||||||
\(408\) | −13.2048 | −0.653733 | ||||||||
\(409\) | −27.0926 | −1.33964 | −0.669820 | − | 0.742523i | \(-0.733629\pi\) | ||||
−0.669820 | + | 0.742523i | \(0.733629\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −51.8434 | −2.55725 | ||||||||
\(412\) | 1.05340 | 0.0518974 | ||||||||
\(413\) | −7.34394 | −0.361372 | ||||||||
\(414\) | 7.32717 | 0.360111 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 9.32201 | 0.457049 | ||||||||
\(417\) | 20.6390 | 1.01069 | ||||||||
\(418\) | −7.68087 | −0.375684 | ||||||||
\(419\) | −23.6925 | −1.15745 | −0.578727 | − | 0.815522i | \(-0.696450\pi\) | ||||
−0.578727 | + | 0.815522i | \(0.696450\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −26.4688 | −1.29001 | −0.645005 | − | 0.764179i | \(-0.723145\pi\) | ||||
−0.645005 | + | 0.764179i | \(0.723145\pi\) | |||||||
\(422\) | 25.4988 | 1.24126 | ||||||||
\(423\) | −35.9763 | −1.74923 | ||||||||
\(424\) | 0.444325 | 0.0215783 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −41.9866 | −2.03426 | ||||||||
\(427\) | −2.26843 | −0.109777 | ||||||||
\(428\) | 1.76730 | 0.0854255 | ||||||||
\(429\) | 16.2217 | 0.783192 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.80682 | −0.327873 | −0.163937 | − | 0.986471i | \(-0.552419\pi\) | ||||
−0.163937 | + | 0.986471i | \(0.552419\pi\) | |||||||
\(432\) | 25.4981 | 1.22678 | ||||||||
\(433\) | 19.2022 | 0.922799 | 0.461399 | − | 0.887192i | \(-0.347347\pi\) | ||||
0.461399 | + | 0.887192i | \(0.347347\pi\) | |||||||
\(434\) | −10.5641 | −0.507091 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.27267 | −0.108841 | ||||||||
\(437\) | −6.70540 | −0.320763 | ||||||||
\(438\) | −7.92766 | −0.378798 | ||||||||
\(439\) | 18.8757 | 0.900890 | 0.450445 | − | 0.892804i | \(-0.351265\pi\) | ||||
0.450445 | + | 0.892804i | \(0.351265\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.55425 | 0.264488 | ||||||||
\(442\) | 12.7620 | 0.607025 | ||||||||
\(443\) | 26.1317 | 1.24155 | 0.620777 | − | 0.783987i | \(-0.286817\pi\) | ||||
0.620777 | + | 0.783987i | \(0.286817\pi\) | |||||||
\(444\) | 0.487868 | 0.0231532 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 12.0561 | 0.570875 | ||||||||
\(447\) | −34.2939 | −1.62205 | ||||||||
\(448\) | −8.75152 | −0.413471 | ||||||||
\(449\) | −16.6696 | −0.786686 | −0.393343 | − | 0.919392i | \(-0.628681\pi\) | ||||
−0.393343 | + | 0.919392i | \(0.628681\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.37354 | 0.111765 | ||||||||
\(452\) | −3.41597 | −0.160674 | ||||||||
\(453\) | −45.5259 | −2.13899 | ||||||||
\(454\) | 14.0210 | 0.658040 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −58.4627 | −2.73777 | ||||||||
\(457\) | 0.813011 | 0.0380311 | 0.0190155 | − | 0.999819i | \(-0.493947\pi\) | ||||
0.0190155 | + | 0.999819i | \(0.493947\pi\) | |||||||
\(458\) | 24.5569 | 1.14747 | ||||||||
\(459\) | −11.3144 | −0.528110 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 31.2050 | 1.45336 | 0.726682 | − | 0.686974i | \(-0.241061\pi\) | ||||
0.726682 | + | 0.686974i | \(0.241061\pi\) | |||||||
\(462\) | −3.35025 | −0.155868 | ||||||||
\(463\) | −8.66426 | −0.402663 | −0.201331 | − | 0.979523i | \(-0.564527\pi\) | ||||
−0.201331 | + | 0.979523i | \(0.564527\pi\) | |||||||
\(464\) | 20.6056 | 0.956593 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7.95089 | 0.368318 | ||||||||
\(467\) | −1.58947 | −0.0735520 | −0.0367760 | − | 0.999324i | \(-0.511709\pi\) | ||||
−0.0367760 | + | 0.999324i | \(0.511709\pi\) | |||||||
\(468\) | 9.21391 | 0.425913 | ||||||||
\(469\) | −15.1477 | −0.699457 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 38.7389 | 1.78500 | ||||||||
\(472\) | 21.8924 | 1.00768 | ||||||||
\(473\) | 1.79629 | 0.0825936 | ||||||||
\(474\) | 50.7822 | 2.33250 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.393336 | 0.0180285 | ||||||||
\(477\) | 0.827872 | 0.0379056 | ||||||||
\(478\) | −2.81487 | −0.128749 | ||||||||
\(479\) | −2.92907 | −0.133833 | −0.0669163 | − | 0.997759i | \(-0.521316\pi\) | ||||
−0.0669163 | + | 0.997759i | \(0.521316\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.10255 | −0.187060 | ||||||||
\(482\) | −2.37803 | −0.108316 | ||||||||
\(483\) | −2.92477 | −0.133081 | ||||||||
\(484\) | 2.66099 | 0.120954 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −9.55252 | −0.433311 | ||||||||
\(487\) | −3.65957 | −0.165831 | −0.0829154 | − | 0.996557i | \(-0.526423\pi\) | ||||
−0.0829154 | + | 0.996557i | \(0.526423\pi\) | |||||||
\(488\) | 6.76221 | 0.306111 | ||||||||
\(489\) | −41.0252 | −1.85523 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 30.2239 | 1.36399 | 0.681993 | − | 0.731359i | \(-0.261114\pi\) | ||||
0.681993 | + | 0.731359i | \(0.261114\pi\) | |||||||
\(492\) | 2.07634 | 0.0936089 | ||||||||
\(493\) | −9.14343 | −0.411799 | ||||||||
\(494\) | 56.5023 | 2.54216 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 27.3321 | 1.22725 | ||||||||
\(497\) | 10.8820 | 0.488124 | ||||||||
\(498\) | −30.8390 | −1.38193 | ||||||||
\(499\) | −36.2393 | −1.62229 | −0.811147 | − | 0.584842i | \(-0.801156\pi\) | ||||
−0.811147 | + | 0.584842i | \(0.801156\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −46.9068 | −2.09564 | ||||||||
\(502\) | 36.7750 | 1.64135 | ||||||||
\(503\) | −20.6137 | −0.919119 | −0.459559 | − | 0.888147i | \(-0.651993\pi\) | ||||
−0.459559 | + | 0.888147i | \(0.651993\pi\) | |||||||
\(504\) | −16.5573 | −0.737520 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.14548 | 0.0509226 | ||||||||
\(507\) | −81.3089 | −3.61106 | ||||||||
\(508\) | 1.27087 | 0.0563859 | ||||||||
\(509\) | 7.86152 | 0.348456 | 0.174228 | − | 0.984705i | \(-0.444257\pi\) | ||||
0.174228 | + | 0.984705i | \(0.444257\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.05467 | 0.0908935 | ||||||||
\(512\) | 25.3303 | 1.11945 | ||||||||
\(513\) | −50.0932 | −2.21167 | ||||||||
\(514\) | −14.2081 | −0.626694 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.57138 | 0.0691760 | ||||||||
\(517\) | −5.62428 | −0.247355 | ||||||||
\(518\) | 0.847294 | 0.0372280 | ||||||||
\(519\) | 28.8778 | 1.26759 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 38.4336 | 1.68380 | 0.841902 | − | 0.539630i | \(-0.181436\pi\) | ||||
0.841902 | + | 0.539630i | \(0.181436\pi\) | |||||||
\(522\) | 44.2353 | 1.93613 | ||||||||
\(523\) | 25.6662 | 1.12230 | 0.561152 | − | 0.827713i | \(-0.310358\pi\) | ||||
0.561152 | + | 0.827713i | \(0.310358\pi\) | |||||||
\(524\) | −0.472543 | −0.0206431 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −33.6344 | −1.46653 | ||||||||
\(527\) | −12.1282 | −0.528312 | ||||||||
\(528\) | 8.66801 | 0.377227 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 40.7901 | 1.77014 | ||||||||
\(532\) | 1.74145 | 0.0755016 | ||||||||
\(533\) | −17.4603 | −0.756289 | ||||||||
\(534\) | 32.6771 | 1.41408 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 45.1555 | 1.95042 | ||||||||
\(537\) | 54.6523 | 2.35842 | ||||||||
\(538\) | 0.383581 | 0.0165373 | ||||||||
\(539\) | 0.868311 | 0.0374008 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.5155 | 0.882030 | 0.441015 | − | 0.897500i | \(-0.354619\pi\) | ||||
0.441015 | + | 0.897500i | \(0.354619\pi\) | |||||||
\(542\) | 8.81939 | 0.378825 | ||||||||
\(543\) | −22.4972 | −0.965449 | ||||||||
\(544\) | −2.21032 | −0.0947666 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 24.6452 | 1.05472 | ||||||||
\(547\) | −33.6480 | −1.43868 | −0.719342 | − | 0.694656i | \(-0.755557\pi\) | ||||
−0.719342 | + | 0.694656i | \(0.755557\pi\) | |||||||
\(548\) | −4.60352 | −0.196653 | ||||||||
\(549\) | 12.5994 | 0.537730 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −40.4816 | −1.72457 | ||||||||
\(552\) | 8.71876 | 0.371095 | ||||||||
\(553\) | −13.1616 | −0.559689 | ||||||||
\(554\) | −29.2803 | −1.24400 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.83267 | 0.0777226 | ||||||||
\(557\) | −17.8611 | −0.756801 | −0.378400 | − | 0.925642i | \(-0.623526\pi\) | ||||
−0.378400 | + | 0.925642i | \(0.623526\pi\) | |||||||
\(558\) | 58.6754 | 2.48393 | ||||||||
\(559\) | −13.2140 | −0.558891 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.84629 | −0.162391 | ||||||||
\(562\) | 32.2588 | 1.36076 | ||||||||
\(563\) | −29.7505 | −1.25383 | −0.626917 | − | 0.779086i | \(-0.715684\pi\) | ||||
−0.626917 | + | 0.779086i | \(0.715684\pi\) | |||||||
\(564\) | −4.92006 | −0.207172 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 36.8830 | 1.55031 | ||||||||
\(567\) | −5.18695 | −0.217831 | ||||||||
\(568\) | −32.4393 | −1.36112 | ||||||||
\(569\) | −41.6993 | −1.74812 | −0.874062 | − | 0.485814i | \(-0.838523\pi\) | ||||
−0.874062 | + | 0.485814i | \(0.838523\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 27.1132 | 1.13465 | 0.567327 | − | 0.823493i | \(-0.307978\pi\) | ||||
0.567327 | + | 0.823493i | \(0.307978\pi\) | |||||||
\(572\) | 1.44044 | 0.0602277 | ||||||||
\(573\) | 65.7705 | 2.74760 | ||||||||
\(574\) | 3.60605 | 0.150514 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 48.6082 | 2.02534 | ||||||||
\(577\) | −6.01146 | −0.250260 | −0.125130 | − | 0.992140i | \(-0.539935\pi\) | ||||
−0.125130 | + | 0.992140i | \(0.539935\pi\) | |||||||
\(578\) | 19.4005 | 0.806953 | ||||||||
\(579\) | −32.6427 | −1.35658 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.99279 | 0.331597 | ||||||||
\(582\) | 23.8807 | 0.989889 | ||||||||
\(583\) | 0.129423 | 0.00536017 | ||||||||
\(584\) | −6.12501 | −0.253455 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 11.2163 | 0.463342 | ||||||||
\(587\) | 28.4080 | 1.17252 | 0.586261 | − | 0.810122i | \(-0.300599\pi\) | ||||
0.586261 | + | 0.810122i | \(0.300599\pi\) | |||||||
\(588\) | 0.759589 | 0.0313249 | ||||||||
\(589\) | −53.6963 | −2.21252 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −65.0343 | −2.67515 | ||||||||
\(592\) | −2.19218 | −0.0900981 | ||||||||
\(593\) | 1.03848 | 0.0426454 | 0.0213227 | − | 0.999773i | \(-0.493212\pi\) | ||||
0.0213227 | + | 0.999773i | \(0.493212\pi\) | |||||||
\(594\) | 8.55738 | 0.351113 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3.04518 | −0.124736 | ||||||||
\(597\) | 6.13373 | 0.251037 | ||||||||
\(598\) | −8.42639 | −0.344581 | ||||||||
\(599\) | −26.1530 | −1.06858 | −0.534292 | − | 0.845300i | \(-0.679422\pi\) | ||||
−0.534292 | + | 0.845300i | \(0.679422\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −34.0822 | −1.39024 | −0.695122 | − | 0.718892i | \(-0.744649\pi\) | ||||
−0.695122 | + | 0.718892i | \(0.744649\pi\) | |||||||
\(602\) | 2.72906 | 0.111228 | ||||||||
\(603\) | 84.1343 | 3.42621 | ||||||||
\(604\) | −4.04255 | −0.164489 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 35.9327 | 1.45967 | ||||||||
\(607\) | −43.4665 | −1.76425 | −0.882125 | − | 0.471016i | \(-0.843887\pi\) | ||||
−0.882125 | + | 0.471016i | \(0.843887\pi\) | |||||||
\(608\) | −9.78595 | −0.396873 | ||||||||
\(609\) | −17.6573 | −0.715509 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 41.3735 | 1.67379 | ||||||||
\(612\) | −2.18469 | −0.0883108 | ||||||||
\(613\) | −24.1027 | −0.973498 | −0.486749 | − | 0.873542i | \(-0.661817\pi\) | ||||
−0.486749 | + | 0.873542i | \(0.661817\pi\) | |||||||
\(614\) | 31.7733 | 1.28226 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.58844 | −0.104291 | ||||||||
\(617\) | −2.76763 | −0.111421 | −0.0557103 | − | 0.998447i | \(-0.517742\pi\) | ||||
−0.0557103 | + | 0.998447i | \(0.517742\pi\) | |||||||
\(618\) | −15.6498 | −0.629527 | ||||||||
\(619\) | 22.0412 | 0.885913 | 0.442956 | − | 0.896543i | \(-0.353930\pi\) | ||||
0.442956 | + | 0.896543i | \(0.353930\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.47058 | 0.299784 | ||||||||
\(622\) | 20.7320 | 0.831279 | ||||||||
\(623\) | −8.46919 | −0.339311 | ||||||||
\(624\) | −63.7639 | −2.55260 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 16.7778 | 0.670574 | ||||||||
\(627\) | −17.0291 | −0.680075 | ||||||||
\(628\) | 3.43989 | 0.137267 | ||||||||
\(629\) | 0.972746 | 0.0387859 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.9191 | 0.992014 | 0.496007 | − | 0.868318i | \(-0.334799\pi\) | ||||
0.496007 | + | 0.868318i | \(0.334799\pi\) | |||||||
\(632\) | 39.2349 | 1.56068 | ||||||||
\(633\) | 56.5326 | 2.24697 | ||||||||
\(634\) | −29.3845 | −1.16701 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0.113218 | 0.00448939 | ||||||||
\(637\) | −6.38750 | −0.253082 | ||||||||
\(638\) | 6.91543 | 0.273784 | ||||||||
\(639\) | −60.4413 | −2.39102 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.33424 | −0.368680 | −0.184340 | − | 0.982863i | \(-0.559015\pi\) | ||||
−0.184340 | + | 0.982863i | \(0.559015\pi\) | |||||||
\(642\) | −26.2557 | −1.03623 | ||||||||
\(643\) | −43.2724 | −1.70650 | −0.853248 | − | 0.521506i | \(-0.825371\pi\) | ||||
−0.853248 | + | 0.521506i | \(0.825371\pi\) | |||||||
\(644\) | −0.259709 | −0.0102340 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −13.3971 | −0.527103 | ||||||||
\(647\) | 0.808444 | 0.0317832 | 0.0158916 | − | 0.999874i | \(-0.494941\pi\) | ||||
0.0158916 | + | 0.999874i | \(0.494941\pi\) | |||||||
\(648\) | 15.4624 | 0.607419 | ||||||||
\(649\) | 6.37683 | 0.250312 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −23.4213 | −0.917952 | ||||||||
\(652\) | −3.64291 | −0.142667 | ||||||||
\(653\) | −2.29590 | −0.0898454 | −0.0449227 | − | 0.998990i | \(-0.514304\pi\) | ||||
−0.0449227 | + | 0.998990i | \(0.514304\pi\) | |||||||
\(654\) | 33.7637 | 1.32027 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −9.32983 | −0.364269 | ||||||||
\(657\) | −11.4122 | −0.445231 | ||||||||
\(658\) | −8.54481 | −0.333111 | ||||||||
\(659\) | −24.6811 | −0.961439 | −0.480719 | − | 0.876874i | \(-0.659624\pi\) | ||||
−0.480719 | + | 0.876874i | \(0.659624\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.918584 | 0.0357288 | 0.0178644 | − | 0.999840i | \(-0.494313\pi\) | ||||
0.0178644 | + | 0.999840i | \(0.494313\pi\) | |||||||
\(662\) | 1.18435 | 0.0460310 | ||||||||
\(663\) | 28.2942 | 1.09886 | ||||||||
\(664\) | −23.8266 | −0.924651 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.70608 | −0.182357 | ||||||||
\(667\) | 6.03716 | 0.233760 | ||||||||
\(668\) | −4.16517 | −0.161155 | ||||||||
\(669\) | 26.7293 | 1.03342 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.96970 | 0.0760395 | ||||||||
\(672\) | −4.26844 | −0.164659 | ||||||||
\(673\) | −35.1370 | −1.35443 | −0.677217 | − | 0.735784i | \(-0.736814\pi\) | ||||
−0.677217 | + | 0.735784i | \(0.736814\pi\) | |||||||
\(674\) | 40.1844 | 1.54784 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7.21996 | −0.277691 | ||||||||
\(677\) | −1.59262 | −0.0612092 | −0.0306046 | − | 0.999532i | \(-0.509743\pi\) | ||||
−0.0306046 | + | 0.999532i | \(0.509743\pi\) | |||||||
\(678\) | 50.7490 | 1.94900 | ||||||||
\(679\) | −6.18936 | −0.237526 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 31.0857 | 1.19121 | ||||||||
\(682\) | 9.17288 | 0.351248 | ||||||||
\(683\) | −6.66803 | −0.255145 | −0.127573 | − | 0.991829i | \(-0.540719\pi\) | ||||
−0.127573 | + | 0.991829i | \(0.540719\pi\) | |||||||
\(684\) | −9.67248 | −0.369836 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.31920 | 0.0503673 | ||||||||
\(687\) | 54.4445 | 2.07719 | ||||||||
\(688\) | −7.06082 | −0.269191 | ||||||||
\(689\) | −0.952069 | −0.0362709 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 47.3256 | 1.80035 | 0.900175 | − | 0.435528i | \(-0.143438\pi\) | ||||
0.900175 | + | 0.435528i | \(0.143438\pi\) | |||||||
\(692\) | 2.56425 | 0.0974783 | ||||||||
\(693\) | −4.82282 | −0.183204 | ||||||||
\(694\) | −26.2504 | −0.996451 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 52.6366 | 1.99518 | ||||||||
\(697\) | 4.13997 | 0.156812 | ||||||||
\(698\) | 44.5187 | 1.68506 | ||||||||
\(699\) | 17.6277 | 0.666741 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 44.8261 | 1.69306 | 0.846530 | − | 0.532341i | \(-0.178688\pi\) | ||||
0.846530 | + | 0.532341i | \(0.178688\pi\) | |||||||
\(702\) | −62.9501 | −2.37590 | ||||||||
\(703\) | 4.30673 | 0.162431 | ||||||||
\(704\) | 7.59904 | 0.286400 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −21.1256 | −0.795072 | ||||||||
\(707\) | −9.31297 | −0.350250 | ||||||||
\(708\) | 5.57838 | 0.209648 | ||||||||
\(709\) | 23.8243 | 0.894742 | 0.447371 | − | 0.894349i | \(-0.352360\pi\) | ||||
0.447371 | + | 0.894349i | \(0.352360\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 73.1029 | 2.74157 | ||||||||
\(712\) | 25.2467 | 0.946162 | ||||||||
\(713\) | 8.00792 | 0.299899 | ||||||||
\(714\) | −5.84357 | −0.218690 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4.85295 | 0.181363 | ||||||||
\(717\) | −6.24077 | −0.233066 | ||||||||
\(718\) | 32.7223 | 1.22119 | ||||||||
\(719\) | 45.6319 | 1.70178 | 0.850890 | − | 0.525343i | \(-0.176063\pi\) | ||||
0.850890 | + | 0.525343i | \(0.176063\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.05608 | 0.151056 | ||||||||
\(722\) | −34.2495 | −1.27464 | ||||||||
\(723\) | −5.27226 | −0.196078 | ||||||||
\(724\) | −1.99768 | −0.0742432 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −39.5328 | −1.46720 | ||||||||
\(727\) | 9.19379 | 0.340979 | 0.170489 | − | 0.985360i | \(-0.445465\pi\) | ||||
0.170489 | + | 0.985360i | \(0.445465\pi\) | |||||||
\(728\) | 19.0412 | 0.705714 | ||||||||
\(729\) | −36.7395 | −1.36072 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.13313 | 0.115883 | ||||||||
\(732\) | 1.72307 | 0.0636866 | ||||||||
\(733\) | −14.4617 | −0.534154 | −0.267077 | − | 0.963675i | \(-0.586058\pi\) | ||||
−0.267077 | + | 0.963675i | \(0.586058\pi\) | |||||||
\(734\) | 10.1171 | 0.373429 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.45941 | 0.0537947 | ||||||||
\(737\) | 13.1529 | 0.484495 | ||||||||
\(738\) | −20.0289 | −0.737274 | ||||||||
\(739\) | −18.6183 | −0.684887 | −0.342443 | − | 0.939538i | \(-0.611254\pi\) | ||||
−0.342443 | + | 0.939538i | \(0.611254\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 125.270 | 4.60190 | ||||||||
\(742\) | 0.196629 | 0.00721849 | ||||||||
\(743\) | −13.5139 | −0.495778 | −0.247889 | − | 0.968788i | \(-0.579737\pi\) | ||||
−0.247889 | + | 0.968788i | \(0.579737\pi\) | |||||||
\(744\) | 69.8191 | 2.55969 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −21.3028 | −0.779950 | ||||||||
\(747\) | −44.3940 | −1.62429 | ||||||||
\(748\) | −0.341538 | −0.0124879 | ||||||||
\(749\) | 6.80490 | 0.248646 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −45.6930 | −1.66736 | −0.833681 | − | 0.552247i | \(-0.813771\pi\) | ||||
−0.833681 | + | 0.552247i | \(0.813771\pi\) | |||||||
\(752\) | 22.1078 | 0.806187 | ||||||||
\(753\) | 81.5328 | 2.97122 | ||||||||
\(754\) | −50.8715 | −1.85263 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.94018 | −0.0705637 | ||||||||
\(757\) | −26.9591 | −0.979846 | −0.489923 | − | 0.871766i | \(-0.662975\pi\) | ||||
−0.489923 | + | 0.871766i | \(0.662975\pi\) | |||||||
\(758\) | −37.2634 | −1.35347 | ||||||||
\(759\) | 2.53961 | 0.0921818 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −45.2806 | −1.64142 | −0.820709 | − | 0.571346i | \(-0.806421\pi\) | ||||
−0.820709 | + | 0.571346i | \(0.806421\pi\) | |||||||
\(762\) | −18.8806 | −0.683973 | ||||||||
\(763\) | −8.75082 | −0.316801 | ||||||||
\(764\) | 5.84020 | 0.211291 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 28.1411 | 1.01678 | ||||||||
\(767\) | −46.9094 | −1.69380 | ||||||||
\(768\) | 17.9094 | 0.646251 | ||||||||
\(769\) | 43.3929 | 1.56479 | 0.782393 | − | 0.622785i | \(-0.213999\pi\) | ||||
0.782393 | + | 0.622785i | \(0.213999\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −31.5005 | −1.13446 | ||||||||
\(772\) | −2.89856 | −0.104322 | ||||||||
\(773\) | 12.0192 | 0.432300 | 0.216150 | − | 0.976360i | \(-0.430650\pi\) | ||||
0.216150 | + | 0.976360i | \(0.430650\pi\) | |||||||
\(774\) | −15.1579 | −0.544838 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 18.4506 | 0.662336 | ||||||||
\(777\) | 1.87851 | 0.0673913 | ||||||||
\(778\) | −43.7508 | −1.56854 | ||||||||
\(779\) | 18.3293 | 0.656714 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.44895 | −0.338110 | ||||||||
\(782\) | 1.99796 | 0.0714469 | ||||||||
\(783\) | 45.1011 | 1.61178 | ||||||||
\(784\) | −3.41313 | −0.121898 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 7.02030 | 0.250406 | ||||||||
\(787\) | 23.5521 | 0.839542 | 0.419771 | − | 0.907630i | \(-0.362110\pi\) | ||||
0.419771 | + | 0.907630i | \(0.362110\pi\) | |||||||
\(788\) | −5.77483 | −0.205720 | ||||||||
\(789\) | −74.5700 | −2.65476 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −13.1530 | −0.467668 | ||||||||
\(792\) | 14.3769 | 0.510860 | ||||||||
\(793\) | −14.4896 | −0.514540 | ||||||||
\(794\) | −33.3194 | −1.18246 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0.544655 | 0.0193048 | ||||||||
\(797\) | −15.0266 | −0.532269 | −0.266134 | − | 0.963936i | \(-0.585747\pi\) | ||||
−0.266134 | + | 0.963936i | \(0.585747\pi\) | |||||||
\(798\) | −25.8718 | −0.915851 | ||||||||
\(799\) | −9.80997 | −0.347052 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 47.0400 | 1.66208 | ||||||||
\(802\) | −6.40974 | −0.226336 | ||||||||
\(803\) | −1.78410 | −0.0629594 | ||||||||
\(804\) | 11.5060 | 0.405787 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −67.4779 | −2.37681 | ||||||||
\(807\) | 0.850426 | 0.0299364 | ||||||||
\(808\) | 27.7621 | 0.976666 | ||||||||
\(809\) | −0.100900 | −0.00354745 | −0.00177373 | − | 0.999998i | \(-0.500565\pi\) | ||||
−0.00177373 | + | 0.999998i | \(0.500565\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26.4645 | 0.929295 | 0.464647 | − | 0.885496i | \(-0.346181\pi\) | ||||
0.464647 | + | 0.885496i | \(0.346181\pi\) | |||||||
\(812\) | −1.56791 | −0.0550228 | ||||||||
\(813\) | 19.5532 | 0.685762 | ||||||||
\(814\) | −0.735715 | −0.0257868 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 15.1189 | 0.529267 | ||||||||
\(817\) | 13.8716 | 0.485306 | ||||||||
\(818\) | 35.7405 | 1.24964 | ||||||||
\(819\) | 35.4778 | 1.23969 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 30.1197 | 1.05118 | 0.525592 | − | 0.850737i | \(-0.323844\pi\) | ||||
0.525592 | + | 0.850737i | \(0.323844\pi\) | |||||||
\(822\) | 68.3918 | 2.38544 | ||||||||
\(823\) | −17.4202 | −0.607231 | −0.303616 | − | 0.952795i | \(-0.598194\pi\) | ||||
−0.303616 | + | 0.952795i | \(0.598194\pi\) | |||||||
\(824\) | −12.0912 | −0.421218 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 9.68813 | 0.337093 | ||||||||
\(827\) | 37.7595 | 1.31303 | 0.656513 | − | 0.754315i | \(-0.272031\pi\) | ||||
0.656513 | + | 0.754315i | \(0.272031\pi\) | |||||||
\(828\) | 1.44249 | 0.0501300 | ||||||||
\(829\) | 0.696165 | 0.0241788 | 0.0120894 | − | 0.999927i | \(-0.496152\pi\) | ||||
0.0120894 | + | 0.999927i | \(0.496152\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −64.9167 | −2.25193 | ||||||||
\(832\) | −55.9004 | −1.93800 | ||||||||
\(833\) | 1.51452 | 0.0524751 | ||||||||
\(834\) | −27.2270 | −0.942792 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.51212 | −0.0522979 | ||||||||
\(837\) | 59.8238 | 2.06781 | ||||||||
\(838\) | 31.2551 | 1.07969 | ||||||||
\(839\) | −50.4825 | −1.74285 | −0.871424 | − | 0.490530i | \(-0.836803\pi\) | ||||
−0.871424 | + | 0.490530i | \(0.836803\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.44735 | 0.256805 | ||||||||
\(842\) | 34.9176 | 1.20334 | ||||||||
\(843\) | 71.5202 | 2.46329 | ||||||||
\(844\) | 5.01991 | 0.172792 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 47.4600 | 1.63171 | ||||||||
\(847\) | 10.2460 | 0.352058 | ||||||||
\(848\) | −0.508734 | −0.0174700 | ||||||||
\(849\) | 81.7723 | 2.80642 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.642278 | −0.0220170 | ||||||||
\(852\) | −8.26584 | −0.283183 | ||||||||
\(853\) | −29.4981 | −1.01000 | −0.504998 | − | 0.863120i | \(-0.668507\pi\) | ||||
−0.504998 | + | 0.863120i | \(0.668507\pi\) | |||||||
\(854\) | 2.99251 | 0.102402 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −20.2855 | −0.693343 | ||||||||
\(857\) | −18.7919 | −0.641921 | −0.320960 | − | 0.947093i | \(-0.604006\pi\) | ||||
−0.320960 | + | 0.947093i | \(0.604006\pi\) | |||||||
\(858\) | −21.3997 | −0.730574 | ||||||||
\(859\) | −4.97637 | −0.169792 | −0.0848958 | − | 0.996390i | \(-0.527056\pi\) | ||||
−0.0848958 | + | 0.996390i | \(0.527056\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7.99488 | 0.272465 | ||||||||
\(862\) | 8.97957 | 0.305845 | ||||||||
\(863\) | −49.6259 | −1.68929 | −0.844643 | − | 0.535331i | \(-0.820187\pi\) | ||||
−0.844643 | + | 0.535331i | \(0.820187\pi\) | |||||||
\(864\) | 10.9027 | 0.370917 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −25.3316 | −0.860801 | ||||||||
\(867\) | 43.0122 | 1.46077 | ||||||||
\(868\) | −2.07973 | −0.0705907 | ||||||||
\(869\) | 11.4284 | 0.387681 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −96.7561 | −3.27846 | ||||||||
\(872\) | 26.0863 | 0.883393 | ||||||||
\(873\) | 34.3773 | 1.16349 | ||||||||
\(874\) | 8.84576 | 0.299212 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.56071 | −0.0527315 | ||||||||
\(877\) | 0.793789 | 0.0268043 | 0.0134022 | − | 0.999910i | \(-0.495734\pi\) | ||||
0.0134022 | + | 0.999910i | \(0.495734\pi\) | |||||||
\(878\) | −24.9009 | −0.840365 | ||||||||
\(879\) | 24.8674 | 0.838757 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 56.2971 | 1.89670 | 0.948349 | − | 0.317227i | \(-0.102752\pi\) | ||||
0.948349 | + | 0.317227i | \(0.102752\pi\) | |||||||
\(882\) | −7.32717 | −0.246719 | ||||||||
\(883\) | −15.9848 | −0.537930 | −0.268965 | − | 0.963150i | \(-0.586682\pi\) | ||||
−0.268965 | + | 0.963150i | \(0.586682\pi\) | |||||||
\(884\) | 2.51243 | 0.0845023 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −34.4730 | −1.15814 | ||||||||
\(887\) | 35.0663 | 1.17741 | 0.588705 | − | 0.808348i | \(-0.299638\pi\) | ||||
0.588705 | + | 0.808348i | \(0.299638\pi\) | |||||||
\(888\) | −5.59987 | −0.187919 | ||||||||
\(889\) | 4.89344 | 0.164121 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.50389 | 0.150886 | ||||||||
\(892\) | 2.37348 | 0.0794699 | ||||||||
\(893\) | −43.4326 | −1.45342 | ||||||||
\(894\) | 45.2405 | 1.51307 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 8.62619 | 0.288181 | ||||||||
\(897\) | −18.6819 | −0.623772 | ||||||||
\(898\) | 21.9905 | 0.733833 | ||||||||
\(899\) | 48.3451 | 1.61240 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.225743 | 0.00752058 | ||||||||
\(902\) | −3.13117 | −0.104257 | ||||||||
\(903\) | 6.05052 | 0.201349 | ||||||||
\(904\) | 39.2093 | 1.30408 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 60.0578 | 1.99529 | ||||||||
\(907\) | −25.1166 | −0.833983 | −0.416991 | − | 0.908910i | \(-0.636916\pi\) | ||||
−0.416991 | + | 0.908910i | \(0.636916\pi\) | |||||||
\(908\) | 2.76030 | 0.0916039 | ||||||||
\(909\) | 51.7266 | 1.71566 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 13.4685 | 0.446231 | 0.223115 | − | 0.974792i | \(-0.428377\pi\) | ||||
0.223115 | + | 0.974792i | \(0.428377\pi\) | |||||||
\(912\) | 66.9374 | 2.21652 | ||||||||
\(913\) | −6.94023 | −0.229688 | ||||||||
\(914\) | −1.07252 | −0.0354760 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.83449 | 0.159736 | ||||||||
\(917\) | −1.81951 | −0.0600854 | ||||||||
\(918\) | 14.9259 | 0.492629 | ||||||||
\(919\) | −36.6860 | −1.21016 | −0.605080 | − | 0.796165i | \(-0.706859\pi\) | ||||
−0.605080 | + | 0.796165i | \(0.706859\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 70.4437 | 2.32120 | ||||||||
\(922\) | −41.1657 | −1.35572 | ||||||||
\(923\) | 69.5087 | 2.28791 | ||||||||
\(924\) | −0.659560 | −0.0216979 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 11.4299 | 0.375610 | ||||||||
\(927\) | −22.5285 | −0.739933 | ||||||||
\(928\) | 8.81072 | 0.289226 | ||||||||
\(929\) | −4.37991 | −0.143700 | −0.0718500 | − | 0.997415i | \(-0.522890\pi\) | ||||
−0.0718500 | + | 0.997415i | \(0.522890\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.70540 | 0.219760 | ||||||||
\(932\) | 1.56528 | 0.0512725 | ||||||||
\(933\) | 45.9645 | 1.50481 | ||||||||
\(934\) | 2.09683 | 0.0686104 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −105.760 | −3.45686 | ||||||||
\(937\) | 25.7783 | 0.842140 | 0.421070 | − | 0.907028i | \(-0.361655\pi\) | ||||
0.421070 | + | 0.907028i | \(0.361655\pi\) | |||||||
\(938\) | 19.9829 | 0.652464 | ||||||||
\(939\) | 37.1975 | 1.21390 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11.8254 | −0.385496 | −0.192748 | − | 0.981248i | \(-0.561740\pi\) | ||||
−0.192748 | + | 0.981248i | \(0.561740\pi\) | |||||||
\(942\) | −51.1044 | −1.66507 | ||||||||
\(943\) | −2.73351 | −0.0890153 | ||||||||
\(944\) | −25.0658 | −0.815824 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.36967 | −0.0770446 | ||||||||
\(947\) | 10.3688 | 0.336942 | 0.168471 | − | 0.985707i | \(-0.446117\pi\) | ||||
0.168471 | + | 0.985707i | \(0.446117\pi\) | |||||||
\(948\) | 9.99743 | 0.324701 | ||||||||
\(949\) | 13.1242 | 0.426031 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −65.1475 | −2.11255 | ||||||||
\(952\) | −4.51481 | −0.146326 | ||||||||
\(953\) | −50.9028 | −1.64890 | −0.824451 | − | 0.565933i | \(-0.808516\pi\) | ||||
−0.824451 | + | 0.565933i | \(0.808516\pi\) | |||||||
\(954\) | −1.09213 | −0.0353590 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −0.554160 | −0.0179228 | ||||||||
\(957\) | 15.3320 | 0.495614 | ||||||||
\(958\) | 3.86403 | 0.124841 | ||||||||
\(959\) | −17.7257 | −0.572391 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 33.1268 | 1.06861 | ||||||||
\(962\) | 5.41209 | 0.174493 | ||||||||
\(963\) | −37.7961 | −1.21796 | ||||||||
\(964\) | −0.468159 | −0.0150784 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 3.85835 | 0.124140 | ||||||||
\(967\) | −26.2198 | −0.843172 | −0.421586 | − | 0.906789i | \(-0.638526\pi\) | ||||
−0.421586 | + | 0.906789i | \(0.638526\pi\) | |||||||
\(968\) | −30.5435 | −0.981707 | ||||||||
\(969\) | −29.7024 | −0.954178 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.27436 | 0.0408962 | 0.0204481 | − | 0.999791i | \(-0.493491\pi\) | ||||
0.0204481 | + | 0.999791i | \(0.493491\pi\) | |||||||
\(972\) | −1.88059 | −0.0603200 | ||||||||
\(973\) | 7.05663 | 0.226225 | ||||||||
\(974\) | 4.82770 | 0.154690 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.74245 | −0.247830 | ||||||||
\(977\) | −45.4142 | −1.45293 | −0.726465 | − | 0.687203i | \(-0.758838\pi\) | ||||
−0.726465 | + | 0.687203i | \(0.758838\pi\) | |||||||
\(978\) | 54.1205 | 1.73058 | ||||||||
\(979\) | 7.35389 | 0.235031 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 48.6043 | 1.55181 | ||||||||
\(982\) | −39.8714 | −1.27235 | ||||||||
\(983\) | 13.8715 | 0.442432 | 0.221216 | − | 0.975225i | \(-0.428997\pi\) | ||||
0.221216 | + | 0.975225i | \(0.428997\pi\) | |||||||
\(984\) | −23.8328 | −0.759762 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 12.0620 | 0.384133 | ||||||||
\(987\) | −18.9445 | −0.603009 | ||||||||
\(988\) | 11.1235 | 0.353887 | ||||||||
\(989\) | −2.06872 | −0.0657815 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20.7205 | −0.658208 | −0.329104 | − | 0.944294i | \(-0.606747\pi\) | ||||
−0.329104 | + | 0.944294i | \(0.606747\pi\) | |||||||
\(992\) | 11.6869 | 0.371059 | ||||||||
\(993\) | 2.62579 | 0.0833269 | ||||||||
\(994\) | −14.3555 | −0.455330 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −6.07124 | −0.192375 | ||||||||
\(997\) | −20.9813 | −0.664485 | −0.332242 | − | 0.943194i | \(-0.607805\pi\) | ||||
−0.332242 | + | 0.943194i | \(0.607805\pi\) | |||||||
\(998\) | 47.8069 | 1.51330 | ||||||||
\(999\) | −4.79819 | −0.151808 |
(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 | 4025.2.a.z.1.5 | ✓ | 14 | |
5.4 | even | 2 | 4025.2.a.bc.1.10 | yes | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4025.2.a.z.1.5 | ✓ | 14 | 1.1 | even | 1 | trivial | |
4025.2.a.bc.1.10 | yes | 14 | 5.4 | even | 2 |