Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7935,2,Mod(1,7935)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7935, 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("7935.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7935 = 3 \cdot 5 \cdot 23^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7935.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: | \(63.3612940039\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.22733568.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 8x^{4} - 2x^{3} + 16x^{2} + 8x - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.90131\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7935.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.90131 | −1.34443 | −0.672214 | − | 0.740357i | \(-0.734657\pi\) | ||||
−0.672214 | + | 0.740357i | \(0.734657\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.61498 | 0.807488 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 1.90131 | 0.776206 | ||||||||
\(7\) | −0.941661 | −0.355915 | −0.177957 | − | 0.984038i | \(-0.556949\pi\) | ||||
−0.177957 | + | 0.984038i | \(0.556949\pi\) | |||||||
\(8\) | 0.732051 | 0.258819 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.90131 | 0.601247 | ||||||||
\(11\) | −0.344672 | −0.103923 | −0.0519613 | − | 0.998649i | \(-0.516547\pi\) | ||||
−0.0519613 | + | 0.998649i | \(0.516547\pi\) | |||||||
\(12\) | −1.61498 | −0.466203 | ||||||||
\(13\) | −3.84980 | −1.06774 | −0.533871 | − | 0.845566i | \(-0.679263\pi\) | ||||
−0.533871 | + | 0.845566i | \(0.679263\pi\) | |||||||
\(14\) | 1.79039 | 0.478502 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | −4.62181 | −1.15545 | ||||||||
\(17\) | −0.110920 | −0.0269019 | −0.0134510 | − | 0.999910i | \(-0.504282\pi\) | ||||
−0.0134510 | + | 0.999910i | \(0.504282\pi\) | |||||||
\(18\) | −1.90131 | −0.448143 | ||||||||
\(19\) | −6.17844 | −1.41743 | −0.708716 | − | 0.705494i | \(-0.750725\pi\) | ||||
−0.708716 | + | 0.705494i | \(0.750725\pi\) | |||||||
\(20\) | −1.61498 | −0.361119 | ||||||||
\(21\) | 0.941661 | 0.205487 | ||||||||
\(22\) | 0.655328 | 0.139716 | ||||||||
\(23\) | 0 | 0 | ||||||||
\(24\) | −0.732051 | −0.149429 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 7.31966 | 1.43550 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.52076 | −0.287397 | ||||||||
\(29\) | −9.60667 | −1.78391 | −0.891957 | − | 0.452121i | \(-0.850668\pi\) | ||||
−0.891957 | + | 0.452121i | \(0.850668\pi\) | |||||||
\(30\) | −1.90131 | −0.347130 | ||||||||
\(31\) | −2.73037 | −0.490389 | −0.245195 | − | 0.969474i | \(-0.578852\pi\) | ||||
−0.245195 | + | 0.969474i | \(0.578852\pi\) | |||||||
\(32\) | 7.32338 | 1.29460 | ||||||||
\(33\) | 0.344672 | 0.0599997 | ||||||||
\(34\) | 0.210892 | 0.0361677 | ||||||||
\(35\) | 0.941661 | 0.159170 | ||||||||
\(36\) | 1.61498 | 0.269163 | ||||||||
\(37\) | −5.89894 | −0.969780 | −0.484890 | − | 0.874575i | \(-0.661140\pi\) | ||||
−0.484890 | + | 0.874575i | \(0.661140\pi\) | |||||||
\(38\) | 11.7471 | 1.90564 | ||||||||
\(39\) | 3.84980 | 0.616461 | ||||||||
\(40\) | −0.732051 | −0.115747 | ||||||||
\(41\) | 7.16778 | 1.11942 | 0.559710 | − | 0.828689i | \(-0.310913\pi\) | ||||
0.559710 | + | 0.828689i | \(0.310913\pi\) | |||||||
\(42\) | −1.79039 | −0.276263 | ||||||||
\(43\) | −0.975678 | −0.148789 | −0.0743947 | − | 0.997229i | \(-0.523702\pi\) | ||||
−0.0743947 | + | 0.997229i | \(0.523702\pi\) | |||||||
\(44\) | −0.556637 | −0.0839162 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.28186 | −0.332843 | −0.166422 | − | 0.986055i | \(-0.553221\pi\) | ||||
−0.166422 | + | 0.986055i | \(0.553221\pi\) | |||||||
\(48\) | 4.62181 | 0.667100 | ||||||||
\(49\) | −6.11327 | −0.873325 | ||||||||
\(50\) | −1.90131 | −0.268886 | ||||||||
\(51\) | 0.110920 | 0.0155318 | ||||||||
\(52\) | −6.21733 | −0.862189 | ||||||||
\(53\) | −13.4086 | −1.84181 | −0.920907 | − | 0.389782i | \(-0.872550\pi\) | ||||
−0.920907 | + | 0.389782i | \(0.872550\pi\) | |||||||
\(54\) | 1.90131 | 0.258735 | ||||||||
\(55\) | 0.344672 | 0.0464756 | ||||||||
\(56\) | −0.689344 | −0.0921175 | ||||||||
\(57\) | 6.17844 | 0.818355 | ||||||||
\(58\) | 18.2652 | 2.39834 | ||||||||
\(59\) | −13.5660 | −1.76615 | −0.883074 | − | 0.469234i | \(-0.844530\pi\) | ||||
−0.883074 | + | 0.469234i | \(0.844530\pi\) | |||||||
\(60\) | 1.61498 | 0.208492 | ||||||||
\(61\) | 2.16478 | 0.277172 | 0.138586 | − | 0.990350i | \(-0.455744\pi\) | ||||
0.138586 | + | 0.990350i | \(0.455744\pi\) | |||||||
\(62\) | 5.19128 | 0.659293 | ||||||||
\(63\) | −0.941661 | −0.118638 | ||||||||
\(64\) | −4.68039 | −0.585049 | ||||||||
\(65\) | 3.84980 | 0.477509 | ||||||||
\(66\) | −0.655328 | −0.0806653 | ||||||||
\(67\) | 2.89143 | 0.353245 | 0.176622 | − | 0.984279i | \(-0.443483\pi\) | ||||
0.176622 | + | 0.984279i | \(0.443483\pi\) | |||||||
\(68\) | −0.179132 | −0.0217230 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.79039 | −0.213992 | ||||||||
\(71\) | 0.0848344 | 0.0100680 | 0.00503400 | − | 0.999987i | \(-0.498398\pi\) | ||||
0.00503400 | + | 0.999987i | \(0.498398\pi\) | |||||||
\(72\) | 0.732051 | 0.0862730 | ||||||||
\(73\) | −2.32129 | −0.271686 | −0.135843 | − | 0.990730i | \(-0.543374\pi\) | ||||
−0.135843 | + | 0.990730i | \(0.543374\pi\) | |||||||
\(74\) | 11.2157 | 1.30380 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | −9.97803 | −1.14456 | ||||||||
\(77\) | 0.324564 | 0.0369875 | ||||||||
\(78\) | −7.31966 | −0.828788 | ||||||||
\(79\) | 6.30863 | 0.709776 | 0.354888 | − | 0.934909i | \(-0.384519\pi\) | ||||
0.354888 | + | 0.934909i | \(0.384519\pi\) | |||||||
\(80\) | 4.62181 | 0.516734 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −13.6282 | −1.50498 | ||||||||
\(83\) | −4.58813 | −0.503613 | −0.251806 | − | 0.967778i | \(-0.581025\pi\) | ||||
−0.251806 | + | 0.967778i | \(0.581025\pi\) | |||||||
\(84\) | 1.52076 | 0.165929 | ||||||||
\(85\) | 0.110920 | 0.0120309 | ||||||||
\(86\) | 1.85506 | 0.200037 | ||||||||
\(87\) | 9.60667 | 1.02994 | ||||||||
\(88\) | −0.252317 | −0.0268971 | ||||||||
\(89\) | −11.8356 | −1.25457 | −0.627285 | − | 0.778790i | \(-0.715834\pi\) | ||||
−0.627285 | + | 0.778790i | \(0.715834\pi\) | |||||||
\(90\) | 1.90131 | 0.200416 | ||||||||
\(91\) | 3.62521 | 0.380025 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.73037 | 0.283126 | ||||||||
\(94\) | 4.33852 | 0.447484 | ||||||||
\(95\) | 6.17844 | 0.633895 | ||||||||
\(96\) | −7.32338 | −0.747439 | ||||||||
\(97\) | 13.6504 | 1.38599 | 0.692994 | − | 0.720944i | \(-0.256291\pi\) | ||||
0.692994 | + | 0.720944i | \(0.256291\pi\) | |||||||
\(98\) | 11.6232 | 1.17412 | ||||||||
\(99\) | −0.344672 | −0.0346408 | ||||||||
\(100\) | 1.61498 | 0.161498 | ||||||||
\(101\) | −6.88325 | −0.684909 | −0.342455 | − | 0.939534i | \(-0.611258\pi\) | ||||
−0.342455 | + | 0.939534i | \(0.611258\pi\) | |||||||
\(102\) | −0.210892 | −0.0208814 | ||||||||
\(103\) | −1.22097 | −0.120306 | −0.0601528 | − | 0.998189i | \(-0.519159\pi\) | ||||
−0.0601528 | + | 0.998189i | \(0.519159\pi\) | |||||||
\(104\) | −2.81825 | −0.276352 | ||||||||
\(105\) | −0.941661 | −0.0918968 | ||||||||
\(106\) | 25.4939 | 2.47619 | ||||||||
\(107\) | 7.09838 | 0.686227 | 0.343113 | − | 0.939294i | \(-0.388519\pi\) | ||||
0.343113 | + | 0.939294i | \(0.388519\pi\) | |||||||
\(108\) | −1.61498 | −0.155401 | ||||||||
\(109\) | 0.640252 | 0.0613250 | 0.0306625 | − | 0.999530i | \(-0.490238\pi\) | ||||
0.0306625 | + | 0.999530i | \(0.490238\pi\) | |||||||
\(110\) | −0.655328 | −0.0624831 | ||||||||
\(111\) | 5.89894 | 0.559902 | ||||||||
\(112\) | 4.35218 | 0.411242 | ||||||||
\(113\) | 8.54956 | 0.804275 | 0.402137 | − | 0.915579i | \(-0.368267\pi\) | ||||
0.402137 | + | 0.915579i | \(0.368267\pi\) | |||||||
\(114\) | −11.7471 | −1.10022 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −15.5145 | −1.44049 | ||||||||
\(117\) | −3.84980 | −0.355914 | ||||||||
\(118\) | 25.7932 | 2.37446 | ||||||||
\(119\) | 0.104449 | 0.00957479 | ||||||||
\(120\) | 0.732051 | 0.0668268 | ||||||||
\(121\) | −10.8812 | −0.989200 | ||||||||
\(122\) | −4.11592 | −0.372638 | ||||||||
\(123\) | −7.16778 | −0.646297 | ||||||||
\(124\) | −4.40948 | −0.395983 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 1.79039 | 0.159501 | ||||||||
\(127\) | 15.5136 | 1.37661 | 0.688304 | − | 0.725422i | \(-0.258355\pi\) | ||||
0.688304 | + | 0.725422i | \(0.258355\pi\) | |||||||
\(128\) | −5.74788 | −0.508046 | ||||||||
\(129\) | 0.975678 | 0.0859036 | ||||||||
\(130\) | −7.31966 | −0.641977 | ||||||||
\(131\) | −9.14324 | −0.798849 | −0.399424 | − | 0.916766i | \(-0.630790\pi\) | ||||
−0.399424 | + | 0.916766i | \(0.630790\pi\) | |||||||
\(132\) | 0.556637 | 0.0484490 | ||||||||
\(133\) | 5.81800 | 0.504485 | ||||||||
\(134\) | −5.49751 | −0.474913 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | −0.0811987 | −0.00696273 | ||||||||
\(137\) | −8.24003 | −0.703993 | −0.351996 | − | 0.936001i | \(-0.614497\pi\) | ||||
−0.351996 | + | 0.936001i | \(0.614497\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.2150 | 1.12088 | 0.560439 | − | 0.828196i | \(-0.310632\pi\) | ||||
0.560439 | + | 0.828196i | \(0.310632\pi\) | |||||||
\(140\) | 1.52076 | 0.128528 | ||||||||
\(141\) | 2.28186 | 0.192167 | ||||||||
\(142\) | −0.161296 | −0.0135357 | ||||||||
\(143\) | 1.32692 | 0.110962 | ||||||||
\(144\) | −4.62181 | −0.385150 | ||||||||
\(145\) | 9.60667 | 0.797790 | ||||||||
\(146\) | 4.41349 | 0.365263 | ||||||||
\(147\) | 6.11327 | 0.504214 | ||||||||
\(148\) | −9.52664 | −0.783085 | ||||||||
\(149\) | −0.317210 | −0.0259869 | −0.0129934 | − | 0.999916i | \(-0.504136\pi\) | ||||
−0.0129934 | + | 0.999916i | \(0.504136\pi\) | |||||||
\(150\) | 1.90131 | 0.155241 | ||||||||
\(151\) | −20.5282 | −1.67056 | −0.835280 | − | 0.549824i | \(-0.814695\pi\) | ||||
−0.835280 | + | 0.549824i | \(0.814695\pi\) | |||||||
\(152\) | −4.52293 | −0.366858 | ||||||||
\(153\) | −0.110920 | −0.00896731 | ||||||||
\(154\) | −0.617097 | −0.0497271 | ||||||||
\(155\) | 2.73037 | 0.219309 | ||||||||
\(156\) | 6.21733 | 0.497785 | ||||||||
\(157\) | 4.24565 | 0.338840 | 0.169420 | − | 0.985544i | \(-0.445811\pi\) | ||||
0.169420 | + | 0.985544i | \(0.445811\pi\) | |||||||
\(158\) | −11.9947 | −0.954243 | ||||||||
\(159\) | 13.4086 | 1.06337 | ||||||||
\(160\) | −7.32338 | −0.578964 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.90131 | −0.149381 | ||||||||
\(163\) | −7.40104 | −0.579694 | −0.289847 | − | 0.957073i | \(-0.593604\pi\) | ||||
−0.289847 | + | 0.957073i | \(0.593604\pi\) | |||||||
\(164\) | 11.5758 | 0.903917 | ||||||||
\(165\) | −0.344672 | −0.0268327 | ||||||||
\(166\) | 8.72346 | 0.677072 | ||||||||
\(167\) | −3.55092 | −0.274778 | −0.137389 | − | 0.990517i | \(-0.543871\pi\) | ||||
−0.137389 | + | 0.990517i | \(0.543871\pi\) | |||||||
\(168\) | 0.689344 | 0.0531840 | ||||||||
\(169\) | 1.82096 | 0.140074 | ||||||||
\(170\) | −0.210892 | −0.0161747 | ||||||||
\(171\) | −6.17844 | −0.472477 | ||||||||
\(172\) | −1.57570 | −0.120146 | ||||||||
\(173\) | −17.2570 | −1.31203 | −0.656013 | − | 0.754750i | \(-0.727758\pi\) | ||||
−0.656013 | + | 0.754750i | \(0.727758\pi\) | |||||||
\(174\) | −18.2652 | −1.38468 | ||||||||
\(175\) | −0.941661 | −0.0711829 | ||||||||
\(176\) | 1.59301 | 0.120077 | ||||||||
\(177\) | 13.5660 | 1.01969 | ||||||||
\(178\) | 22.5031 | 1.68668 | ||||||||
\(179\) | −12.3387 | −0.922238 | −0.461119 | − | 0.887338i | \(-0.652552\pi\) | ||||
−0.461119 | + | 0.887338i | \(0.652552\pi\) | |||||||
\(180\) | −1.61498 | −0.120373 | ||||||||
\(181\) | −12.5319 | −0.931489 | −0.465745 | − | 0.884919i | \(-0.654213\pi\) | ||||
−0.465745 | + | 0.884919i | \(0.654213\pi\) | |||||||
\(182\) | −6.89264 | −0.510917 | ||||||||
\(183\) | −2.16478 | −0.160025 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.89894 | 0.433699 | ||||||||
\(186\) | −5.19128 | −0.380643 | ||||||||
\(187\) | 0.0382309 | 0.00279572 | ||||||||
\(188\) | −3.68514 | −0.268767 | ||||||||
\(189\) | 0.941661 | 0.0684958 | ||||||||
\(190\) | −11.7471 | −0.852226 | ||||||||
\(191\) | −12.1534 | −0.879386 | −0.439693 | − | 0.898148i | \(-0.644913\pi\) | ||||
−0.439693 | + | 0.898148i | \(0.644913\pi\) | |||||||
\(192\) | 4.68039 | 0.337778 | ||||||||
\(193\) | 11.6399 | 0.837858 | 0.418929 | − | 0.908019i | \(-0.362406\pi\) | ||||
0.418929 | + | 0.908019i | \(0.362406\pi\) | |||||||
\(194\) | −25.9536 | −1.86336 | ||||||||
\(195\) | −3.84980 | −0.275690 | ||||||||
\(196\) | −9.87279 | −0.705199 | ||||||||
\(197\) | −3.20805 | −0.228564 | −0.114282 | − | 0.993448i | \(-0.536457\pi\) | ||||
−0.114282 | + | 0.993448i | \(0.536457\pi\) | |||||||
\(198\) | 0.655328 | 0.0465721 | ||||||||
\(199\) | 12.4391 | 0.881786 | 0.440893 | − | 0.897560i | \(-0.354662\pi\) | ||||
0.440893 | + | 0.897560i | \(0.354662\pi\) | |||||||
\(200\) | 0.732051 | 0.0517638 | ||||||||
\(201\) | −2.89143 | −0.203946 | ||||||||
\(202\) | 13.0872 | 0.920811 | ||||||||
\(203\) | 9.04623 | 0.634921 | ||||||||
\(204\) | 0.179132 | 0.0125418 | ||||||||
\(205\) | −7.16778 | −0.500619 | ||||||||
\(206\) | 2.32144 | 0.161742 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 17.7930 | 1.23372 | ||||||||
\(209\) | 2.12954 | 0.147303 | ||||||||
\(210\) | 1.79039 | 0.123549 | ||||||||
\(211\) | −19.6039 | −1.34959 | −0.674794 | − | 0.738006i | \(-0.735768\pi\) | ||||
−0.674794 | + | 0.738006i | \(0.735768\pi\) | |||||||
\(212\) | −21.6546 | −1.48724 | ||||||||
\(213\) | −0.0848344 | −0.00581276 | ||||||||
\(214\) | −13.4962 | −0.922583 | ||||||||
\(215\) | 0.975678 | 0.0665407 | ||||||||
\(216\) | −0.732051 | −0.0498097 | ||||||||
\(217\) | 2.57108 | 0.174537 | ||||||||
\(218\) | −1.21732 | −0.0824471 | ||||||||
\(219\) | 2.32129 | 0.156858 | ||||||||
\(220\) | 0.556637 | 0.0375284 | ||||||||
\(221\) | 0.427018 | 0.0287243 | ||||||||
\(222\) | −11.2157 | −0.752749 | ||||||||
\(223\) | 1.31636 | 0.0881501 | 0.0440751 | − | 0.999028i | \(-0.485966\pi\) | ||||
0.0440751 | + | 0.999028i | \(0.485966\pi\) | |||||||
\(224\) | −6.89614 | −0.460768 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −16.2554 | −1.08129 | ||||||||
\(227\) | −17.7799 | −1.18010 | −0.590048 | − | 0.807368i | \(-0.700891\pi\) | ||||
−0.590048 | + | 0.807368i | \(0.700891\pi\) | |||||||
\(228\) | 9.97803 | 0.660811 | ||||||||
\(229\) | −7.45996 | −0.492968 | −0.246484 | − | 0.969147i | \(-0.579275\pi\) | ||||
−0.246484 | + | 0.969147i | \(0.579275\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.324564 | −0.0213548 | ||||||||
\(232\) | −7.03257 | −0.461711 | ||||||||
\(233\) | 3.05893 | 0.200397 | 0.100199 | − | 0.994967i | \(-0.468052\pi\) | ||||
0.100199 | + | 0.994967i | \(0.468052\pi\) | |||||||
\(234\) | 7.31966 | 0.478501 | ||||||||
\(235\) | 2.28186 | 0.148852 | ||||||||
\(236\) | −21.9088 | −1.42614 | ||||||||
\(237\) | −6.30863 | −0.409789 | ||||||||
\(238\) | −0.198589 | −0.0128726 | ||||||||
\(239\) | 14.1780 | 0.917101 | 0.458550 | − | 0.888668i | \(-0.348369\pi\) | ||||
0.458550 | + | 0.888668i | \(0.348369\pi\) | |||||||
\(240\) | −4.62181 | −0.298336 | ||||||||
\(241\) | 29.2388 | 1.88343 | 0.941717 | − | 0.336405i | \(-0.109211\pi\) | ||||
0.941717 | + | 0.336405i | \(0.109211\pi\) | |||||||
\(242\) | 20.6885 | 1.32991 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 3.49607 | 0.223813 | ||||||||
\(245\) | 6.11327 | 0.390563 | ||||||||
\(246\) | 13.6282 | 0.868900 | ||||||||
\(247\) | 23.7858 | 1.51345 | ||||||||
\(248\) | −1.99877 | −0.126922 | ||||||||
\(249\) | 4.58813 | 0.290761 | ||||||||
\(250\) | 1.90131 | 0.120249 | ||||||||
\(251\) | −26.8739 | −1.69627 | −0.848133 | − | 0.529783i | \(-0.822273\pi\) | ||||
−0.848133 | + | 0.529783i | \(0.822273\pi\) | |||||||
\(252\) | −1.52076 | −0.0957989 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −29.4961 | −1.85075 | ||||||||
\(255\) | −0.110920 | −0.00694605 | ||||||||
\(256\) | 20.2893 | 1.26808 | ||||||||
\(257\) | 23.6429 | 1.47481 | 0.737403 | − | 0.675453i | \(-0.236052\pi\) | ||||
0.737403 | + | 0.675453i | \(0.236052\pi\) | |||||||
\(258\) | −1.85506 | −0.115491 | ||||||||
\(259\) | 5.55480 | 0.345159 | ||||||||
\(260\) | 6.21733 | 0.385583 | ||||||||
\(261\) | −9.60667 | −0.594638 | ||||||||
\(262\) | 17.3841 | 1.07399 | ||||||||
\(263\) | −11.3133 | −0.697605 | −0.348803 | − | 0.937196i | \(-0.613412\pi\) | ||||
−0.348803 | + | 0.937196i | \(0.613412\pi\) | |||||||
\(264\) | 0.252317 | 0.0155291 | ||||||||
\(265\) | 13.4086 | 0.823684 | ||||||||
\(266\) | −11.0618 | −0.678244 | ||||||||
\(267\) | 11.8356 | 0.724326 | ||||||||
\(268\) | 4.66960 | 0.285241 | ||||||||
\(269\) | −5.84484 | −0.356366 | −0.178183 | − | 0.983997i | \(-0.557022\pi\) | ||||
−0.178183 | + | 0.983997i | \(0.557022\pi\) | |||||||
\(270\) | −1.90131 | −0.115710 | ||||||||
\(271\) | −20.0827 | −1.21993 | −0.609967 | − | 0.792427i | \(-0.708817\pi\) | ||||
−0.609967 | + | 0.792427i | \(0.708817\pi\) | |||||||
\(272\) | 0.512648 | 0.0310839 | ||||||||
\(273\) | −3.62521 | −0.219408 | ||||||||
\(274\) | 15.6668 | 0.946468 | ||||||||
\(275\) | −0.344672 | −0.0207845 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −22.5451 | −1.35460 | −0.677302 | − | 0.735705i | \(-0.736851\pi\) | ||||
−0.677302 | + | 0.735705i | \(0.736851\pi\) | |||||||
\(278\) | −25.1257 | −1.50694 | ||||||||
\(279\) | −2.73037 | −0.163463 | ||||||||
\(280\) | 0.689344 | 0.0411962 | ||||||||
\(281\) | −21.4649 | −1.28049 | −0.640244 | − | 0.768172i | \(-0.721167\pi\) | ||||
−0.640244 | + | 0.768172i | \(0.721167\pi\) | |||||||
\(282\) | −4.33852 | −0.258355 | ||||||||
\(283\) | −25.9275 | −1.54123 | −0.770616 | − | 0.637300i | \(-0.780051\pi\) | ||||
−0.770616 | + | 0.637300i | \(0.780051\pi\) | |||||||
\(284\) | 0.137006 | 0.00812978 | ||||||||
\(285\) | −6.17844 | −0.365979 | ||||||||
\(286\) | −2.52288 | −0.149181 | ||||||||
\(287\) | −6.74962 | −0.398418 | ||||||||
\(288\) | 7.32338 | 0.431534 | ||||||||
\(289\) | −16.9877 | −0.999276 | ||||||||
\(290\) | −18.2652 | −1.07257 | ||||||||
\(291\) | −13.6504 | −0.800200 | ||||||||
\(292\) | −3.74882 | −0.219383 | ||||||||
\(293\) | −20.0884 | −1.17358 | −0.586790 | − | 0.809739i | \(-0.699608\pi\) | ||||
−0.586790 | + | 0.809739i | \(0.699608\pi\) | |||||||
\(294\) | −11.6232 | −0.677880 | ||||||||
\(295\) | 13.5660 | 0.789845 | ||||||||
\(296\) | −4.31832 | −0.250997 | ||||||||
\(297\) | 0.344672 | 0.0199999 | ||||||||
\(298\) | 0.603115 | 0.0349375 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1.61498 | −0.0932406 | ||||||||
\(301\) | 0.918758 | 0.0529563 | ||||||||
\(302\) | 39.0304 | 2.24595 | ||||||||
\(303\) | 6.88325 | 0.395432 | ||||||||
\(304\) | 28.5556 | 1.63777 | ||||||||
\(305\) | −2.16478 | −0.123955 | ||||||||
\(306\) | 0.210892 | 0.0120559 | ||||||||
\(307\) | 11.9672 | 0.683004 | 0.341502 | − | 0.939881i | \(-0.389064\pi\) | ||||
0.341502 | + | 0.939881i | \(0.389064\pi\) | |||||||
\(308\) | 0.524163 | 0.0298670 | ||||||||
\(309\) | 1.22097 | 0.0694585 | ||||||||
\(310\) | −5.19128 | −0.294845 | ||||||||
\(311\) | 2.55209 | 0.144716 | 0.0723579 | − | 0.997379i | \(-0.476948\pi\) | ||||
0.0723579 | + | 0.997379i | \(0.476948\pi\) | |||||||
\(312\) | 2.81825 | 0.159552 | ||||||||
\(313\) | 30.7169 | 1.73622 | 0.868111 | − | 0.496370i | \(-0.165334\pi\) | ||||
0.868111 | + | 0.496370i | \(0.165334\pi\) | |||||||
\(314\) | −8.07230 | −0.455546 | ||||||||
\(315\) | 0.941661 | 0.0530566 | ||||||||
\(316\) | 10.1883 | 0.573136 | ||||||||
\(317\) | 32.9632 | 1.85140 | 0.925699 | − | 0.378260i | \(-0.123478\pi\) | ||||
0.925699 | + | 0.378260i | \(0.123478\pi\) | |||||||
\(318\) | −25.4939 | −1.42963 | ||||||||
\(319\) | 3.31115 | 0.185389 | ||||||||
\(320\) | 4.68039 | 0.261642 | ||||||||
\(321\) | −7.09838 | −0.396193 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.685310 | 0.0381317 | ||||||||
\(324\) | 1.61498 | 0.0897209 | ||||||||
\(325\) | −3.84980 | −0.213549 | ||||||||
\(326\) | 14.0717 | 0.779357 | ||||||||
\(327\) | −0.640252 | −0.0354060 | ||||||||
\(328\) | 5.24718 | 0.289727 | ||||||||
\(329\) | 2.14874 | 0.118464 | ||||||||
\(330\) | 0.655328 | 0.0360746 | ||||||||
\(331\) | 22.3176 | 1.22669 | 0.613343 | − | 0.789817i | \(-0.289824\pi\) | ||||
0.613343 | + | 0.789817i | \(0.289824\pi\) | |||||||
\(332\) | −7.40972 | −0.406661 | ||||||||
\(333\) | −5.89894 | −0.323260 | ||||||||
\(334\) | 6.75139 | 0.369420 | ||||||||
\(335\) | −2.89143 | −0.157976 | ||||||||
\(336\) | −4.35218 | −0.237431 | ||||||||
\(337\) | −17.4215 | −0.949010 | −0.474505 | − | 0.880253i | \(-0.657373\pi\) | ||||
−0.474505 | + | 0.880253i | \(0.657373\pi\) | |||||||
\(338\) | −3.46221 | −0.188320 | ||||||||
\(339\) | −8.54956 | −0.464348 | ||||||||
\(340\) | 0.179132 | 0.00971481 | ||||||||
\(341\) | 0.941082 | 0.0509625 | ||||||||
\(342\) | 11.7471 | 0.635212 | ||||||||
\(343\) | 12.3483 | 0.666744 | ||||||||
\(344\) | −0.714246 | −0.0385095 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 32.8109 | 1.76392 | ||||||||
\(347\) | −25.5751 | −1.37294 | −0.686471 | − | 0.727157i | \(-0.740841\pi\) | ||||
−0.686471 | + | 0.727157i | \(0.740841\pi\) | |||||||
\(348\) | 15.5145 | 0.831666 | ||||||||
\(349\) | −25.3037 | −1.35447 | −0.677237 | − | 0.735765i | \(-0.736823\pi\) | ||||
−0.677237 | + | 0.735765i | \(0.736823\pi\) | |||||||
\(350\) | 1.79039 | 0.0957003 | ||||||||
\(351\) | 3.84980 | 0.205487 | ||||||||
\(352\) | −2.52416 | −0.134538 | ||||||||
\(353\) | 17.7951 | 0.947135 | 0.473568 | − | 0.880757i | \(-0.342966\pi\) | ||||
0.473568 | + | 0.880757i | \(0.342966\pi\) | |||||||
\(354\) | −25.7932 | −1.37089 | ||||||||
\(355\) | −0.0848344 | −0.00450254 | ||||||||
\(356\) | −19.1142 | −1.01305 | ||||||||
\(357\) | −0.104449 | −0.00552801 | ||||||||
\(358\) | 23.4597 | 1.23988 | ||||||||
\(359\) | −20.8242 | −1.09906 | −0.549530 | − | 0.835474i | \(-0.685193\pi\) | ||||
−0.549530 | + | 0.835474i | \(0.685193\pi\) | |||||||
\(360\) | −0.732051 | −0.0385825 | ||||||||
\(361\) | 19.1731 | 1.00911 | ||||||||
\(362\) | 23.8270 | 1.25232 | ||||||||
\(363\) | 10.8812 | 0.571115 | ||||||||
\(364\) | 5.85462 | 0.306866 | ||||||||
\(365\) | 2.32129 | 0.121502 | ||||||||
\(366\) | 4.11592 | 0.215143 | ||||||||
\(367\) | 6.24844 | 0.326166 | 0.163083 | − | 0.986612i | \(-0.447856\pi\) | ||||
0.163083 | + | 0.986612i | \(0.447856\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 7.16778 | 0.373140 | ||||||||
\(370\) | −11.2157 | −0.583077 | ||||||||
\(371\) | 12.6264 | 0.655529 | ||||||||
\(372\) | 4.40948 | 0.228621 | ||||||||
\(373\) | 2.04949 | 0.106119 | 0.0530593 | − | 0.998591i | \(-0.483103\pi\) | ||||
0.0530593 | + | 0.998591i | \(0.483103\pi\) | |||||||
\(374\) | −0.0726887 | −0.00375864 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | −1.67044 | −0.0861461 | ||||||||
\(377\) | 36.9838 | 1.90476 | ||||||||
\(378\) | −1.79039 | −0.0920877 | ||||||||
\(379\) | −20.7709 | −1.06693 | −0.533464 | − | 0.845823i | \(-0.679110\pi\) | ||||
−0.533464 | + | 0.845823i | \(0.679110\pi\) | |||||||
\(380\) | 9.97803 | 0.511862 | ||||||||
\(381\) | −15.5136 | −0.794785 | ||||||||
\(382\) | 23.1073 | 1.18227 | ||||||||
\(383\) | 21.6361 | 1.10555 | 0.552776 | − | 0.833330i | \(-0.313569\pi\) | ||||
0.552776 | + | 0.833330i | \(0.313569\pi\) | |||||||
\(384\) | 5.74788 | 0.293320 | ||||||||
\(385\) | −0.324564 | −0.0165413 | ||||||||
\(386\) | −22.1310 | −1.12644 | ||||||||
\(387\) | −0.975678 | −0.0495965 | ||||||||
\(388\) | 22.0450 | 1.11917 | ||||||||
\(389\) | 33.6439 | 1.70582 | 0.852908 | − | 0.522061i | \(-0.174837\pi\) | ||||
0.852908 | + | 0.522061i | \(0.174837\pi\) | |||||||
\(390\) | 7.31966 | 0.370645 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −4.47523 | −0.226033 | ||||||||
\(393\) | 9.14324 | 0.461215 | ||||||||
\(394\) | 6.09950 | 0.307288 | ||||||||
\(395\) | −6.30863 | −0.317422 | ||||||||
\(396\) | −0.556637 | −0.0279721 | ||||||||
\(397\) | 15.5549 | 0.780679 | 0.390340 | − | 0.920671i | \(-0.372358\pi\) | ||||
0.390340 | + | 0.920671i | \(0.372358\pi\) | |||||||
\(398\) | −23.6506 | −1.18550 | ||||||||
\(399\) | −5.81800 | −0.291264 | ||||||||
\(400\) | −4.62181 | −0.231090 | ||||||||
\(401\) | −38.5160 | −1.92340 | −0.961699 | − | 0.274108i | \(-0.911617\pi\) | ||||
−0.961699 | + | 0.274108i | \(0.911617\pi\) | |||||||
\(402\) | 5.49751 | 0.274191 | ||||||||
\(403\) | 10.5114 | 0.523609 | ||||||||
\(404\) | −11.1163 | −0.553056 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | −17.1997 | −0.853605 | ||||||||
\(407\) | 2.03320 | 0.100782 | ||||||||
\(408\) | 0.0811987 | 0.00401994 | ||||||||
\(409\) | −35.6798 | −1.76425 | −0.882126 | − | 0.471014i | \(-0.843888\pi\) | ||||
−0.882126 | + | 0.471014i | \(0.843888\pi\) | |||||||
\(410\) | 13.6282 | 0.673047 | ||||||||
\(411\) | 8.24003 | 0.406451 | ||||||||
\(412\) | −1.97183 | −0.0971453 | ||||||||
\(413\) | 12.7746 | 0.628598 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.58813 | 0.225223 | ||||||||
\(416\) | −28.1935 | −1.38230 | ||||||||
\(417\) | −13.2150 | −0.647139 | ||||||||
\(418\) | −4.04891 | −0.198038 | ||||||||
\(419\) | 28.0247 | 1.36909 | 0.684547 | − | 0.728969i | \(-0.260000\pi\) | ||||
0.684547 | + | 0.728969i | \(0.260000\pi\) | |||||||
\(420\) | −1.52076 | −0.0742055 | ||||||||
\(421\) | 29.8972 | 1.45710 | 0.728551 | − | 0.684991i | \(-0.240194\pi\) | ||||
0.728551 | + | 0.684991i | \(0.240194\pi\) | |||||||
\(422\) | 37.2731 | 1.81442 | ||||||||
\(423\) | −2.28186 | −0.110948 | ||||||||
\(424\) | −9.81578 | −0.476697 | ||||||||
\(425\) | −0.110920 | −0.00538039 | ||||||||
\(426\) | 0.161296 | 0.00781484 | ||||||||
\(427\) | −2.03849 | −0.0986495 | ||||||||
\(428\) | 11.4637 | 0.554120 | ||||||||
\(429\) | −1.32692 | −0.0640642 | ||||||||
\(430\) | −1.85506 | −0.0894591 | ||||||||
\(431\) | 2.99611 | 0.144318 | 0.0721588 | − | 0.997393i | \(-0.477011\pi\) | ||||
0.0721588 | + | 0.997393i | \(0.477011\pi\) | |||||||
\(432\) | 4.62181 | 0.222367 | ||||||||
\(433\) | −3.55693 | −0.170935 | −0.0854677 | − | 0.996341i | \(-0.527238\pi\) | ||||
−0.0854677 | + | 0.996341i | \(0.527238\pi\) | |||||||
\(434\) | −4.88843 | −0.234652 | ||||||||
\(435\) | −9.60667 | −0.460604 | ||||||||
\(436\) | 1.03399 | 0.0495192 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −4.41349 | −0.210884 | ||||||||
\(439\) | −8.50958 | −0.406140 | −0.203070 | − | 0.979164i | \(-0.565092\pi\) | ||||
−0.203070 | + | 0.979164i | \(0.565092\pi\) | |||||||
\(440\) | 0.252317 | 0.0120288 | ||||||||
\(441\) | −6.11327 | −0.291108 | ||||||||
\(442\) | −0.811893 | −0.0386178 | ||||||||
\(443\) | −14.9149 | −0.708629 | −0.354315 | − | 0.935126i | \(-0.615286\pi\) | ||||
−0.354315 | + | 0.935126i | \(0.615286\pi\) | |||||||
\(444\) | 9.52664 | 0.452114 | ||||||||
\(445\) | 11.8356 | 0.561061 | ||||||||
\(446\) | −2.50281 | −0.118511 | ||||||||
\(447\) | 0.317210 | 0.0150035 | ||||||||
\(448\) | 4.40735 | 0.208227 | ||||||||
\(449\) | −22.6007 | −1.06659 | −0.533296 | − | 0.845928i | \(-0.679047\pi\) | ||||
−0.533296 | + | 0.845928i | \(0.679047\pi\) | |||||||
\(450\) | −1.90131 | −0.0896286 | ||||||||
\(451\) | −2.47053 | −0.116333 | ||||||||
\(452\) | 13.8073 | 0.649442 | ||||||||
\(453\) | 20.5282 | 0.964499 | ||||||||
\(454\) | 33.8052 | 1.58655 | ||||||||
\(455\) | −3.62521 | −0.169952 | ||||||||
\(456\) | 4.52293 | 0.211806 | ||||||||
\(457\) | 39.3091 | 1.83880 | 0.919400 | − | 0.393323i | \(-0.128675\pi\) | ||||
0.919400 | + | 0.393323i | \(0.128675\pi\) | |||||||
\(458\) | 14.1837 | 0.662760 | ||||||||
\(459\) | 0.110920 | 0.00517728 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 20.2367 | 0.942516 | 0.471258 | − | 0.881995i | \(-0.343800\pi\) | ||||
0.471258 | + | 0.881995i | \(0.343800\pi\) | |||||||
\(462\) | 0.617097 | 0.0287100 | ||||||||
\(463\) | −36.4822 | −1.69547 | −0.847736 | − | 0.530419i | \(-0.822035\pi\) | ||||
−0.847736 | + | 0.530419i | \(0.822035\pi\) | |||||||
\(464\) | 44.4001 | 2.06122 | ||||||||
\(465\) | −2.73037 | −0.126618 | ||||||||
\(466\) | −5.81598 | −0.269420 | ||||||||
\(467\) | 19.5589 | 0.905077 | 0.452538 | − | 0.891745i | \(-0.350519\pi\) | ||||
0.452538 | + | 0.891745i | \(0.350519\pi\) | |||||||
\(468\) | −6.21733 | −0.287396 | ||||||||
\(469\) | −2.72275 | −0.125725 | ||||||||
\(470\) | −4.33852 | −0.200121 | ||||||||
\(471\) | −4.24565 | −0.195629 | ||||||||
\(472\) | −9.93103 | −0.457113 | ||||||||
\(473\) | 0.336289 | 0.0154626 | ||||||||
\(474\) | 11.9947 | 0.550933 | ||||||||
\(475\) | −6.17844 | −0.283486 | ||||||||
\(476\) | 0.168682 | 0.00773153 | ||||||||
\(477\) | −13.4086 | −0.613938 | ||||||||
\(478\) | −26.9568 | −1.23298 | ||||||||
\(479\) | −16.7397 | −0.764856 | −0.382428 | − | 0.923985i | \(-0.624912\pi\) | ||||
−0.382428 | + | 0.923985i | \(0.624912\pi\) | |||||||
\(480\) | 7.32338 | 0.334265 | ||||||||
\(481\) | 22.7097 | 1.03547 | ||||||||
\(482\) | −55.5919 | −2.53214 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −17.5729 | −0.798767 | ||||||||
\(485\) | −13.6504 | −0.619832 | ||||||||
\(486\) | 1.90131 | 0.0862451 | ||||||||
\(487\) | 1.26249 | 0.0572087 | 0.0286044 | − | 0.999591i | \(-0.490894\pi\) | ||||
0.0286044 | + | 0.999591i | \(0.490894\pi\) | |||||||
\(488\) | 1.58473 | 0.0717374 | ||||||||
\(489\) | 7.40104 | 0.334687 | ||||||||
\(490\) | −11.6232 | −0.525084 | ||||||||
\(491\) | 1.58626 | 0.0715871 | 0.0357935 | − | 0.999359i | \(-0.488604\pi\) | ||||
0.0357935 | + | 0.999359i | \(0.488604\pi\) | |||||||
\(492\) | −11.5758 | −0.521877 | ||||||||
\(493\) | 1.06557 | 0.0479907 | ||||||||
\(494\) | −45.2241 | −2.03473 | ||||||||
\(495\) | 0.344672 | 0.0154919 | ||||||||
\(496\) | 12.6192 | 0.566621 | ||||||||
\(497\) | −0.0798853 | −0.00358335 | ||||||||
\(498\) | −8.72346 | −0.390907 | ||||||||
\(499\) | −13.9364 | −0.623877 | −0.311939 | − | 0.950102i | \(-0.600978\pi\) | ||||
−0.311939 | + | 0.950102i | \(0.600978\pi\) | |||||||
\(500\) | −1.61498 | −0.0722239 | ||||||||
\(501\) | 3.55092 | 0.158643 | ||||||||
\(502\) | 51.0956 | 2.28051 | ||||||||
\(503\) | −16.5341 | −0.737219 | −0.368609 | − | 0.929584i | \(-0.620166\pi\) | ||||
−0.368609 | + | 0.929584i | \(0.620166\pi\) | |||||||
\(504\) | −0.689344 | −0.0307058 | ||||||||
\(505\) | 6.88325 | 0.306301 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.82096 | −0.0808718 | ||||||||
\(508\) | 25.0541 | 1.11159 | ||||||||
\(509\) | 6.67931 | 0.296055 | 0.148028 | − | 0.988983i | \(-0.452708\pi\) | ||||
0.148028 | + | 0.988983i | \(0.452708\pi\) | |||||||
\(510\) | 0.210892 | 0.00933847 | ||||||||
\(511\) | 2.18587 | 0.0966971 | ||||||||
\(512\) | −27.0804 | −1.19680 | ||||||||
\(513\) | 6.17844 | 0.272785 | ||||||||
\(514\) | −44.9525 | −1.98277 | ||||||||
\(515\) | 1.22097 | 0.0538023 | ||||||||
\(516\) | 1.57570 | 0.0693661 | ||||||||
\(517\) | 0.786492 | 0.0345899 | ||||||||
\(518\) | −10.5614 | −0.464041 | ||||||||
\(519\) | 17.2570 | 0.757499 | ||||||||
\(520\) | 2.81825 | 0.123588 | ||||||||
\(521\) | 31.1155 | 1.36320 | 0.681598 | − | 0.731727i | \(-0.261285\pi\) | ||||
0.681598 | + | 0.731727i | \(0.261285\pi\) | |||||||
\(522\) | 18.2652 | 0.799448 | ||||||||
\(523\) | 4.20093 | 0.183694 | 0.0918470 | − | 0.995773i | \(-0.470723\pi\) | ||||
0.0918470 | + | 0.995773i | \(0.470723\pi\) | |||||||
\(524\) | −14.7661 | −0.645060 | ||||||||
\(525\) | 0.941661 | 0.0410975 | ||||||||
\(526\) | 21.5100 | 0.937881 | ||||||||
\(527\) | 0.302851 | 0.0131924 | ||||||||
\(528\) | −1.59301 | −0.0693267 | ||||||||
\(529\) | 0 | 0 | ||||||||
\(530\) | −25.4939 | −1.10738 | ||||||||
\(531\) | −13.5660 | −0.588716 | ||||||||
\(532\) | 9.39593 | 0.407365 | ||||||||
\(533\) | −27.5945 | −1.19525 | ||||||||
\(534\) | −22.5031 | −0.973804 | ||||||||
\(535\) | −7.09838 | −0.306890 | ||||||||
\(536\) | 2.11668 | 0.0914265 | ||||||||
\(537\) | 12.3387 | 0.532454 | ||||||||
\(538\) | 11.1129 | 0.479109 | ||||||||
\(539\) | 2.10707 | 0.0907581 | ||||||||
\(540\) | 1.61498 | 0.0694975 | ||||||||
\(541\) | 13.0314 | 0.560265 | 0.280133 | − | 0.959961i | \(-0.409622\pi\) | ||||
0.280133 | + | 0.959961i | \(0.409622\pi\) | |||||||
\(542\) | 38.1833 | 1.64011 | ||||||||
\(543\) | 12.5319 | 0.537796 | ||||||||
\(544\) | −0.812306 | −0.0348273 | ||||||||
\(545\) | −0.640252 | −0.0274254 | ||||||||
\(546\) | 6.89264 | 0.294978 | ||||||||
\(547\) | 24.4746 | 1.04646 | 0.523228 | − | 0.852193i | \(-0.324728\pi\) | ||||
0.523228 | + | 0.852193i | \(0.324728\pi\) | |||||||
\(548\) | −13.3074 | −0.568466 | ||||||||
\(549\) | 2.16478 | 0.0923907 | ||||||||
\(550\) | 0.655328 | 0.0279433 | ||||||||
\(551\) | 59.3542 | 2.52858 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.94059 | −0.252620 | ||||||||
\(554\) | 42.8652 | 1.82117 | ||||||||
\(555\) | −5.89894 | −0.250396 | ||||||||
\(556\) | 21.3418 | 0.905096 | ||||||||
\(557\) | −32.6808 | −1.38473 | −0.692364 | − | 0.721548i | \(-0.743431\pi\) | ||||
−0.692364 | + | 0.721548i | \(0.743431\pi\) | |||||||
\(558\) | 5.19128 | 0.219764 | ||||||||
\(559\) | 3.75616 | 0.158869 | ||||||||
\(560\) | −4.35218 | −0.183913 | ||||||||
\(561\) | −0.0382309 | −0.00161411 | ||||||||
\(562\) | 40.8114 | 1.72152 | ||||||||
\(563\) | 32.4830 | 1.36899 | 0.684497 | − | 0.729016i | \(-0.260022\pi\) | ||||
0.684497 | + | 0.729016i | \(0.260022\pi\) | |||||||
\(564\) | 3.68514 | 0.155173 | ||||||||
\(565\) | −8.54956 | −0.359683 | ||||||||
\(566\) | 49.2962 | 2.07207 | ||||||||
\(567\) | −0.941661 | −0.0395461 | ||||||||
\(568\) | 0.0621031 | 0.00260579 | ||||||||
\(569\) | −13.2468 | −0.555334 | −0.277667 | − | 0.960677i | \(-0.589561\pi\) | ||||
−0.277667 | + | 0.960677i | \(0.589561\pi\) | |||||||
\(570\) | 11.7471 | 0.492033 | ||||||||
\(571\) | 36.5638 | 1.53015 | 0.765074 | − | 0.643942i | \(-0.222702\pi\) | ||||
0.765074 | + | 0.643942i | \(0.222702\pi\) | |||||||
\(572\) | 2.14294 | 0.0896008 | ||||||||
\(573\) | 12.1534 | 0.507714 | ||||||||
\(574\) | 12.8331 | 0.535644 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −4.68039 | −0.195016 | ||||||||
\(577\) | −3.59443 | −0.149638 | −0.0748191 | − | 0.997197i | \(-0.523838\pi\) | ||||
−0.0748191 | + | 0.997197i | \(0.523838\pi\) | |||||||
\(578\) | 32.2989 | 1.34346 | ||||||||
\(579\) | −11.6399 | −0.483738 | ||||||||
\(580\) | 15.5145 | 0.644206 | ||||||||
\(581\) | 4.32047 | 0.179243 | ||||||||
\(582\) | 25.9536 | 1.07581 | ||||||||
\(583\) | 4.62157 | 0.191406 | ||||||||
\(584\) | −1.69930 | −0.0703176 | ||||||||
\(585\) | 3.84980 | 0.159170 | ||||||||
\(586\) | 38.1943 | 1.57779 | ||||||||
\(587\) | 12.7193 | 0.524980 | 0.262490 | − | 0.964935i | \(-0.415456\pi\) | ||||
0.262490 | + | 0.964935i | \(0.415456\pi\) | |||||||
\(588\) | 9.87279 | 0.407147 | ||||||||
\(589\) | 16.8694 | 0.695093 | ||||||||
\(590\) | −25.7932 | −1.06189 | ||||||||
\(591\) | 3.20805 | 0.131962 | ||||||||
\(592\) | 27.2637 | 1.12053 | ||||||||
\(593\) | −9.87033 | −0.405326 | −0.202663 | − | 0.979249i | \(-0.564960\pi\) | ||||
−0.202663 | + | 0.979249i | \(0.564960\pi\) | |||||||
\(594\) | −0.655328 | −0.0268884 | ||||||||
\(595\) | −0.104449 | −0.00428198 | ||||||||
\(596\) | −0.512287 | −0.0209841 | ||||||||
\(597\) | −12.4391 | −0.509099 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −42.1809 | −1.72346 | −0.861732 | − | 0.507364i | \(-0.830620\pi\) | ||||
−0.861732 | + | 0.507364i | \(0.830620\pi\) | |||||||
\(600\) | −0.732051 | −0.0298858 | ||||||||
\(601\) | −23.0857 | −0.941684 | −0.470842 | − | 0.882218i | \(-0.656050\pi\) | ||||
−0.470842 | + | 0.882218i | \(0.656050\pi\) | |||||||
\(602\) | −1.74684 | −0.0711960 | ||||||||
\(603\) | 2.89143 | 0.117748 | ||||||||
\(604\) | −33.1525 | −1.34896 | ||||||||
\(605\) | 10.8812 | 0.442384 | ||||||||
\(606\) | −13.0872 | −0.531631 | ||||||||
\(607\) | 41.7202 | 1.69337 | 0.846685 | − | 0.532095i | \(-0.178595\pi\) | ||||
0.846685 | + | 0.532095i | \(0.178595\pi\) | |||||||
\(608\) | −45.2471 | −1.83501 | ||||||||
\(609\) | −9.04623 | −0.366572 | ||||||||
\(610\) | 4.11592 | 0.166649 | ||||||||
\(611\) | 8.78470 | 0.355391 | ||||||||
\(612\) | −0.179132 | −0.00724099 | ||||||||
\(613\) | 6.36682 | 0.257153 | 0.128577 | − | 0.991700i | \(-0.458959\pi\) | ||||
0.128577 | + | 0.991700i | \(0.458959\pi\) | |||||||
\(614\) | −22.7533 | −0.918250 | ||||||||
\(615\) | 7.16778 | 0.289033 | ||||||||
\(616\) | 0.237598 | 0.00957308 | ||||||||
\(617\) | 33.2714 | 1.33946 | 0.669728 | − | 0.742607i | \(-0.266411\pi\) | ||||
0.669728 | + | 0.742607i | \(0.266411\pi\) | |||||||
\(618\) | −2.32144 | −0.0933819 | ||||||||
\(619\) | 43.7641 | 1.75903 | 0.879515 | − | 0.475872i | \(-0.157867\pi\) | ||||
0.879515 | + | 0.475872i | \(0.157867\pi\) | |||||||
\(620\) | 4.40948 | 0.177089 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −4.85231 | −0.194560 | ||||||||
\(623\) | 11.1451 | 0.446520 | ||||||||
\(624\) | −17.7930 | −0.712291 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −58.4023 | −2.33423 | ||||||||
\(627\) | −2.12954 | −0.0850455 | ||||||||
\(628\) | 6.85663 | 0.273609 | ||||||||
\(629\) | 0.654307 | 0.0260889 | ||||||||
\(630\) | −1.79039 | −0.0713308 | ||||||||
\(631\) | 29.3769 | 1.16948 | 0.584738 | − | 0.811222i | \(-0.301197\pi\) | ||||
0.584738 | + | 0.811222i | \(0.301197\pi\) | |||||||
\(632\) | 4.61824 | 0.183704 | ||||||||
\(633\) | 19.6039 | 0.779185 | ||||||||
\(634\) | −62.6732 | −2.48907 | ||||||||
\(635\) | −15.5136 | −0.615638 | ||||||||
\(636\) | 21.6546 | 0.858660 | ||||||||
\(637\) | 23.5349 | 0.932486 | ||||||||
\(638\) | −6.29552 | −0.249242 | ||||||||
\(639\) | 0.0848344 | 0.00335600 | ||||||||
\(640\) | 5.74788 | 0.227205 | ||||||||
\(641\) | −44.1549 | −1.74401 | −0.872007 | − | 0.489493i | \(-0.837182\pi\) | ||||
−0.872007 | + | 0.489493i | \(0.837182\pi\) | |||||||
\(642\) | 13.4962 | 0.532653 | ||||||||
\(643\) | 29.7768 | 1.17428 | 0.587142 | − | 0.809484i | \(-0.300253\pi\) | ||||
0.587142 | + | 0.809484i | \(0.300253\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.975678 | −0.0384173 | ||||||||
\(646\) | −1.30299 | −0.0512653 | ||||||||
\(647\) | −31.4784 | −1.23754 | −0.618772 | − | 0.785571i | \(-0.712369\pi\) | ||||
−0.618772 | + | 0.785571i | \(0.712369\pi\) | |||||||
\(648\) | 0.732051 | 0.0287577 | ||||||||
\(649\) | 4.67583 | 0.183543 | ||||||||
\(650\) | 7.31966 | 0.287101 | ||||||||
\(651\) | −2.57108 | −0.100769 | ||||||||
\(652\) | −11.9525 | −0.468096 | ||||||||
\(653\) | −11.8058 | −0.461998 | −0.230999 | − | 0.972954i | \(-0.574199\pi\) | ||||
−0.230999 | + | 0.972954i | \(0.574199\pi\) | |||||||
\(654\) | 1.21732 | 0.0476009 | ||||||||
\(655\) | 9.14324 | 0.357256 | ||||||||
\(656\) | −33.1281 | −1.29343 | ||||||||
\(657\) | −2.32129 | −0.0905621 | ||||||||
\(658\) | −4.08541 | −0.159266 | ||||||||
\(659\) | 22.9082 | 0.892379 | 0.446189 | − | 0.894939i | \(-0.352781\pi\) | ||||
0.446189 | + | 0.894939i | \(0.352781\pi\) | |||||||
\(660\) | −0.556637 | −0.0216671 | ||||||||
\(661\) | −20.0826 | −0.781123 | −0.390562 | − | 0.920577i | \(-0.627719\pi\) | ||||
−0.390562 | + | 0.920577i | \(0.627719\pi\) | |||||||
\(662\) | −42.4326 | −1.64919 | ||||||||
\(663\) | −0.427018 | −0.0165840 | ||||||||
\(664\) | −3.35875 | −0.130345 | ||||||||
\(665\) | −5.81800 | −0.225612 | ||||||||
\(666\) | 11.2157 | 0.434600 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −5.73464 | −0.221880 | ||||||||
\(669\) | −1.31636 | −0.0508935 | ||||||||
\(670\) | 5.49751 | 0.212387 | ||||||||
\(671\) | −0.746140 | −0.0288044 | ||||||||
\(672\) | 6.89614 | 0.266024 | ||||||||
\(673\) | 31.2670 | 1.20526 | 0.602628 | − | 0.798023i | \(-0.294120\pi\) | ||||
0.602628 | + | 0.798023i | \(0.294120\pi\) | |||||||
\(674\) | 33.1237 | 1.27588 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 2.94081 | 0.113108 | ||||||||
\(677\) | 21.8318 | 0.839065 | 0.419533 | − | 0.907740i | \(-0.362194\pi\) | ||||
0.419533 | + | 0.907740i | \(0.362194\pi\) | |||||||
\(678\) | 16.2554 | 0.624283 | ||||||||
\(679\) | −12.8540 | −0.493293 | ||||||||
\(680\) | 0.0811987 | 0.00311383 | ||||||||
\(681\) | 17.7799 | 0.681329 | ||||||||
\(682\) | −1.78929 | −0.0685154 | ||||||||
\(683\) | −4.96284 | −0.189898 | −0.0949488 | − | 0.995482i | \(-0.530269\pi\) | ||||
−0.0949488 | + | 0.995482i | \(0.530269\pi\) | |||||||
\(684\) | −9.97803 | −0.381520 | ||||||||
\(685\) | 8.24003 | 0.314835 | ||||||||
\(686\) | −23.4779 | −0.896389 | ||||||||
\(687\) | 7.45996 | 0.284615 | ||||||||
\(688\) | 4.50939 | 0.171919 | ||||||||
\(689\) | 51.6205 | 1.96658 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 43.0193 | 1.63653 | 0.818266 | − | 0.574840i | \(-0.194936\pi\) | ||||
0.818266 | + | 0.574840i | \(0.194936\pi\) | |||||||
\(692\) | −27.8696 | −1.05944 | ||||||||
\(693\) | 0.324564 | 0.0123292 | ||||||||
\(694\) | 48.6261 | 1.84582 | ||||||||
\(695\) | −13.2150 | −0.501272 | ||||||||
\(696\) | 7.03257 | 0.266569 | ||||||||
\(697\) | −0.795047 | −0.0301145 | ||||||||
\(698\) | 48.1101 | 1.82099 | ||||||||
\(699\) | −3.05893 | −0.115699 | ||||||||
\(700\) | −1.52076 | −0.0574793 | ||||||||
\(701\) | 2.19600 | 0.0829419 | 0.0414709 | − | 0.999140i | \(-0.486796\pi\) | ||||
0.0414709 | + | 0.999140i | \(0.486796\pi\) | |||||||
\(702\) | −7.31966 | −0.276263 | ||||||||
\(703\) | 36.4463 | 1.37460 | ||||||||
\(704\) | 1.61320 | 0.0607998 | ||||||||
\(705\) | −2.28186 | −0.0859397 | ||||||||
\(706\) | −33.8339 | −1.27336 | ||||||||
\(707\) | 6.48169 | 0.243769 | ||||||||
\(708\) | 21.9088 | 0.823384 | ||||||||
\(709\) | 18.5085 | 0.695100 | 0.347550 | − | 0.937662i | \(-0.387014\pi\) | ||||
0.347550 | + | 0.937662i | \(0.387014\pi\) | |||||||
\(710\) | 0.161296 | 0.00605335 | ||||||||
\(711\) | 6.30863 | 0.236592 | ||||||||
\(712\) | −8.66425 | −0.324706 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0.198589 | 0.00743201 | ||||||||
\(715\) | −1.32692 | −0.0496239 | ||||||||
\(716\) | −19.9267 | −0.744696 | ||||||||
\(717\) | −14.1780 | −0.529488 | ||||||||
\(718\) | 39.5933 | 1.47761 | ||||||||
\(719\) | 9.96118 | 0.371489 | 0.185745 | − | 0.982598i | \(-0.440530\pi\) | ||||
0.185745 | + | 0.982598i | \(0.440530\pi\) | |||||||
\(720\) | 4.62181 | 0.172245 | ||||||||
\(721\) | 1.14974 | 0.0428185 | ||||||||
\(722\) | −36.4541 | −1.35668 | ||||||||
\(723\) | −29.2388 | −1.08740 | ||||||||
\(724\) | −20.2387 | −0.752166 | ||||||||
\(725\) | −9.60667 | −0.356783 | ||||||||
\(726\) | −20.6885 | −0.767823 | ||||||||
\(727\) | −31.8475 | −1.18116 | −0.590579 | − | 0.806980i | \(-0.701100\pi\) | ||||
−0.590579 | + | 0.806980i | \(0.701100\pi\) | |||||||
\(728\) | 2.65384 | 0.0983577 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −4.41349 | −0.163350 | ||||||||
\(731\) | 0.108222 | 0.00400272 | ||||||||
\(732\) | −3.49607 | −0.129218 | ||||||||
\(733\) | 11.0828 | 0.409354 | 0.204677 | − | 0.978830i | \(-0.434386\pi\) | ||||
0.204677 | + | 0.978830i | \(0.434386\pi\) | |||||||
\(734\) | −11.8802 | −0.438506 | ||||||||
\(735\) | −6.11327 | −0.225491 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.996597 | −0.0367101 | ||||||||
\(738\) | −13.6282 | −0.501660 | ||||||||
\(739\) | −33.3039 | −1.22510 | −0.612551 | − | 0.790431i | \(-0.709857\pi\) | ||||
−0.612551 | + | 0.790431i | \(0.709857\pi\) | |||||||
\(740\) | 9.52664 | 0.350206 | ||||||||
\(741\) | −23.7858 | −0.873792 | ||||||||
\(742\) | −24.0066 | −0.881311 | ||||||||
\(743\) | −31.8767 | −1.16944 | −0.584721 | − | 0.811234i | \(-0.698796\pi\) | ||||
−0.584721 | + | 0.811234i | \(0.698796\pi\) | |||||||
\(744\) | 1.99877 | 0.0732785 | ||||||||
\(745\) | 0.317210 | 0.0116217 | ||||||||
\(746\) | −3.89671 | −0.142669 | ||||||||
\(747\) | −4.58813 | −0.167871 | ||||||||
\(748\) | 0.0617419 | 0.00225751 | ||||||||
\(749\) | −6.68427 | −0.244238 | ||||||||
\(750\) | −1.90131 | −0.0694260 | ||||||||
\(751\) | −4.00249 | −0.146053 | −0.0730264 | − | 0.997330i | \(-0.523266\pi\) | ||||
−0.0730264 | + | 0.997330i | \(0.523266\pi\) | |||||||
\(752\) | 10.5463 | 0.384584 | ||||||||
\(753\) | 26.8739 | 0.979340 | ||||||||
\(754\) | −70.3175 | −2.56081 | ||||||||
\(755\) | 20.5282 | 0.747097 | ||||||||
\(756\) | 1.52076 | 0.0553095 | ||||||||
\(757\) | −24.2980 | −0.883124 | −0.441562 | − | 0.897231i | \(-0.645576\pi\) | ||||
−0.441562 | + | 0.897231i | \(0.645576\pi\) | |||||||
\(758\) | 39.4918 | 1.43441 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.52293 | 0.164064 | ||||||||
\(761\) | 24.2036 | 0.877379 | 0.438689 | − | 0.898639i | \(-0.355443\pi\) | ||||
0.438689 | + | 0.898639i | \(0.355443\pi\) | |||||||
\(762\) | 29.4961 | 1.06853 | ||||||||
\(763\) | −0.602901 | −0.0218265 | ||||||||
\(764\) | −19.6274 | −0.710094 | ||||||||
\(765\) | 0.110920 | 0.00401030 | ||||||||
\(766\) | −41.1368 | −1.48633 | ||||||||
\(767\) | 52.2265 | 1.88579 | ||||||||
\(768\) | −20.2893 | −0.732127 | ||||||||
\(769\) | 13.9566 | 0.503288 | 0.251644 | − | 0.967820i | \(-0.419029\pi\) | ||||
0.251644 | + | 0.967820i | \(0.419029\pi\) | |||||||
\(770\) | 0.617097 | 0.0222386 | ||||||||
\(771\) | −23.6429 | −0.851480 | ||||||||
\(772\) | 18.7981 | 0.676560 | ||||||||
\(773\) | −13.9560 | −0.501962 | −0.250981 | − | 0.967992i | \(-0.580753\pi\) | ||||
−0.250981 | + | 0.967992i | \(0.580753\pi\) | |||||||
\(774\) | 1.85506 | 0.0666789 | ||||||||
\(775\) | −2.73037 | −0.0980778 | ||||||||
\(776\) | 9.99278 | 0.358720 | ||||||||
\(777\) | −5.55480 | −0.199277 | ||||||||
\(778\) | −63.9675 | −2.29335 | ||||||||
\(779\) | −44.2857 | −1.58670 | ||||||||
\(780\) | −6.21733 | −0.222616 | ||||||||
\(781\) | −0.0292401 | −0.00104629 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.60667 | 0.343314 | ||||||||
\(784\) | 28.2544 | 1.00908 | ||||||||
\(785\) | −4.24565 | −0.151534 | ||||||||
\(786\) | −17.3841 | −0.620071 | ||||||||
\(787\) | −53.1643 | −1.89510 | −0.947551 | − | 0.319605i | \(-0.896450\pi\) | ||||
−0.947551 | + | 0.319605i | \(0.896450\pi\) | |||||||
\(788\) | −5.18093 | −0.184563 | ||||||||
\(789\) | 11.3133 | 0.402763 | ||||||||
\(790\) | 11.9947 | 0.426751 | ||||||||
\(791\) | −8.05079 | −0.286253 | ||||||||
\(792\) | −0.252317 | −0.00896571 | ||||||||
\(793\) | −8.33398 | −0.295948 | ||||||||
\(794\) | −29.5747 | −1.04957 | ||||||||
\(795\) | −13.4086 | −0.475554 | ||||||||
\(796\) | 20.0889 | 0.712031 | ||||||||
\(797\) | 12.7288 | 0.450876 | 0.225438 | − | 0.974258i | \(-0.427619\pi\) | ||||
0.225438 | + | 0.974258i | \(0.427619\pi\) | |||||||
\(798\) | 11.0618 | 0.391584 | ||||||||
\(799\) | 0.253103 | 0.00895413 | ||||||||
\(800\) | 7.32338 | 0.258921 | ||||||||
\(801\) | −11.8356 | −0.418190 | ||||||||
\(802\) | 73.2308 | 2.58587 | ||||||||
\(803\) | 0.800083 | 0.0282343 | ||||||||
\(804\) | −4.66960 | −0.164684 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −19.9854 | −0.703955 | ||||||||
\(807\) | 5.84484 | 0.205748 | ||||||||
\(808\) | −5.03889 | −0.177268 | ||||||||
\(809\) | −8.00024 | −0.281273 | −0.140637 | − | 0.990061i | \(-0.544915\pi\) | ||||
−0.140637 | + | 0.990061i | \(0.544915\pi\) | |||||||
\(810\) | 1.90131 | 0.0668052 | ||||||||
\(811\) | −35.6166 | −1.25067 | −0.625334 | − | 0.780357i | \(-0.715037\pi\) | ||||
−0.625334 | + | 0.780357i | \(0.715037\pi\) | |||||||
\(812\) | 14.6094 | 0.512691 | ||||||||
\(813\) | 20.0827 | 0.704329 | ||||||||
\(814\) | −3.86574 | −0.135494 | ||||||||
\(815\) | 7.40104 | 0.259247 | ||||||||
\(816\) | −0.512648 | −0.0179463 | ||||||||
\(817\) | 6.02817 | 0.210899 | ||||||||
\(818\) | 67.8383 | 2.37191 | ||||||||
\(819\) | 3.62521 | 0.126675 | ||||||||
\(820\) | −11.5758 | −0.404244 | ||||||||
\(821\) | 32.9309 | 1.14930 | 0.574648 | − | 0.818401i | \(-0.305139\pi\) | ||||
0.574648 | + | 0.818401i | \(0.305139\pi\) | |||||||
\(822\) | −15.6668 | −0.546444 | ||||||||
\(823\) | −10.3159 | −0.359588 | −0.179794 | − | 0.983704i | \(-0.557543\pi\) | ||||
−0.179794 | + | 0.983704i | \(0.557543\pi\) | |||||||
\(824\) | −0.893811 | −0.0311374 | ||||||||
\(825\) | 0.344672 | 0.0119999 | ||||||||
\(826\) | −24.2885 | −0.845105 | ||||||||
\(827\) | 19.6441 | 0.683093 | 0.341546 | − | 0.939865i | \(-0.389049\pi\) | ||||
0.341546 | + | 0.939865i | \(0.389049\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −40.0323 | −1.39038 | −0.695190 | − | 0.718826i | \(-0.744680\pi\) | ||||
−0.695190 | + | 0.718826i | \(0.744680\pi\) | |||||||
\(830\) | −8.72346 | −0.302796 | ||||||||
\(831\) | 22.5451 | 0.782081 | ||||||||
\(832\) | 18.0186 | 0.624682 | ||||||||
\(833\) | 0.678081 | 0.0234941 | ||||||||
\(834\) | 25.1257 | 0.870033 | ||||||||
\(835\) | 3.55092 | 0.122885 | ||||||||
\(836\) | 3.43915 | 0.118945 | ||||||||
\(837\) | 2.73037 | 0.0943754 | ||||||||
\(838\) | −53.2835 | −1.84065 | ||||||||
\(839\) | 38.1380 | 1.31667 | 0.658335 | − | 0.752725i | \(-0.271261\pi\) | ||||
0.658335 | + | 0.752725i | \(0.271261\pi\) | |||||||
\(840\) | −0.689344 | −0.0237846 | ||||||||
\(841\) | 63.2881 | 2.18235 | ||||||||
\(842\) | −56.8439 | −1.95897 | ||||||||
\(843\) | 21.4649 | 0.739290 | ||||||||
\(844\) | −31.6598 | −1.08978 | ||||||||
\(845\) | −1.82096 | −0.0626430 | ||||||||
\(846\) | 4.33852 | 0.149161 | ||||||||
\(847\) | 10.2464 | 0.352071 | ||||||||
\(848\) | 61.9720 | 2.12813 | ||||||||
\(849\) | 25.9275 | 0.889830 | ||||||||
\(850\) | 0.210892 | 0.00723355 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | −0.137006 | −0.00469373 | ||||||||
\(853\) | 15.3040 | 0.523998 | 0.261999 | − | 0.965068i | \(-0.415618\pi\) | ||||
0.261999 | + | 0.965068i | \(0.415618\pi\) | |||||||
\(854\) | 3.87580 | 0.132627 | ||||||||
\(855\) | 6.17844 | 0.211298 | ||||||||
\(856\) | 5.19638 | 0.177609 | ||||||||
\(857\) | −20.8576 | −0.712483 | −0.356242 | − | 0.934394i | \(-0.615942\pi\) | ||||
−0.356242 | + | 0.934394i | \(0.615942\pi\) | |||||||
\(858\) | 2.52288 | 0.0861298 | ||||||||
\(859\) | −48.2744 | −1.64710 | −0.823551 | − | 0.567242i | \(-0.808010\pi\) | ||||
−0.823551 | + | 0.567242i | \(0.808010\pi\) | |||||||
\(860\) | 1.57570 | 0.0537308 | ||||||||
\(861\) | 6.74962 | 0.230027 | ||||||||
\(862\) | −5.69653 | −0.194025 | ||||||||
\(863\) | −38.4817 | −1.30993 | −0.654966 | − | 0.755659i | \(-0.727317\pi\) | ||||
−0.654966 | + | 0.755659i | \(0.727317\pi\) | |||||||
\(864\) | −7.32338 | −0.249146 | ||||||||
\(865\) | 17.2570 | 0.586756 | ||||||||
\(866\) | 6.76283 | 0.229810 | ||||||||
\(867\) | 16.9877 | 0.576932 | ||||||||
\(868\) | 4.15224 | 0.140936 | ||||||||
\(869\) | −2.17441 | −0.0737617 | ||||||||
\(870\) | 18.2652 | 0.619250 | ||||||||
\(871\) | −11.1314 | −0.377175 | ||||||||
\(872\) | 0.468697 | 0.0158721 | ||||||||
\(873\) | 13.6504 | 0.461996 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.941661 | 0.0318340 | ||||||||
\(876\) | 3.74882 | 0.126661 | ||||||||
\(877\) | −0.202222 | −0.00682856 | −0.00341428 | − | 0.999994i | \(-0.501087\pi\) | ||||
−0.00341428 | + | 0.999994i | \(0.501087\pi\) | |||||||
\(878\) | 16.1793 | 0.546026 | ||||||||
\(879\) | 20.0884 | 0.677566 | ||||||||
\(880\) | −1.59301 | −0.0537003 | ||||||||
\(881\) | 57.9770 | 1.95329 | 0.976647 | − | 0.214850i | \(-0.0689263\pi\) | ||||
0.976647 | + | 0.214850i | \(0.0689263\pi\) | |||||||
\(882\) | 11.6232 | 0.391374 | ||||||||
\(883\) | −39.6491 | −1.33430 | −0.667149 | − | 0.744924i | \(-0.732486\pi\) | ||||
−0.667149 | + | 0.744924i | \(0.732486\pi\) | |||||||
\(884\) | 0.689624 | 0.0231946 | ||||||||
\(885\) | −13.5660 | −0.456017 | ||||||||
\(886\) | 28.3579 | 0.952702 | ||||||||
\(887\) | −5.67369 | −0.190504 | −0.0952520 | − | 0.995453i | \(-0.530366\pi\) | ||||
−0.0952520 | + | 0.995453i | \(0.530366\pi\) | |||||||
\(888\) | 4.31832 | 0.144913 | ||||||||
\(889\) | −14.6086 | −0.489955 | ||||||||
\(890\) | −22.5031 | −0.754306 | ||||||||
\(891\) | −0.344672 | −0.0115469 | ||||||||
\(892\) | 2.12589 | 0.0711801 | ||||||||
\(893\) | 14.0983 | 0.471782 | ||||||||
\(894\) | −0.603115 | −0.0201712 | ||||||||
\(895\) | 12.3387 | 0.412437 | ||||||||
\(896\) | 5.41256 | 0.180821 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 42.9709 | 1.43396 | ||||||||
\(899\) | 26.2298 | 0.874812 | ||||||||
\(900\) | 1.61498 | 0.0538325 | ||||||||
\(901\) | 1.48728 | 0.0495484 | ||||||||
\(902\) | 4.69725 | 0.156401 | ||||||||
\(903\) | −0.918758 | −0.0305744 | ||||||||
\(904\) | 6.25871 | 0.208162 | ||||||||
\(905\) | 12.5319 | 0.416575 | ||||||||
\(906\) | −39.0304 | −1.29670 | ||||||||
\(907\) | −22.5215 | −0.747814 | −0.373907 | − | 0.927466i | \(-0.621982\pi\) | ||||
−0.373907 | + | 0.927466i | \(0.621982\pi\) | |||||||
\(908\) | −28.7142 | −0.952913 | ||||||||
\(909\) | −6.88325 | −0.228303 | ||||||||
\(910\) | 6.89264 | 0.228489 | ||||||||
\(911\) | −42.7622 | −1.41678 | −0.708388 | − | 0.705823i | \(-0.750577\pi\) | ||||
−0.708388 | + | 0.705823i | \(0.750577\pi\) | |||||||
\(912\) | −28.5556 | −0.945569 | ||||||||
\(913\) | 1.58140 | 0.0523367 | ||||||||
\(914\) | −74.7387 | −2.47214 | ||||||||
\(915\) | 2.16478 | 0.0715655 | ||||||||
\(916\) | −12.0477 | −0.398066 | ||||||||
\(917\) | 8.60984 | 0.284322 | ||||||||
\(918\) | −0.210892 | −0.00696048 | ||||||||
\(919\) | 40.2318 | 1.32713 | 0.663563 | − | 0.748120i | \(-0.269043\pi\) | ||||
0.663563 | + | 0.748120i | \(0.269043\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11.9672 | −0.394333 | ||||||||
\(922\) | −38.4762 | −1.26715 | ||||||||
\(923\) | −0.326596 | −0.0107500 | ||||||||
\(924\) | −0.524163 | −0.0172437 | ||||||||
\(925\) | −5.89894 | −0.193956 | ||||||||
\(926\) | 69.3639 | 2.27944 | ||||||||
\(927\) | −1.22097 | −0.0401019 | ||||||||
\(928\) | −70.3533 | −2.30946 | ||||||||
\(929\) | −8.72947 | −0.286405 | −0.143202 | − | 0.989693i | \(-0.545740\pi\) | ||||
−0.143202 | + | 0.989693i | \(0.545740\pi\) | |||||||
\(930\) | 5.19128 | 0.170229 | ||||||||
\(931\) | 37.7705 | 1.23788 | ||||||||
\(932\) | 4.94010 | 0.161818 | ||||||||
\(933\) | −2.55209 | −0.0835517 | ||||||||
\(934\) | −37.1875 | −1.21681 | ||||||||
\(935\) | −0.0382309 | −0.00125028 | ||||||||
\(936\) | −2.81825 | −0.0921174 | ||||||||
\(937\) | 58.5218 | 1.91182 | 0.955912 | − | 0.293653i | \(-0.0948711\pi\) | ||||
0.955912 | + | 0.293653i | \(0.0948711\pi\) | |||||||
\(938\) | 5.17679 | 0.169028 | ||||||||
\(939\) | −30.7169 | −1.00241 | ||||||||
\(940\) | 3.68514 | 0.120196 | ||||||||
\(941\) | 8.73847 | 0.284866 | 0.142433 | − | 0.989804i | \(-0.454507\pi\) | ||||
0.142433 | + | 0.989804i | \(0.454507\pi\) | |||||||
\(942\) | 8.07230 | 0.263010 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 62.6996 | 2.04070 | ||||||||
\(945\) | −0.941661 | −0.0306323 | ||||||||
\(946\) | −0.639389 | −0.0207883 | ||||||||
\(947\) | 35.4912 | 1.15331 | 0.576654 | − | 0.816988i | \(-0.304358\pi\) | ||||
0.576654 | + | 0.816988i | \(0.304358\pi\) | |||||||
\(948\) | −10.1883 | −0.330900 | ||||||||
\(949\) | 8.93649 | 0.290091 | ||||||||
\(950\) | 11.7471 | 0.381127 | ||||||||
\(951\) | −32.9632 | −1.06891 | ||||||||
\(952\) | 0.0764617 | 0.00247814 | ||||||||
\(953\) | 59.0366 | 1.91238 | 0.956191 | − | 0.292744i | \(-0.0945682\pi\) | ||||
0.956191 | + | 0.292744i | \(0.0945682\pi\) | |||||||
\(954\) | 25.4939 | 0.825396 | ||||||||
\(955\) | 12.1534 | 0.393274 | ||||||||
\(956\) | 22.8972 | 0.740548 | ||||||||
\(957\) | −3.31115 | −0.107034 | ||||||||
\(958\) | 31.8273 | 1.02829 | ||||||||
\(959\) | 7.75932 | 0.250561 | ||||||||
\(960\) | −4.68039 | −0.151059 | ||||||||
\(961\) | −23.5451 | −0.759519 | ||||||||
\(962\) | −43.1782 | −1.39212 | ||||||||
\(963\) | 7.09838 | 0.228742 | ||||||||
\(964\) | 47.2199 | 1.52085 | ||||||||
\(965\) | −11.6399 | −0.374702 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −10.2838 | −0.330704 | −0.165352 | − | 0.986235i | \(-0.552876\pi\) | ||||
−0.165352 | + | 0.986235i | \(0.552876\pi\) | |||||||
\(968\) | −7.96559 | −0.256024 | ||||||||
\(969\) | −0.685310 | −0.0220153 | ||||||||
\(970\) | 25.9536 | 0.833320 | ||||||||
\(971\) | 29.3045 | 0.940428 | 0.470214 | − | 0.882553i | \(-0.344177\pi\) | ||||
0.470214 | + | 0.882553i | \(0.344177\pi\) | |||||||
\(972\) | −1.61498 | −0.0518004 | ||||||||
\(973\) | −12.4440 | −0.398937 | ||||||||
\(974\) | −2.40038 | −0.0769130 | ||||||||
\(975\) | 3.84980 | 0.123292 | ||||||||
\(976\) | −10.0052 | −0.320259 | ||||||||
\(977\) | 49.6960 | 1.58991 | 0.794957 | − | 0.606666i | \(-0.207493\pi\) | ||||
0.794957 | + | 0.606666i | \(0.207493\pi\) | |||||||
\(978\) | −14.0717 | −0.449962 | ||||||||
\(979\) | 4.07939 | 0.130378 | ||||||||
\(980\) | 9.87279 | 0.315375 | ||||||||
\(981\) | 0.640252 | 0.0204417 | ||||||||
\(982\) | −3.01598 | −0.0962437 | ||||||||
\(983\) | −46.8606 | −1.49462 | −0.747310 | − | 0.664475i | \(-0.768655\pi\) | ||||
−0.747310 | + | 0.664475i | \(0.768655\pi\) | |||||||
\(984\) | −5.24718 | −0.167274 | ||||||||
\(985\) | 3.20805 | 0.102217 | ||||||||
\(986\) | −2.02597 | −0.0645201 | ||||||||
\(987\) | −2.14874 | −0.0683951 | ||||||||
\(988\) | 38.4134 | 1.22209 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −0.655328 | −0.0208277 | ||||||||
\(991\) | 49.5901 | 1.57528 | 0.787640 | − | 0.616135i | \(-0.211303\pi\) | ||||
0.787640 | + | 0.616135i | \(0.211303\pi\) | |||||||
\(992\) | −19.9955 | −0.634859 | ||||||||
\(993\) | −22.3176 | −0.708227 | ||||||||
\(994\) | 0.151887 | 0.00481755 | ||||||||
\(995\) | −12.4391 | −0.394346 | ||||||||
\(996\) | 7.40972 | 0.234786 | ||||||||
\(997\) | −28.5373 | −0.903787 | −0.451893 | − | 0.892072i | \(-0.649251\pi\) | ||||
−0.451893 | + | 0.892072i | \(0.649251\pi\) | |||||||
\(998\) | 26.4973 | 0.838758 | ||||||||
\(999\) | 5.89894 | 0.186634 |
(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 | 7935.2.a.bd.1.2 | ✓ | 6 | |
23.22 | odd | 2 | 7935.2.a.be.1.2 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7935.2.a.bd.1.2 | ✓ | 6 | 1.1 | even | 1 | trivial | |
7935.2.a.be.1.2 | yes | 6 | 23.22 | odd | 2 |