Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1225,2,Mod(1,1225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1225, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1225.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1225 = 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1225.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: | \(9.78167424761\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 6x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-2.28825\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1225.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.61803 | 1.85123 | 0.925615 | − | 0.378467i | \(-0.123549\pi\) | ||||
0.925615 | + | 0.378467i | \(0.123549\pi\) | |||||||
\(3\) | −2.28825 | −1.32112 | −0.660560 | − | 0.750774i | \(-0.729681\pi\) | ||||
−0.660560 | + | 0.750774i | \(0.729681\pi\) | |||||||
\(4\) | 4.85410 | 2.42705 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −5.99070 | −2.44569 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 7.47214 | 2.64180 | ||||||||
\(9\) | 2.23607 | 0.745356 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.23607 | −0.674200 | −0.337100 | − | 0.941469i | \(-0.609446\pi\) | ||||
−0.337100 | + | 0.941469i | \(0.609446\pi\) | |||||||
\(12\) | −11.1074 | −3.20642 | ||||||||
\(13\) | 5.45052 | 1.51170 | 0.755852 | − | 0.654743i | \(-0.227223\pi\) | ||||
0.755852 | + | 0.654743i | \(0.227223\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 9.85410 | 2.46353 | ||||||||
\(17\) | 1.08036 | 0.262027 | 0.131013 | − | 0.991381i | \(-0.458177\pi\) | ||||
0.131013 | + | 0.991381i | \(0.458177\pi\) | |||||||
\(18\) | 5.85410 | 1.37983 | ||||||||
\(19\) | 4.24264 | 0.973329 | 0.486664 | − | 0.873589i | \(-0.338214\pi\) | ||||
0.486664 | + | 0.873589i | \(0.338214\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.85410 | −1.24810 | ||||||||
\(23\) | 8.23607 | 1.71734 | 0.858669 | − | 0.512530i | \(-0.171292\pi\) | ||||
0.858669 | + | 0.512530i | \(0.171292\pi\) | |||||||
\(24\) | −17.0981 | −3.49013 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 14.2697 | 2.79851 | ||||||||
\(27\) | 1.74806 | 0.336415 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.23607 | −0.415227 | −0.207614 | − | 0.978211i | \(-0.566570\pi\) | ||||
−0.207614 | + | 0.978211i | \(0.566570\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.62210 | −0.470942 | −0.235471 | − | 0.971881i | \(-0.575663\pi\) | ||||
−0.235471 | + | 0.971881i | \(0.575663\pi\) | |||||||
\(32\) | 10.8541 | 1.91875 | ||||||||
\(33\) | 5.11667 | 0.890698 | ||||||||
\(34\) | 2.82843 | 0.485071 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 10.8541 | 1.80902 | ||||||||
\(37\) | −2.70820 | −0.445226 | −0.222613 | − | 0.974907i | \(-0.571459\pi\) | ||||
−0.222613 | + | 0.974907i | \(0.571459\pi\) | |||||||
\(38\) | 11.1074 | 1.80185 | ||||||||
\(39\) | −12.4721 | −1.99714 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.94510 | −1.24082 | −0.620408 | − | 0.784279i | \(-0.713033\pi\) | ||||
−0.620408 | + | 0.784279i | \(0.713033\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.00000 | 0.762493 | 0.381246 | − | 0.924473i | \(-0.375495\pi\) | ||||
0.381246 | + | 0.924473i | \(0.375495\pi\) | |||||||
\(44\) | −10.8541 | −1.63632 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 21.5623 | 3.17919 | ||||||||
\(47\) | 9.48683 | 1.38380 | 0.691898 | − | 0.721995i | \(-0.256775\pi\) | ||||
0.691898 | + | 0.721995i | \(0.256775\pi\) | |||||||
\(48\) | −22.5486 | −3.25461 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.47214 | −0.346168 | ||||||||
\(52\) | 26.4574 | 3.66898 | ||||||||
\(53\) | −3.70820 | −0.509361 | −0.254680 | − | 0.967025i | \(-0.581970\pi\) | ||||
−0.254680 | + | 0.967025i | \(0.581970\pi\) | |||||||
\(54\) | 4.57649 | 0.622782 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −9.70820 | −1.28588 | ||||||||
\(58\) | −5.85410 | −0.768681 | ||||||||
\(59\) | 8.94665 | 1.16475 | 0.582377 | − | 0.812919i | \(-0.302123\pi\) | ||||
0.582377 | + | 0.812919i | \(0.302123\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.5216 | −1.60323 | −0.801613 | − | 0.597844i | \(-0.796024\pi\) | ||||
−0.801613 | + | 0.597844i | \(0.796024\pi\) | |||||||
\(62\) | −6.86474 | −0.871822 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.70820 | 1.08853 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 13.3956 | 1.64889 | ||||||||
\(67\) | −4.70820 | −0.575199 | −0.287599 | − | 0.957751i | \(-0.592857\pi\) | ||||
−0.287599 | + | 0.957751i | \(0.592857\pi\) | |||||||
\(68\) | 5.24419 | 0.635952 | ||||||||
\(69\) | −18.8461 | −2.26881 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.47214 | 0.174710 | 0.0873552 | − | 0.996177i | \(-0.472158\pi\) | ||||
0.0873552 | + | 0.996177i | \(0.472158\pi\) | |||||||
\(72\) | 16.7082 | 1.96908 | ||||||||
\(73\) | −6.86474 | −0.803457 | −0.401728 | − | 0.915759i | \(-0.631590\pi\) | ||||
−0.401728 | + | 0.915759i | \(0.631590\pi\) | |||||||
\(74\) | −7.09017 | −0.824216 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 20.5942 | 2.36232 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −32.6525 | −3.69716 | ||||||||
\(79\) | 8.70820 | 0.979749 | 0.489875 | − | 0.871793i | \(-0.337043\pi\) | ||||
0.489875 | + | 0.871793i | \(0.337043\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.7082 | −1.18980 | ||||||||
\(82\) | −20.8005 | −2.29704 | ||||||||
\(83\) | −2.62210 | −0.287812 | −0.143906 | − | 0.989591i | \(-0.545966\pi\) | ||||
−0.143906 | + | 0.989591i | \(0.545966\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 13.0902 | 1.41155 | ||||||||
\(87\) | 5.11667 | 0.548565 | ||||||||
\(88\) | −16.7082 | −1.78110 | ||||||||
\(89\) | 4.78282 | 0.506978 | 0.253489 | − | 0.967338i | \(-0.418422\pi\) | ||||
0.253489 | + | 0.967338i | \(0.418422\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 39.9787 | 4.16807 | ||||||||
\(93\) | 6.00000 | 0.622171 | ||||||||
\(94\) | 24.8369 | 2.56173 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −24.8369 | −2.53490 | ||||||||
\(97\) | −19.5927 | −1.98933 | −0.994667 | − | 0.103143i | \(-0.967110\pi\) | ||||
−0.994667 | + | 0.103143i | \(0.967110\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.00000 | −0.502519 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.62054 | 0.161250 | 0.0806251 | − | 0.996744i | \(-0.474308\pi\) | ||||
0.0806251 | + | 0.996744i | \(0.474308\pi\) | |||||||
\(102\) | −6.47214 | −0.640837 | ||||||||
\(103\) | −9.48683 | −0.934765 | −0.467383 | − | 0.884055i | \(-0.654803\pi\) | ||||
−0.467383 | + | 0.884055i | \(0.654803\pi\) | |||||||
\(104\) | 40.7271 | 3.99362 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.70820 | −0.942944 | ||||||||
\(107\) | 6.00000 | 0.580042 | 0.290021 | − | 0.957020i | \(-0.406338\pi\) | ||||
0.290021 | + | 0.957020i | \(0.406338\pi\) | |||||||
\(108\) | 8.48528 | 0.816497 | ||||||||
\(109\) | −1.00000 | −0.0957826 | −0.0478913 | − | 0.998853i | \(-0.515250\pi\) | ||||
−0.0478913 | + | 0.998853i | \(0.515250\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.19704 | 0.588197 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.2361 | 1.33922 | 0.669608 | − | 0.742714i | \(-0.266462\pi\) | ||||
0.669608 | + | 0.742714i | \(0.266462\pi\) | |||||||
\(114\) | −25.4164 | −2.38046 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −10.8541 | −1.00778 | ||||||||
\(117\) | 12.1877 | 1.12676 | ||||||||
\(118\) | 23.4226 | 2.15623 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.00000 | −0.545455 | ||||||||
\(122\) | −32.7820 | −2.96794 | ||||||||
\(123\) | 18.1803 | 1.63927 | ||||||||
\(124\) | −12.7279 | −1.14300 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.00000 | 0.621150 | 0.310575 | − | 0.950549i | \(-0.399478\pi\) | ||||
0.310575 | + | 0.950549i | \(0.399478\pi\) | |||||||
\(128\) | 1.09017 | 0.0963583 | ||||||||
\(129\) | −11.4412 | −1.00734 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.16073 | −0.188784 | −0.0943918 | − | 0.995535i | \(-0.530091\pi\) | ||||
−0.0943918 | + | 0.995535i | \(0.530091\pi\) | |||||||
\(132\) | 24.8369 | 2.16177 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −12.3262 | −1.06482 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 8.07262 | 0.692221 | ||||||||
\(137\) | −6.00000 | −0.512615 | −0.256307 | − | 0.966595i | \(-0.582506\pi\) | ||||
−0.256307 | + | 0.966595i | \(0.582506\pi\) | |||||||
\(138\) | −49.3399 | −4.20009 | ||||||||
\(139\) | −10.1058 | −0.857165 | −0.428582 | − | 0.903503i | \(-0.640987\pi\) | ||||
−0.428582 | + | 0.903503i | \(0.640987\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −21.7082 | −1.82816 | ||||||||
\(142\) | 3.85410 | 0.323429 | ||||||||
\(143\) | −12.1877 | −1.01919 | ||||||||
\(144\) | 22.0344 | 1.83620 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −17.9721 | −1.48738 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −13.1459 | −1.08059 | ||||||||
\(149\) | −21.6525 | −1.77384 | −0.886920 | − | 0.461923i | \(-0.847160\pi\) | ||||
−0.886920 | + | 0.461923i | \(0.847160\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.4164 | −1.49871 | −0.749353 | − | 0.662171i | \(-0.769635\pi\) | ||||
−0.749353 | + | 0.662171i | \(0.769635\pi\) | |||||||
\(152\) | 31.7016 | 2.57134 | ||||||||
\(153\) | 2.41577 | 0.195303 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −60.5410 | −4.84716 | ||||||||
\(157\) | 4.03631 | 0.322133 | 0.161066 | − | 0.986944i | \(-0.448507\pi\) | ||||
0.161066 | + | 0.986944i | \(0.448507\pi\) | |||||||
\(158\) | 22.7984 | 1.81374 | ||||||||
\(159\) | 8.48528 | 0.672927 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −28.0344 | −2.20259 | ||||||||
\(163\) | −15.7082 | −1.23036 | −0.615181 | − | 0.788386i | \(-0.710917\pi\) | ||||
−0.615181 | + | 0.788386i | \(0.710917\pi\) | |||||||
\(164\) | −38.5663 | −3.01152 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.86474 | −0.532807 | ||||||||
\(167\) | −1.54173 | −0.119303 | −0.0596514 | − | 0.998219i | \(-0.518999\pi\) | ||||
−0.0596514 | + | 0.998219i | \(0.518999\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 16.7082 | 1.28525 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 9.48683 | 0.725476 | ||||||||
\(172\) | 24.2705 | 1.85061 | ||||||||
\(173\) | 4.24264 | 0.322562 | 0.161281 | − | 0.986909i | \(-0.448437\pi\) | ||||
0.161281 | + | 0.986909i | \(0.448437\pi\) | |||||||
\(174\) | 13.3956 | 1.01552 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −22.0344 | −1.66091 | ||||||||
\(177\) | −20.4721 | −1.53878 | ||||||||
\(178\) | 12.5216 | 0.938533 | ||||||||
\(179\) | −9.70820 | −0.725625 | −0.362813 | − | 0.931862i | \(-0.618183\pi\) | ||||
−0.362813 | + | 0.931862i | \(0.618183\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.62054 | 0.120454 | 0.0602271 | − | 0.998185i | \(-0.480818\pi\) | ||||
0.0602271 | + | 0.998185i | \(0.480818\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 28.6525 | 2.11805 | ||||||||
\(184\) | 61.5410 | 4.53686 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 15.7082 | 1.15178 | ||||||||
\(187\) | −2.41577 | −0.176658 | ||||||||
\(188\) | 46.0501 | 3.35855 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 17.1246 | 1.23909 | 0.619547 | − | 0.784960i | \(-0.287316\pi\) | ||||
0.619547 | + | 0.784960i | \(0.287316\pi\) | |||||||
\(192\) | −19.9265 | −1.43807 | ||||||||
\(193\) | 2.70820 | 0.194941 | 0.0974704 | − | 0.995238i | \(-0.468925\pi\) | ||||
0.0974704 | + | 0.995238i | \(0.468925\pi\) | |||||||
\(194\) | −51.2942 | −3.68271 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.9443 | 0.850994 | 0.425497 | − | 0.904960i | \(-0.360099\pi\) | ||||
0.425497 | + | 0.904960i | \(0.360099\pi\) | |||||||
\(198\) | −13.0902 | −0.930278 | ||||||||
\(199\) | 15.7627 | 1.11739 | 0.558693 | − | 0.829374i | \(-0.311303\pi\) | ||||
0.558693 | + | 0.829374i | \(0.311303\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.7735 | 0.759906 | ||||||||
\(202\) | 4.24264 | 0.298511 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −12.0000 | −0.840168 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −24.8369 | −1.73047 | ||||||||
\(207\) | 18.4164 | 1.28003 | ||||||||
\(208\) | 53.7100 | 3.72412 | ||||||||
\(209\) | −9.48683 | −0.656218 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.4164 | −1.33668 | −0.668340 | − | 0.743856i | \(-0.732995\pi\) | ||||
−0.668340 | + | 0.743856i | \(0.732995\pi\) | |||||||
\(212\) | −18.0000 | −1.23625 | ||||||||
\(213\) | −3.36861 | −0.230813 | ||||||||
\(214\) | 15.7082 | 1.07379 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 13.0618 | 0.888741 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −2.61803 | −0.177316 | ||||||||
\(219\) | 15.7082 | 1.06146 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.88854 | 0.396106 | ||||||||
\(222\) | 16.2241 | 1.08889 | ||||||||
\(223\) | −15.3500 | −1.02791 | −0.513957 | − | 0.857816i | \(-0.671821\pi\) | ||||
−0.513957 | + | 0.857816i | \(0.671821\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 37.2705 | 2.47920 | ||||||||
\(227\) | −7.48373 | −0.496713 | −0.248356 | − | 0.968669i | \(-0.579890\pi\) | ||||
−0.248356 | + | 0.968669i | \(0.579890\pi\) | |||||||
\(228\) | −47.1246 | −3.12090 | ||||||||
\(229\) | −7.07107 | −0.467269 | −0.233635 | − | 0.972324i | \(-0.575062\pi\) | ||||
−0.233635 | + | 0.972324i | \(0.575062\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −16.7082 | −1.09695 | ||||||||
\(233\) | 13.4721 | 0.882589 | 0.441294 | − | 0.897362i | \(-0.354519\pi\) | ||||
0.441294 | + | 0.897362i | \(0.354519\pi\) | |||||||
\(234\) | 31.9079 | 2.08589 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 43.4280 | 2.82692 | ||||||||
\(237\) | −19.9265 | −1.29437 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.1246 | −0.719591 | −0.359796 | − | 0.933031i | \(-0.617154\pi\) | ||||
−0.359796 | + | 0.933031i | \(0.617154\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 23.2163 | 1.49549 | 0.747747 | − | 0.663984i | \(-0.231136\pi\) | ||||
0.747747 | + | 0.663984i | \(0.231136\pi\) | |||||||
\(242\) | −15.7082 | −1.00976 | ||||||||
\(243\) | 19.2588 | 1.23545 | ||||||||
\(244\) | −60.7811 | −3.89111 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 47.5967 | 3.03466 | ||||||||
\(247\) | 23.1246 | 1.47138 | ||||||||
\(248\) | −19.5927 | −1.24414 | ||||||||
\(249\) | 6.00000 | 0.380235 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 20.0540 | 1.26580 | 0.632900 | − | 0.774234i | \(-0.281865\pi\) | ||||
0.632900 | + | 0.774234i | \(0.281865\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −18.4164 | −1.15783 | ||||||||
\(254\) | 18.3262 | 1.14989 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −14.5623 | −0.910144 | ||||||||
\(257\) | −16.3516 | −1.01998 | −0.509991 | − | 0.860179i | \(-0.670351\pi\) | ||||
−0.509991 | + | 0.860179i | \(0.670351\pi\) | |||||||
\(258\) | −29.9535 | −1.86482 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.00000 | −0.309492 | ||||||||
\(262\) | −5.65685 | −0.349482 | ||||||||
\(263\) | 12.0557 | 0.743388 | 0.371694 | − | 0.928355i | \(-0.378777\pi\) | ||||
0.371694 | + | 0.928355i | \(0.378777\pi\) | |||||||
\(264\) | 38.2325 | 2.35305 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10.9443 | −0.669779 | ||||||||
\(268\) | −22.8541 | −1.39604 | ||||||||
\(269\) | −5.86319 | −0.357485 | −0.178742 | − | 0.983896i | \(-0.557203\pi\) | ||||
−0.178742 | + | 0.983896i | \(0.557203\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.9358 | −0.846540 | −0.423270 | − | 0.906004i | \(-0.639118\pi\) | ||||
−0.423270 | + | 0.906004i | \(0.639118\pi\) | |||||||
\(272\) | 10.6460 | 0.645509 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −15.7082 | −0.948967 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −91.4811 | −5.50652 | ||||||||
\(277\) | −24.0000 | −1.44202 | −0.721010 | − | 0.692925i | \(-0.756322\pi\) | ||||
−0.721010 | + | 0.692925i | \(0.756322\pi\) | |||||||
\(278\) | −26.4574 | −1.58681 | ||||||||
\(279\) | −5.86319 | −0.351020 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.5967 | 1.46732 | 0.733659 | − | 0.679517i | \(-0.237811\pi\) | ||||
0.733659 | + | 0.679517i | \(0.237811\pi\) | |||||||
\(282\) | −56.8328 | −3.38434 | ||||||||
\(283\) | −1.82688 | −0.108596 | −0.0542982 | − | 0.998525i | \(-0.517292\pi\) | ||||
−0.0542982 | + | 0.998525i | \(0.517292\pi\) | |||||||
\(284\) | 7.14590 | 0.424031 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −31.9079 | −1.88675 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 24.2705 | 1.43015 | ||||||||
\(289\) | −15.8328 | −0.931342 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 44.8328 | 2.62815 | ||||||||
\(292\) | −33.3221 | −1.95003 | ||||||||
\(293\) | −22.6761 | −1.32475 | −0.662377 | − | 0.749171i | \(-0.730452\pi\) | ||||
−0.662377 | + | 0.749171i | \(0.730452\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −20.2361 | −1.17620 | ||||||||
\(297\) | −3.90879 | −0.226811 | ||||||||
\(298\) | −56.6869 | −3.28378 | ||||||||
\(299\) | 44.8909 | 2.59611 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −48.2148 | −2.77445 | ||||||||
\(303\) | −3.70820 | −0.213031 | ||||||||
\(304\) | 41.8074 | 2.39782 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 6.32456 | 0.361551 | ||||||||
\(307\) | 33.5285 | 1.91357 | 0.956785 | − | 0.290795i | \(-0.0939199\pi\) | ||||
0.956785 | + | 0.290795i | \(0.0939199\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 21.7082 | 1.23494 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.8902 | −0.901051 | −0.450525 | − | 0.892764i | \(-0.648763\pi\) | ||||
−0.450525 | + | 0.892764i | \(0.648763\pi\) | |||||||
\(312\) | −93.1935 | −5.27604 | ||||||||
\(313\) | 21.2132 | 1.19904 | 0.599521 | − | 0.800359i | \(-0.295358\pi\) | ||||
0.599521 | + | 0.800359i | \(0.295358\pi\) | |||||||
\(314\) | 10.5672 | 0.596341 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 42.2705 | 2.37790 | ||||||||
\(317\) | 5.94427 | 0.333864 | 0.166932 | − | 0.985968i | \(-0.446614\pi\) | ||||
0.166932 | + | 0.985968i | \(0.446614\pi\) | |||||||
\(318\) | 22.2148 | 1.24574 | ||||||||
\(319\) | 5.00000 | 0.279946 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −13.7295 | −0.766304 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.58359 | 0.255038 | ||||||||
\(324\) | −51.9787 | −2.88771 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −41.1246 | −2.27768 | ||||||||
\(327\) | 2.28825 | 0.126540 | ||||||||
\(328\) | −59.3669 | −3.27799 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.7082 | −0.808436 | −0.404218 | − | 0.914663i | \(-0.632456\pi\) | ||||
−0.404218 | + | 0.914663i | \(0.632456\pi\) | |||||||
\(332\) | −12.7279 | −0.698535 | ||||||||
\(333\) | −6.05573 | −0.331852 | ||||||||
\(334\) | −4.03631 | −0.220857 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.1246 | 0.932837 | 0.466419 | − | 0.884564i | \(-0.345544\pi\) | ||||
0.466419 | + | 0.884564i | \(0.345544\pi\) | |||||||
\(338\) | 43.7426 | 2.37929 | ||||||||
\(339\) | −32.5756 | −1.76926 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.86319 | 0.317509 | ||||||||
\(342\) | 24.8369 | 1.34302 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 37.3607 | 2.01435 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 11.1074 | 0.597136 | ||||||||
\(347\) | −3.65248 | −0.196075 | −0.0980376 | − | 0.995183i | \(-0.531257\pi\) | ||||
−0.0980376 | + | 0.995183i | \(0.531257\pi\) | |||||||
\(348\) | 24.8369 | 1.33139 | ||||||||
\(349\) | 17.9721 | 0.962025 | 0.481013 | − | 0.876714i | \(-0.340269\pi\) | ||||
0.481013 | + | 0.876714i | \(0.340269\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.52786 | 0.508560 | ||||||||
\(352\) | −24.2705 | −1.29362 | ||||||||
\(353\) | 16.3516 | 0.870306 | 0.435153 | − | 0.900356i | \(-0.356694\pi\) | ||||
0.435153 | + | 0.900356i | \(0.356694\pi\) | |||||||
\(354\) | −53.5967 | −2.84864 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 23.2163 | 1.23046 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −25.4164 | −1.34330 | ||||||||
\(359\) | 17.9443 | 0.947062 | 0.473531 | − | 0.880777i | \(-0.342979\pi\) | ||||
0.473531 | + | 0.880777i | \(0.342979\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.00000 | −0.0526316 | ||||||||
\(362\) | 4.24264 | 0.222988 | ||||||||
\(363\) | 13.7295 | 0.720610 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 75.0132 | 3.92100 | ||||||||
\(367\) | −18.1784 | −0.948907 | −0.474454 | − | 0.880281i | \(-0.657354\pi\) | ||||
−0.474454 | + | 0.880281i | \(0.657354\pi\) | |||||||
\(368\) | 81.1591 | 4.23071 | ||||||||
\(369\) | −17.7658 | −0.924850 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 29.1246 | 1.51004 | ||||||||
\(373\) | 24.1246 | 1.24913 | 0.624563 | − | 0.780975i | \(-0.285277\pi\) | ||||
0.624563 | + | 0.780975i | \(0.285277\pi\) | |||||||
\(374\) | −6.32456 | −0.327035 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 70.8869 | 3.65571 | ||||||||
\(377\) | −12.1877 | −0.627701 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −19.0000 | −0.975964 | −0.487982 | − | 0.872854i | \(-0.662267\pi\) | ||||
−0.487982 | + | 0.872854i | \(0.662267\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −16.0177 | −0.820613 | ||||||||
\(382\) | 44.8328 | 2.29385 | ||||||||
\(383\) | 8.94665 | 0.457153 | 0.228576 | − | 0.973526i | \(-0.426593\pi\) | ||||
0.228576 | + | 0.973526i | \(0.426593\pi\) | |||||||
\(384\) | −2.49458 | −0.127301 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 7.09017 | 0.360880 | ||||||||
\(387\) | 11.1803 | 0.568329 | ||||||||
\(388\) | −95.1048 | −4.82821 | ||||||||
\(389\) | 32.2361 | 1.63443 | 0.817217 | − | 0.576330i | \(-0.195516\pi\) | ||||
0.817217 | + | 0.576330i | \(0.195516\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.89794 | 0.449988 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.94427 | 0.249406 | ||||||||
\(394\) | 31.2705 | 1.57539 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −24.2705 | −1.21964 | ||||||||
\(397\) | 9.89949 | 0.496841 | 0.248421 | − | 0.968652i | \(-0.420088\pi\) | ||||
0.248421 | + | 0.968652i | \(0.420088\pi\) | |||||||
\(398\) | 41.2672 | 2.06854 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −35.0689 | −1.75126 | −0.875628 | − | 0.482986i | \(-0.839552\pi\) | ||||
−0.875628 | + | 0.482986i | \(0.839552\pi\) | |||||||
\(402\) | 28.2055 | 1.40676 | ||||||||
\(403\) | −14.2918 | −0.711925 | ||||||||
\(404\) | 7.86629 | 0.391362 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.05573 | 0.300171 | ||||||||
\(408\) | −18.4721 | −0.914507 | ||||||||
\(409\) | 23.2163 | 1.14797 | 0.573986 | − | 0.818865i | \(-0.305396\pi\) | ||||
0.573986 | + | 0.818865i | \(0.305396\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13.7295 | 0.677225 | ||||||||
\(412\) | −46.0501 | −2.26872 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 48.2148 | 2.36963 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 59.1605 | 2.90058 | ||||||||
\(417\) | 23.1246 | 1.13242 | ||||||||
\(418\) | −24.8369 | −1.21481 | ||||||||
\(419\) | 33.3221 | 1.62789 | 0.813946 | − | 0.580940i | \(-0.197315\pi\) | ||||
0.813946 | + | 0.580940i | \(0.197315\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −22.7082 | −1.10673 | −0.553365 | − | 0.832939i | \(-0.686657\pi\) | ||||
−0.553365 | + | 0.832939i | \(0.686657\pi\) | |||||||
\(422\) | −50.8328 | −2.47450 | ||||||||
\(423\) | 21.2132 | 1.03142 | ||||||||
\(424\) | −27.7082 | −1.34563 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −8.81913 | −0.427288 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 29.1246 | 1.40779 | ||||||||
\(429\) | 27.8885 | 1.34647 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.2361 | 0.541222 | 0.270611 | − | 0.962689i | \(-0.412774\pi\) | ||||
0.270611 | + | 0.962689i | \(0.412774\pi\) | |||||||
\(432\) | 17.2256 | 0.828767 | ||||||||
\(433\) | 24.2179 | 1.16384 | 0.581918 | − | 0.813247i | \(-0.302302\pi\) | ||||
0.581918 | + | 0.813247i | \(0.302302\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.85410 | −0.232469 | ||||||||
\(437\) | 34.9427 | 1.67153 | ||||||||
\(438\) | 41.1246 | 1.96501 | ||||||||
\(439\) | −10.6947 | −0.510431 | −0.255215 | − | 0.966884i | \(-0.582146\pi\) | ||||
−0.255215 | + | 0.966884i | \(0.582146\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 15.4164 | 0.733284 | ||||||||
\(443\) | −2.18034 | −0.103591 | −0.0517955 | − | 0.998658i | \(-0.516494\pi\) | ||||
−0.0517955 | + | 0.998658i | \(0.516494\pi\) | |||||||
\(444\) | 30.0810 | 1.42758 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −40.1869 | −1.90290 | ||||||||
\(447\) | 49.5462 | 2.34345 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 36.5967 | 1.72711 | 0.863554 | − | 0.504257i | \(-0.168234\pi\) | ||||
0.863554 | + | 0.504257i | \(0.168234\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 17.7658 | 0.836558 | ||||||||
\(452\) | 69.1033 | 3.25035 | ||||||||
\(453\) | 42.1413 | 1.97997 | ||||||||
\(454\) | −19.5927 | −0.919529 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −72.5410 | −3.39704 | ||||||||
\(457\) | 20.7082 | 0.968689 | 0.484344 | − | 0.874877i | \(-0.339058\pi\) | ||||
0.484344 | + | 0.874877i | \(0.339058\pi\) | |||||||
\(458\) | −18.5123 | −0.865023 | ||||||||
\(459\) | 1.88854 | 0.0881497 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −30.2387 | −1.40836 | −0.704178 | − | 0.710024i | \(-0.748684\pi\) | ||||
−0.704178 | + | 0.710024i | \(0.748684\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.0000 | −0.650635 | −0.325318 | − | 0.945605i | \(-0.605471\pi\) | ||||
−0.325318 | + | 0.945605i | \(0.605471\pi\) | |||||||
\(464\) | −22.0344 | −1.02292 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 35.2705 | 1.63387 | ||||||||
\(467\) | −41.2672 | −1.90962 | −0.954810 | − | 0.297217i | \(-0.903941\pi\) | ||||
−0.954810 | + | 0.297217i | \(0.903941\pi\) | |||||||
\(468\) | 59.1605 | 2.73470 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.23607 | −0.425576 | ||||||||
\(472\) | 66.8506 | 3.07705 | ||||||||
\(473\) | −11.1803 | −0.514073 | ||||||||
\(474\) | −52.1683 | −2.39617 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.29180 | −0.379655 | ||||||||
\(478\) | −29.1246 | −1.33213 | ||||||||
\(479\) | −12.1877 | −0.556872 | −0.278436 | − | 0.960455i | \(-0.589816\pi\) | ||||
−0.278436 | + | 0.960455i | \(0.589816\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −14.7611 | −0.673050 | ||||||||
\(482\) | 60.7811 | 2.76850 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −29.1246 | −1.32385 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 50.4202 | 2.28711 | ||||||||
\(487\) | 15.2918 | 0.692937 | 0.346469 | − | 0.938062i | \(-0.387381\pi\) | ||||
0.346469 | + | 0.938062i | \(0.387381\pi\) | |||||||
\(488\) | −93.5630 | −4.23540 | ||||||||
\(489\) | 35.9442 | 1.62545 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.47214 | −0.0664366 | −0.0332183 | − | 0.999448i | \(-0.510576\pi\) | ||||
−0.0332183 | + | 0.999448i | \(0.510576\pi\) | |||||||
\(492\) | 88.2492 | 3.97858 | ||||||||
\(493\) | −2.41577 | −0.108801 | ||||||||
\(494\) | 60.5410 | 2.72387 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −25.8384 | −1.16018 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 15.7082 | 0.703901 | ||||||||
\(499\) | 1.41641 | 0.0634071 | 0.0317036 | − | 0.999497i | \(-0.489907\pi\) | ||||
0.0317036 | + | 0.999497i | \(0.489907\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.52786 | 0.157613 | ||||||||
\(502\) | 52.5021 | 2.34328 | ||||||||
\(503\) | −8.40647 | −0.374826 | −0.187413 | − | 0.982281i | \(-0.560010\pi\) | ||||
−0.187413 | + | 0.982281i | \(0.560010\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −48.2148 | −2.14341 | ||||||||
\(507\) | −38.2325 | −1.69796 | ||||||||
\(508\) | 33.9787 | 1.50756 | ||||||||
\(509\) | −10.0270 | −0.444440 | −0.222220 | − | 0.974997i | \(-0.571330\pi\) | ||||
−0.222220 | + | 0.974997i | \(0.571330\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −40.3050 | −1.78124 | ||||||||
\(513\) | 7.41641 | 0.327442 | ||||||||
\(514\) | −42.8090 | −1.88822 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −55.5369 | −2.44488 | ||||||||
\(517\) | −21.2132 | −0.932956 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9.70820 | −0.426143 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 23.3739 | 1.02403 | 0.512015 | − | 0.858976i | \(-0.328899\pi\) | ||||
0.512015 | + | 0.858976i | \(0.328899\pi\) | |||||||
\(522\) | −13.0902 | −0.572941 | ||||||||
\(523\) | −22.2148 | −0.971383 | −0.485692 | − | 0.874130i | \(-0.661432\pi\) | ||||
−0.485692 | + | 0.874130i | \(0.661432\pi\) | |||||||
\(524\) | −10.4884 | −0.458187 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 31.5623 | 1.37618 | ||||||||
\(527\) | −2.83282 | −0.123399 | ||||||||
\(528\) | 50.4202 | 2.19426 | ||||||||
\(529\) | 44.8328 | 1.94925 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 20.0053 | 0.868157 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −43.3050 | −1.87575 | ||||||||
\(534\) | −28.6525 | −1.23991 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −35.1803 | −1.51956 | ||||||||
\(537\) | 22.2148 | 0.958637 | ||||||||
\(538\) | −15.3500 | −0.661786 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.70820 | 0.202421 | 0.101211 | − | 0.994865i | \(-0.467728\pi\) | ||||
0.101211 | + | 0.994865i | \(0.467728\pi\) | |||||||
\(542\) | −36.4844 | −1.56714 | ||||||||
\(543\) | −3.70820 | −0.159134 | ||||||||
\(544\) | 11.7264 | 0.502764 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 29.0000 | 1.23995 | 0.619975 | − | 0.784621i | \(-0.287143\pi\) | ||||
0.619975 | + | 0.784621i | \(0.287143\pi\) | |||||||
\(548\) | −29.1246 | −1.24414 | ||||||||
\(549\) | −27.9991 | −1.19497 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.48683 | −0.404153 | ||||||||
\(552\) | −140.821 | −5.99374 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −62.8328 | −2.66951 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −49.0547 | −2.08038 | ||||||||
\(557\) | −24.5967 | −1.04220 | −0.521099 | − | 0.853496i | \(-0.674478\pi\) | ||||
−0.521099 | + | 0.853496i | \(0.674478\pi\) | |||||||
\(558\) | −15.3500 | −0.649818 | ||||||||
\(559\) | 27.2526 | 1.15266 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.52786 | 0.233387 | ||||||||
\(562\) | 64.3951 | 2.71634 | ||||||||
\(563\) | −20.1328 | −0.848498 | −0.424249 | − | 0.905546i | \(-0.639462\pi\) | ||||
−0.424249 | + | 0.905546i | \(0.639462\pi\) | |||||||
\(564\) | −105.374 | −4.43704 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −4.78282 | −0.201037 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 11.0000 | 0.461550 | ||||||||
\(569\) | −12.0557 | −0.505402 | −0.252701 | − | 0.967544i | \(-0.581319\pi\) | ||||
−0.252701 | + | 0.967544i | \(0.581319\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.416408 | −0.0174261 | −0.00871306 | − | 0.999962i | \(-0.502773\pi\) | ||||
−0.00871306 | + | 0.999962i | \(0.502773\pi\) | |||||||
\(572\) | −59.1605 | −2.47363 | ||||||||
\(573\) | −39.1853 | −1.63699 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 19.4721 | 0.811339 | ||||||||
\(577\) | −33.7047 | −1.40314 | −0.701572 | − | 0.712598i | \(-0.747518\pi\) | ||||
−0.701572 | + | 0.712598i | \(0.747518\pi\) | |||||||
\(578\) | −41.4508 | −1.72413 | ||||||||
\(579\) | −6.19704 | −0.257540 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 117.374 | 4.86530 | ||||||||
\(583\) | 8.29180 | 0.343411 | ||||||||
\(584\) | −51.2942 | −2.12257 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −59.3669 | −2.45242 | ||||||||
\(587\) | 15.3500 | 0.633563 | 0.316782 | − | 0.948499i | \(-0.397398\pi\) | ||||
0.316782 | + | 0.948499i | \(0.397398\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11.1246 | −0.458382 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −27.3314 | −1.12426 | ||||||||
\(592\) | −26.6869 | −1.09683 | ||||||||
\(593\) | −11.7264 | −0.481544 | −0.240772 | − | 0.970582i | \(-0.577401\pi\) | ||||
−0.240772 | + | 0.970582i | \(0.577401\pi\) | |||||||
\(594\) | −10.2333 | −0.419879 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −105.103 | −4.30520 | ||||||||
\(597\) | −36.0689 | −1.47620 | ||||||||
\(598\) | 117.526 | 4.80599 | ||||||||
\(599\) | −29.1803 | −1.19228 | −0.596138 | − | 0.802882i | \(-0.703299\pi\) | ||||
−0.596138 | + | 0.802882i | \(0.703299\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 46.4326 | 1.89403 | 0.947013 | − | 0.321196i | \(-0.104085\pi\) | ||||
0.947013 | + | 0.321196i | \(0.104085\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10.5279 | −0.428728 | ||||||||
\(604\) | −89.3951 | −3.63744 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −9.70820 | −0.394369 | ||||||||
\(607\) | 21.1831 | 0.859796 | 0.429898 | − | 0.902878i | \(-0.358550\pi\) | ||||
0.429898 | + | 0.902878i | \(0.358550\pi\) | |||||||
\(608\) | 46.0501 | 1.86758 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 51.7082 | 2.09189 | ||||||||
\(612\) | 11.7264 | 0.474010 | ||||||||
\(613\) | −12.4164 | −0.501494 | −0.250747 | − | 0.968053i | \(-0.580676\pi\) | ||||
−0.250747 | + | 0.968053i | \(0.580676\pi\) | |||||||
\(614\) | 87.7787 | 3.54246 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −25.3607 | −1.02098 | −0.510491 | − | 0.859883i | \(-0.670536\pi\) | ||||
−0.510491 | + | 0.859883i | \(0.670536\pi\) | |||||||
\(618\) | 56.8328 | 2.28615 | ||||||||
\(619\) | 19.1800 | 0.770909 | 0.385455 | − | 0.922727i | \(-0.374045\pi\) | ||||
0.385455 | + | 0.922727i | \(0.374045\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 14.3972 | 0.577739 | ||||||||
\(622\) | −41.6011 | −1.66805 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −122.902 | −4.92001 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 55.5369 | 2.21970 | ||||||||
\(627\) | 21.7082 | 0.866942 | ||||||||
\(628\) | 19.5927 | 0.781832 | ||||||||
\(629\) | −2.92584 | −0.116661 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.1246 | 0.482673 | 0.241337 | − | 0.970441i | \(-0.422414\pi\) | ||||
0.241337 | + | 0.970441i | \(0.422414\pi\) | |||||||
\(632\) | 65.0689 | 2.58830 | ||||||||
\(633\) | 44.4295 | 1.76591 | ||||||||
\(634\) | 15.5623 | 0.618058 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 41.1884 | 1.63323 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 13.0902 | 0.518245 | ||||||||
\(639\) | 3.29180 | 0.130221 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −25.4721 | −1.00609 | −0.503044 | − | 0.864261i | \(-0.667787\pi\) | ||||
−0.503044 | + | 0.864261i | \(0.667787\pi\) | |||||||
\(642\) | −35.9442 | −1.41861 | ||||||||
\(643\) | 3.24109 | 0.127816 | 0.0639080 | − | 0.997956i | \(-0.479644\pi\) | ||||
0.0639080 | + | 0.997956i | \(0.479644\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 12.0000 | 0.472134 | ||||||||
\(647\) | 6.40337 | 0.251742 | 0.125871 | − | 0.992047i | \(-0.459827\pi\) | ||||
0.125871 | + | 0.992047i | \(0.459827\pi\) | |||||||
\(648\) | −80.0132 | −3.14321 | ||||||||
\(649\) | −20.0053 | −0.785278 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −76.2492 | −2.98615 | ||||||||
\(653\) | −25.4164 | −0.994621 | −0.497310 | − | 0.867573i | \(-0.665679\pi\) | ||||
−0.497310 | + | 0.867573i | \(0.665679\pi\) | |||||||
\(654\) | 5.99070 | 0.234255 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −78.2918 | −3.05678 | ||||||||
\(657\) | −15.3500 | −0.598861 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 44.8328 | 1.74644 | 0.873219 | − | 0.487328i | \(-0.162028\pi\) | ||||
0.873219 | + | 0.487328i | \(0.162028\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −36.9458 | −1.43702 | −0.718512 | − | 0.695514i | \(-0.755177\pi\) | ||||
−0.718512 | + | 0.695514i | \(0.755177\pi\) | |||||||
\(662\) | −38.5066 | −1.49660 | ||||||||
\(663\) | −13.4744 | −0.523304 | ||||||||
\(664\) | −19.5927 | −0.760343 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −15.8541 | −0.614334 | ||||||||
\(667\) | −18.4164 | −0.713086 | ||||||||
\(668\) | −7.48373 | −0.289554 | ||||||||
\(669\) | 35.1246 | 1.35800 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 27.9991 | 1.08089 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.875388 | −0.0337437 | −0.0168719 | − | 0.999858i | \(-0.505371\pi\) | ||||
−0.0168719 | + | 0.999858i | \(0.505371\pi\) | |||||||
\(674\) | 44.8328 | 1.72690 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 81.1033 | 3.11936 | ||||||||
\(677\) | −20.1328 | −0.773768 | −0.386884 | − | 0.922128i | \(-0.626449\pi\) | ||||
−0.386884 | + | 0.922128i | \(0.626449\pi\) | |||||||
\(678\) | −85.2841 | −3.27532 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 17.1246 | 0.656217 | ||||||||
\(682\) | 15.3500 | 0.587783 | ||||||||
\(683\) | −17.0689 | −0.653123 | −0.326561 | − | 0.945176i | \(-0.605890\pi\) | ||||
−0.326561 | + | 0.945176i | \(0.605890\pi\) | |||||||
\(684\) | 46.0501 | 1.76077 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 16.1803 | 0.617318 | ||||||||
\(688\) | 49.2705 | 1.87842 | ||||||||
\(689\) | −20.2117 | −0.770003 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −45.6374 | −1.73613 | −0.868064 | − | 0.496452i | \(-0.834636\pi\) | ||||
−0.868064 | + | 0.496452i | \(0.834636\pi\) | |||||||
\(692\) | 20.5942 | 0.782874 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −9.56231 | −0.362980 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 38.2325 | 1.44920 | ||||||||
\(697\) | −8.58359 | −0.325127 | ||||||||
\(698\) | 47.0516 | 1.78093 | ||||||||
\(699\) | −30.8276 | −1.16601 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.58359 | 0.173120 | 0.0865599 | − | 0.996247i | \(-0.472413\pi\) | ||||
0.0865599 | + | 0.996247i | \(0.472413\pi\) | |||||||
\(702\) | 24.9443 | 0.941461 | ||||||||
\(703\) | −11.4899 | −0.433351 | ||||||||
\(704\) | −19.4721 | −0.733884 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 42.8090 | 1.61114 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −99.3738 | −3.73470 | ||||||||
\(709\) | −10.0000 | −0.375558 | −0.187779 | − | 0.982211i | \(-0.560129\pi\) | ||||
−0.187779 | + | 0.982211i | \(0.560129\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 19.4721 | 0.730262 | ||||||||
\(712\) | 35.7379 | 1.33933 | ||||||||
\(713\) | −21.5958 | −0.808768 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −47.1246 | −1.76113 | ||||||||
\(717\) | 25.4558 | 0.950666 | ||||||||
\(718\) | 46.9787 | 1.75323 | ||||||||
\(719\) | −14.2697 | −0.532168 | −0.266084 | − | 0.963950i | \(-0.585730\pi\) | ||||
−0.266084 | + | 0.963950i | \(0.585730\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −2.61803 | −0.0974331 | ||||||||
\(723\) | −53.1246 | −1.97573 | ||||||||
\(724\) | 7.86629 | 0.292348 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 35.9442 | 1.33402 | ||||||||
\(727\) | 5.65685 | 0.209801 | 0.104901 | − | 0.994483i | \(-0.466548\pi\) | ||||
0.104901 | + | 0.994483i | \(0.466548\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −11.9443 | −0.442380 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.40182 | 0.199793 | ||||||||
\(732\) | 139.082 | 5.14062 | ||||||||
\(733\) | −44.4295 | −1.64104 | −0.820521 | − | 0.571617i | \(-0.806316\pi\) | ||||
−0.820521 | + | 0.571617i | \(0.806316\pi\) | |||||||
\(734\) | −47.5918 | −1.75664 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 89.3951 | 3.29515 | ||||||||
\(737\) | 10.5279 | 0.387799 | ||||||||
\(738\) | −46.5114 | −1.71211 | ||||||||
\(739\) | −20.7082 | −0.761764 | −0.380882 | − | 0.924624i | \(-0.624380\pi\) | ||||
−0.380882 | + | 0.924624i | \(0.624380\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −52.9148 | −1.94387 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 20.2918 | 0.744434 | 0.372217 | − | 0.928146i | \(-0.378598\pi\) | ||||
0.372217 | + | 0.928146i | \(0.378598\pi\) | |||||||
\(744\) | 44.8328 | 1.64365 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 63.1591 | 2.31242 | ||||||||
\(747\) | −5.86319 | −0.214523 | ||||||||
\(748\) | −11.7264 | −0.428759 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26.8328 | −0.979143 | −0.489572 | − | 0.871963i | \(-0.662847\pi\) | ||||
−0.489572 | + | 0.871963i | \(0.662847\pi\) | |||||||
\(752\) | 93.4842 | 3.40902 | ||||||||
\(753\) | −45.8885 | −1.67227 | ||||||||
\(754\) | −31.9079 | −1.16202 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14.4164 | 0.523973 | 0.261987 | − | 0.965072i | \(-0.415622\pi\) | ||||
0.261987 | + | 0.965072i | \(0.415622\pi\) | |||||||
\(758\) | −49.7426 | −1.80673 | ||||||||
\(759\) | 42.1413 | 1.52963 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14.9675 | 0.542570 | 0.271285 | − | 0.962499i | \(-0.412551\pi\) | ||||
0.271285 | + | 0.962499i | \(0.412551\pi\) | |||||||
\(762\) | −41.9349 | −1.51914 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 83.1246 | 3.00734 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 23.4226 | 0.846294 | ||||||||
\(767\) | 48.7639 | 1.76076 | ||||||||
\(768\) | 33.3221 | 1.20241 | ||||||||
\(769\) | 18.1784 | 0.655532 | 0.327766 | − | 0.944759i | \(-0.393704\pi\) | ||||
0.327766 | + | 0.944759i | \(0.393704\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 37.4164 | 1.34752 | ||||||||
\(772\) | 13.1459 | 0.473131 | ||||||||
\(773\) | 5.86319 | 0.210884 | 0.105442 | − | 0.994425i | \(-0.466374\pi\) | ||||
0.105442 | + | 0.994425i | \(0.466374\pi\) | |||||||
\(774\) | 29.2705 | 1.05211 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −146.399 | −5.25542 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 84.3951 | 3.02571 | ||||||||
\(779\) | −33.7082 | −1.20772 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.29180 | −0.117790 | ||||||||
\(782\) | 23.2951 | 0.833032 | ||||||||
\(783\) | −3.90879 | −0.139689 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 12.9443 | 0.461707 | ||||||||
\(787\) | 12.1089 | 0.431637 | 0.215818 | − | 0.976434i | \(-0.430758\pi\) | ||||
0.215818 | + | 0.976434i | \(0.430758\pi\) | |||||||
\(788\) | 57.9787 | 2.06541 | ||||||||
\(789\) | −27.5865 | −0.982104 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −37.3607 | −1.32755 | ||||||||
\(793\) | −68.2492 | −2.42360 | ||||||||
\(794\) | 25.9172 | 0.919768 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 76.5137 | 2.71195 | ||||||||
\(797\) | 30.5424 | 1.08187 | 0.540934 | − | 0.841065i | \(-0.318071\pi\) | ||||
0.540934 | + | 0.841065i | \(0.318071\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.2492 | 0.362591 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10.6947 | 0.377879 | ||||||||
\(802\) | −91.8115 | −3.24198 | ||||||||
\(803\) | 15.3500 | 0.541690 | ||||||||
\(804\) | 52.2958 | 1.84433 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −37.4164 | −1.31794 | ||||||||
\(807\) | 13.4164 | 0.472280 | ||||||||
\(808\) | 12.1089 | 0.425991 | ||||||||
\(809\) | −29.0689 | −1.02201 | −0.511004 | − | 0.859578i | \(-0.670726\pi\) | ||||
−0.511004 | + | 0.859578i | \(0.670726\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.07107 | 0.248299 | 0.124149 | − | 0.992264i | \(-0.460380\pi\) | ||||
0.124149 | + | 0.992264i | \(0.460380\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 31.8885 | 1.11838 | ||||||||
\(814\) | 15.8541 | 0.555686 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −24.3607 | −0.852794 | ||||||||
\(817\) | 21.2132 | 0.742156 | ||||||||
\(818\) | 60.7811 | 2.12516 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 37.4164 | 1.30584 | 0.652921 | − | 0.757426i | \(-0.273543\pi\) | ||||
0.652921 | + | 0.757426i | \(0.273543\pi\) | |||||||
\(822\) | 35.9442 | 1.25370 | ||||||||
\(823\) | 37.5410 | 1.30860 | 0.654299 | − | 0.756236i | \(-0.272964\pi\) | ||||
0.654299 | + | 0.756236i | \(0.272964\pi\) | |||||||
\(824\) | −70.8869 | −2.46946 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7.47214 | 0.259832 | 0.129916 | − | 0.991525i | \(-0.458529\pi\) | ||||
0.129916 | + | 0.991525i | \(0.458529\pi\) | |||||||
\(828\) | 89.3951 | 3.10670 | ||||||||
\(829\) | −46.8453 | −1.62700 | −0.813502 | − | 0.581562i | \(-0.802442\pi\) | ||||
−0.813502 | + | 0.581562i | \(0.802442\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 54.9179 | 1.90508 | ||||||||
\(832\) | 47.4643 | 1.64553 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 60.5410 | 2.09636 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −46.0501 | −1.59267 | ||||||||
\(837\) | −4.58359 | −0.158432 | ||||||||
\(838\) | 87.2385 | 3.01360 | ||||||||
\(839\) | −40.8059 | −1.40877 | −0.704387 | − | 0.709816i | \(-0.748778\pi\) | ||||
−0.704387 | + | 0.709816i | \(0.748778\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.0000 | −0.827586 | ||||||||
\(842\) | −59.4508 | −2.04881 | ||||||||
\(843\) | −56.2834 | −1.93850 | ||||||||
\(844\) | −94.2492 | −3.24419 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 55.5369 | 1.90940 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −36.5410 | −1.25482 | ||||||||
\(849\) | 4.18034 | 0.143469 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −22.3050 | −0.764604 | ||||||||
\(852\) | −16.3516 | −0.560196 | ||||||||
\(853\) | −3.24109 | −0.110973 | −0.0554864 | − | 0.998459i | \(-0.517671\pi\) | ||||
−0.0554864 | + | 0.998459i | \(0.517671\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 44.8328 | 1.53235 | ||||||||
\(857\) | 17.5107 | 0.598156 | 0.299078 | − | 0.954229i | \(-0.403321\pi\) | ||||
0.299078 | + | 0.954229i | \(0.403321\pi\) | |||||||
\(858\) | 73.0132 | 2.49263 | ||||||||
\(859\) | −17.1468 | −0.585041 | −0.292520 | − | 0.956259i | \(-0.594494\pi\) | ||||
−0.292520 | + | 0.956259i | \(0.594494\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 29.4164 | 1.00193 | ||||||||
\(863\) | 43.3607 | 1.47601 | 0.738007 | − | 0.674793i | \(-0.235767\pi\) | ||||
0.738007 | + | 0.674793i | \(0.235767\pi\) | |||||||
\(864\) | 18.9737 | 0.645497 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 63.4032 | 2.15453 | ||||||||
\(867\) | 36.2294 | 1.23041 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −19.4721 | −0.660547 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −25.6622 | −0.869530 | ||||||||
\(872\) | −7.47214 | −0.253038 | ||||||||
\(873\) | −43.8105 | −1.48276 | ||||||||
\(874\) | 91.4811 | 3.09439 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 76.2492 | 2.57622 | ||||||||
\(877\) | −51.7082 | −1.74606 | −0.873031 | − | 0.487665i | \(-0.837849\pi\) | ||||
−0.873031 | + | 0.487665i | \(0.837849\pi\) | |||||||
\(878\) | −27.9991 | −0.944925 | ||||||||
\(879\) | 51.8885 | 1.75016 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −11.1074 | −0.374217 | −0.187109 | − | 0.982339i | \(-0.559912\pi\) | ||||
−0.187109 | + | 0.982339i | \(0.559912\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19.2918 | −0.649221 | −0.324610 | − | 0.945848i | \(-0.605233\pi\) | ||||
−0.324610 | + | 0.945848i | \(0.605233\pi\) | |||||||
\(884\) | 28.5836 | 0.961370 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −5.70820 | −0.191771 | ||||||||
\(887\) | −47.1304 | −1.58248 | −0.791242 | − | 0.611503i | \(-0.790565\pi\) | ||||
−0.791242 | + | 0.611503i | \(0.790565\pi\) | |||||||
\(888\) | 46.3051 | 1.55390 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 23.9443 | 0.802163 | ||||||||
\(892\) | −74.5106 | −2.49480 | ||||||||
\(893\) | 40.2492 | 1.34689 | ||||||||
\(894\) | 129.714 | 4.33827 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −102.721 | −3.42977 | ||||||||
\(898\) | 95.8115 | 3.19727 | ||||||||
\(899\) | 5.86319 | 0.195548 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.00621 | −0.133466 | ||||||||
\(902\) | 46.5114 | 1.54866 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 106.374 | 3.53794 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 110.327 | 3.66538 | ||||||||
\(907\) | 38.8328 | 1.28942 | 0.644711 | − | 0.764426i | \(-0.276978\pi\) | ||||
0.644711 | + | 0.764426i | \(0.276978\pi\) | |||||||
\(908\) | −36.3268 | −1.20555 | ||||||||
\(909\) | 3.62365 | 0.120189 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26.2361 | 0.869240 | 0.434620 | − | 0.900614i | \(-0.356883\pi\) | ||||
0.434620 | + | 0.900614i | \(0.356883\pi\) | |||||||
\(912\) | −95.6656 | −3.16781 | ||||||||
\(913\) | 5.86319 | 0.194043 | ||||||||
\(914\) | 54.2148 | 1.79327 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −34.3237 | −1.13409 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 4.94427 | 0.163185 | ||||||||
\(919\) | −21.8328 | −0.720198 | −0.360099 | − | 0.932914i | \(-0.617257\pi\) | ||||
−0.360099 | + | 0.932914i | \(0.617257\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −76.7214 | −2.52805 | ||||||||
\(922\) | −79.1659 | −2.60719 | ||||||||
\(923\) | 8.02391 | 0.264110 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −36.6525 | −1.20448 | ||||||||
\(927\) | −21.2132 | −0.696733 | ||||||||
\(928\) | −24.2705 | −0.796719 | ||||||||
\(929\) | 0.382559 | 0.0125513 | 0.00627567 | − | 0.999980i | \(-0.498002\pi\) | ||||
0.00627567 | + | 0.999980i | \(0.498002\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 65.3951 | 2.14209 | ||||||||
\(933\) | 36.3607 | 1.19040 | ||||||||
\(934\) | −108.039 | −3.53514 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 91.0685 | 2.97667 | ||||||||
\(937\) | −37.9774 | −1.24067 | −0.620334 | − | 0.784337i | \(-0.713003\pi\) | ||||
−0.620334 | + | 0.784337i | \(0.713003\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −48.5410 | −1.58408 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24.8369 | −0.809658 | −0.404829 | − | 0.914392i | \(-0.632669\pi\) | ||||
−0.404829 | + | 0.914392i | \(0.632669\pi\) | |||||||
\(942\) | −24.1803 | −0.787838 | ||||||||
\(943\) | −65.4364 | −2.13090 | ||||||||
\(944\) | 88.1612 | 2.86940 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −29.2705 | −0.951666 | ||||||||
\(947\) | −12.0000 | −0.389948 | −0.194974 | − | 0.980808i | \(-0.562462\pi\) | ||||
−0.194974 | + | 0.980808i | \(0.562462\pi\) | |||||||
\(948\) | −96.7253 | −3.14149 | ||||||||
\(949\) | −37.4164 | −1.21459 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −13.6020 | −0.441074 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12.5967 | 0.408049 | 0.204024 | − | 0.978966i | \(-0.434598\pi\) | ||||
0.204024 | + | 0.978966i | \(0.434598\pi\) | |||||||
\(954\) | −21.7082 | −0.702829 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −54.0000 | −1.74648 | ||||||||
\(957\) | −11.4412 | −0.369842 | ||||||||
\(958\) | −31.9079 | −1.03090 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.1246 | −0.778213 | ||||||||
\(962\) | −38.6451 | −1.24597 | ||||||||
\(963\) | 13.4164 | 0.432338 | ||||||||
\(964\) | 112.694 | 3.62964 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 34.2492 | 1.10138 | 0.550690 | − | 0.834710i | \(-0.314365\pi\) | ||||
0.550690 | + | 0.834710i | \(0.314365\pi\) | |||||||
\(968\) | −44.8328 | −1.44098 | ||||||||
\(969\) | −10.4884 | −0.336935 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.7279 | −0.408458 | −0.204229 | − | 0.978923i | \(-0.565469\pi\) | ||||
−0.204229 | + | 0.978923i | \(0.565469\pi\) | |||||||
\(972\) | 93.4842 | 2.99851 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 40.0344 | 1.28279 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −123.389 | −3.94959 | ||||||||
\(977\) | −32.2361 | −1.03132 | −0.515662 | − | 0.856792i | \(-0.672454\pi\) | ||||
−0.515662 | + | 0.856792i | \(0.672454\pi\) | |||||||
\(978\) | 94.1032 | 3.00909 | ||||||||
\(979\) | −10.6947 | −0.341805 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.23607 | −0.0713922 | ||||||||
\(982\) | −3.85410 | −0.122989 | ||||||||
\(983\) | 55.5369 | 1.77135 | 0.885676 | − | 0.464304i | \(-0.153696\pi\) | ||||
0.885676 | + | 0.464304i | \(0.153696\pi\) | |||||||
\(984\) | 135.846 | 4.33061 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −6.32456 | −0.201415 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 112.249 | 3.57112 | ||||||||
\(989\) | 41.1803 | 1.30946 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.00000 | −0.158830 | −0.0794151 | − | 0.996842i | \(-0.525305\pi\) | ||||
−0.0794151 | + | 0.996842i | \(0.525305\pi\) | |||||||
\(992\) | −28.4605 | −0.903622 | ||||||||
\(993\) | 33.6560 | 1.06804 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 29.1246 | 0.922849 | ||||||||
\(997\) | −10.7248 | −0.339658 | −0.169829 | − | 0.985474i | \(-0.554322\pi\) | ||||
−0.169829 | + | 0.985474i | \(0.554322\pi\) | |||||||
\(998\) | 3.70820 | 0.117381 | ||||||||
\(999\) | −4.73411 | −0.149781 |
(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 | 1225.2.a.bc.1.3 | yes | 4 | |
5.2 | odd | 4 | 1225.2.b.n.99.8 | 8 | |||
5.3 | odd | 4 | 1225.2.b.n.99.1 | 8 | |||
5.4 | even | 2 | 1225.2.a.ba.1.2 | yes | 4 | ||
7.6 | odd | 2 | inner | 1225.2.a.bc.1.4 | yes | 4 | |
35.13 | even | 4 | 1225.2.b.n.99.2 | 8 | |||
35.27 | even | 4 | 1225.2.b.n.99.7 | 8 | |||
35.34 | odd | 2 | 1225.2.a.ba.1.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1225.2.a.ba.1.1 | ✓ | 4 | 35.34 | odd | 2 | ||
1225.2.a.ba.1.2 | yes | 4 | 5.4 | even | 2 | ||
1225.2.a.bc.1.3 | yes | 4 | 1.1 | even | 1 | trivial | |
1225.2.a.bc.1.4 | yes | 4 | 7.6 | odd | 2 | inner | |
1225.2.b.n.99.1 | 8 | 5.3 | odd | 4 | |||
1225.2.b.n.99.2 | 8 | 35.13 | even | 4 | |||
1225.2.b.n.99.7 | 8 | 35.27 | even | 4 | |||
1225.2.b.n.99.8 | 8 | 5.2 | odd | 4 |