Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3675,2,Mod(1,3675)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3675, 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("3675.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3675 = 3 \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3675.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: | \(29.3450227428\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{24})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 4x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 735) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(1.93185\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3675.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.93185 | 1.36603 | 0.683013 | − | 0.730406i | \(-0.260669\pi\) | ||||
0.683013 | + | 0.730406i | \(0.260669\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.73205 | 0.866025 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.93185 | 0.788675 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −0.517638 | −0.183013 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.46410 | −1.04447 | −0.522233 | − | 0.852803i | \(-0.674901\pi\) | ||||
−0.522233 | + | 0.852803i | \(0.674901\pi\) | |||||||
\(12\) | 1.73205 | 0.500000 | ||||||||
\(13\) | −4.00000 | −1.10940 | −0.554700 | − | 0.832050i | \(-0.687167\pi\) | ||||
−0.554700 | + | 0.832050i | \(0.687167\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.46410 | −1.11603 | ||||||||
\(17\) | −4.00000 | −0.970143 | −0.485071 | − | 0.874475i | \(-0.661206\pi\) | ||||
−0.485071 | + | 0.874475i | \(0.661206\pi\) | |||||||
\(18\) | 1.93185 | 0.455342 | ||||||||
\(19\) | −0.378937 | −0.0869342 | −0.0434671 | − | 0.999055i | \(-0.513840\pi\) | ||||
−0.0434671 | + | 0.999055i | \(0.513840\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.69213 | −1.42677 | ||||||||
\(23\) | −6.31319 | −1.31639 | −0.658196 | − | 0.752847i | \(-0.728680\pi\) | ||||
−0.658196 | + | 0.752847i | \(0.728680\pi\) | |||||||
\(24\) | −0.517638 | −0.105662 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −7.72741 | −1.51547 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.92820 | 1.65793 | 0.828963 | − | 0.559304i | \(-0.188931\pi\) | ||||
0.828963 | + | 0.559304i | \(0.188931\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.34847 | −1.31982 | −0.659912 | − | 0.751343i | \(-0.729406\pi\) | ||||
−0.659912 | + | 0.751343i | \(0.729406\pi\) | |||||||
\(32\) | −7.58871 | −1.34151 | ||||||||
\(33\) | −3.46410 | −0.603023 | ||||||||
\(34\) | −7.72741 | −1.32524 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.73205 | 0.288675 | ||||||||
\(37\) | 0.757875 | 0.124594 | 0.0622969 | − | 0.998058i | \(-0.480157\pi\) | ||||
0.0622969 | + | 0.998058i | \(0.480157\pi\) | |||||||
\(38\) | −0.732051 | −0.118754 | ||||||||
\(39\) | −4.00000 | −0.640513 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.48528 | −1.32518 | −0.662589 | − | 0.748983i | \(-0.730542\pi\) | ||||
−0.662589 | + | 0.748983i | \(0.730542\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(44\) | −6.00000 | −0.904534 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −12.1962 | −1.79822 | ||||||||
\(47\) | −6.00000 | −0.875190 | −0.437595 | − | 0.899172i | \(-0.644170\pi\) | ||||
−0.437595 | + | 0.899172i | \(0.644170\pi\) | |||||||
\(48\) | −4.46410 | −0.644338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.00000 | −0.560112 | ||||||||
\(52\) | −6.92820 | −0.960769 | ||||||||
\(53\) | 7.34847 | 1.00939 | 0.504695 | − | 0.863298i | \(-0.331605\pi\) | ||||
0.504695 | + | 0.863298i | \(0.331605\pi\) | |||||||
\(54\) | 1.93185 | 0.262892 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.378937 | −0.0501915 | ||||||||
\(58\) | 17.2480 | 2.26477 | ||||||||
\(59\) | 10.5558 | 1.37425 | 0.687126 | − | 0.726538i | \(-0.258872\pi\) | ||||
0.687126 | + | 0.726538i | \(0.258872\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.14162 | 1.17046 | 0.585232 | − | 0.810866i | \(-0.301003\pi\) | ||||
0.585232 | + | 0.810866i | \(0.301003\pi\) | |||||||
\(62\) | −14.1962 | −1.80291 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −5.73205 | −0.716506 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −6.69213 | −0.823744 | ||||||||
\(67\) | 6.96953 | 0.851464 | 0.425732 | − | 0.904849i | \(-0.360017\pi\) | ||||
0.425732 | + | 0.904849i | \(0.360017\pi\) | |||||||
\(68\) | −6.92820 | −0.840168 | ||||||||
\(69\) | −6.31319 | −0.760019 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.3923 | 1.70805 | 0.854026 | − | 0.520230i | \(-0.174154\pi\) | ||||
0.854026 | + | 0.520230i | \(0.174154\pi\) | |||||||
\(72\) | −0.517638 | −0.0610042 | ||||||||
\(73\) | −10.9282 | −1.27905 | −0.639525 | − | 0.768771i | \(-0.720869\pi\) | ||||
−0.639525 | + | 0.768771i | \(0.720869\pi\) | |||||||
\(74\) | 1.46410 | 0.170198 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.656339 | −0.0752872 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −7.72741 | −0.874957 | ||||||||
\(79\) | −11.4641 | −1.28981 | −0.644906 | − | 0.764262i | \(-0.723104\pi\) | ||||
−0.644906 | + | 0.764262i | \(0.723104\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −16.3923 | −1.81023 | ||||||||
\(83\) | −6.00000 | −0.658586 | −0.329293 | − | 0.944228i | \(-0.606810\pi\) | ||||
−0.329293 | + | 0.944228i | \(0.606810\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.92820 | 0.957204 | ||||||||
\(88\) | 1.79315 | 0.191151 | ||||||||
\(89\) | −4.14110 | −0.438956 | −0.219478 | − | 0.975617i | \(-0.570435\pi\) | ||||
−0.219478 | + | 0.975617i | \(0.570435\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −10.9348 | −1.14003 | ||||||||
\(93\) | −7.34847 | −0.762001 | ||||||||
\(94\) | −11.5911 | −1.19553 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −7.58871 | −0.774519 | ||||||||
\(97\) | −5.07180 | −0.514963 | −0.257481 | − | 0.966283i | \(-0.582893\pi\) | ||||
−0.257481 | + | 0.966283i | \(0.582893\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.46410 | −0.348155 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.6264 | −1.25637 | −0.628186 | − | 0.778063i | \(-0.716202\pi\) | ||||
−0.628186 | + | 0.778063i | \(0.716202\pi\) | |||||||
\(102\) | −7.72741 | −0.765127 | ||||||||
\(103\) | 13.8564 | 1.36531 | 0.682656 | − | 0.730740i | \(-0.260825\pi\) | ||||
0.682656 | + | 0.730740i | \(0.260825\pi\) | |||||||
\(104\) | 2.07055 | 0.203034 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 14.1962 | 1.37885 | ||||||||
\(107\) | 15.5563 | 1.50389 | 0.751945 | − | 0.659226i | \(-0.229116\pi\) | ||||
0.751945 | + | 0.659226i | \(0.229116\pi\) | |||||||
\(108\) | 1.73205 | 0.166667 | ||||||||
\(109\) | −11.8564 | −1.13564 | −0.567819 | − | 0.823154i | \(-0.692213\pi\) | ||||
−0.567819 | + | 0.823154i | \(0.692213\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.757875 | 0.0719343 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.378937 | −0.0356474 | −0.0178237 | − | 0.999841i | \(-0.505674\pi\) | ||||
−0.0178237 | + | 0.999841i | \(0.505674\pi\) | |||||||
\(114\) | −0.732051 | −0.0685628 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 15.4641 | 1.43581 | ||||||||
\(117\) | −4.00000 | −0.369800 | ||||||||
\(118\) | 20.3923 | 1.87726 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 17.6603 | 1.59888 | ||||||||
\(123\) | −8.48528 | −0.765092 | ||||||||
\(124\) | −12.7279 | −1.14300 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.82843 | 0.250982 | 0.125491 | − | 0.992095i | \(-0.459949\pi\) | ||||
0.125491 | + | 0.992095i | \(0.459949\pi\) | |||||||
\(128\) | 4.10394 | 0.362740 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.65685 | 0.494242 | 0.247121 | − | 0.968985i | \(-0.420516\pi\) | ||||
0.247121 | + | 0.968985i | \(0.420516\pi\) | |||||||
\(132\) | −6.00000 | −0.522233 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 13.4641 | 1.16312 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.07055 | 0.177548 | ||||||||
\(137\) | −4.52004 | −0.386173 | −0.193087 | − | 0.981182i | \(-0.561850\pi\) | ||||
−0.193087 | + | 0.981182i | \(0.561850\pi\) | |||||||
\(138\) | −12.1962 | −1.03821 | ||||||||
\(139\) | 5.27792 | 0.447667 | 0.223834 | − | 0.974627i | \(-0.428143\pi\) | ||||
0.223834 | + | 0.974627i | \(0.428143\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.00000 | −0.505291 | ||||||||
\(142\) | 27.8038 | 2.33324 | ||||||||
\(143\) | 13.8564 | 1.15873 | ||||||||
\(144\) | −4.46410 | −0.372008 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −21.1117 | −1.74721 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.31268 | 0.107901 | ||||||||
\(149\) | 20.9282 | 1.71451 | 0.857253 | − | 0.514896i | \(-0.172169\pi\) | ||||
0.857253 | + | 0.514896i | \(0.172169\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.5359 | −1.02016 | −0.510078 | − | 0.860128i | \(-0.670384\pi\) | ||||
−0.510078 | + | 0.860128i | \(0.670384\pi\) | |||||||
\(152\) | 0.196152 | 0.0159101 | ||||||||
\(153\) | −4.00000 | −0.323381 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −6.92820 | −0.554700 | ||||||||
\(157\) | −18.9282 | −1.51064 | −0.755318 | − | 0.655359i | \(-0.772517\pi\) | ||||
−0.755318 | + | 0.655359i | \(0.772517\pi\) | |||||||
\(158\) | −22.1469 | −1.76192 | ||||||||
\(159\) | 7.34847 | 0.582772 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.93185 | 0.151781 | ||||||||
\(163\) | 16.7675 | 1.31333 | 0.656666 | − | 0.754182i | \(-0.271966\pi\) | ||||
0.656666 | + | 0.754182i | \(0.271966\pi\) | |||||||
\(164\) | −14.6969 | −1.14764 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −11.5911 | −0.899645 | ||||||||
\(167\) | −5.07180 | −0.392467 | −0.196234 | − | 0.980557i | \(-0.562871\pi\) | ||||
−0.196234 | + | 0.980557i | \(0.562871\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.00000 | 0.230769 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.378937 | −0.0289781 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −16.0000 | −1.21646 | −0.608229 | − | 0.793762i | \(-0.708120\pi\) | ||||
−0.608229 | + | 0.793762i | \(0.708120\pi\) | |||||||
\(174\) | 17.2480 | 1.30756 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 15.4641 | 1.16565 | ||||||||
\(177\) | 10.5558 | 0.793425 | ||||||||
\(178\) | −8.00000 | −0.599625 | ||||||||
\(179\) | −10.3923 | −0.776757 | −0.388379 | − | 0.921500i | \(-0.626965\pi\) | ||||
−0.388379 | + | 0.921500i | \(0.626965\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.48477 | −0.259021 | −0.129510 | − | 0.991578i | \(-0.541341\pi\) | ||||
−0.129510 | + | 0.991578i | \(0.541341\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.14162 | 0.675768 | ||||||||
\(184\) | 3.26795 | 0.240916 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −14.1962 | −1.04091 | ||||||||
\(187\) | 13.8564 | 1.01328 | ||||||||
\(188\) | −10.3923 | −0.757937 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.535898 | −0.0387762 | −0.0193881 | − | 0.999812i | \(-0.506172\pi\) | ||||
−0.0193881 | + | 0.999812i | \(0.506172\pi\) | |||||||
\(192\) | −5.73205 | −0.413675 | ||||||||
\(193\) | −16.2127 | −1.16701 | −0.583507 | − | 0.812108i | \(-0.698320\pi\) | ||||
−0.583507 | + | 0.812108i | \(0.698320\pi\) | |||||||
\(194\) | −9.79796 | −0.703452 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.4896 | 0.818598 | 0.409299 | − | 0.912400i | \(-0.365773\pi\) | ||||
0.409299 | + | 0.912400i | \(0.365773\pi\) | |||||||
\(198\) | −6.69213 | −0.475589 | ||||||||
\(199\) | −3.20736 | −0.227364 | −0.113682 | − | 0.993517i | \(-0.536265\pi\) | ||||
−0.113682 | + | 0.993517i | \(0.536265\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.96953 | 0.491593 | ||||||||
\(202\) | −24.3923 | −1.71624 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −6.92820 | −0.485071 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 26.7685 | 1.86505 | ||||||||
\(207\) | −6.31319 | −0.438797 | ||||||||
\(208\) | 17.8564 | 1.23812 | ||||||||
\(209\) | 1.31268 | 0.0907998 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.0718 | −0.899900 | −0.449950 | − | 0.893054i | \(-0.648558\pi\) | ||||
−0.449950 | + | 0.893054i | \(0.648558\pi\) | |||||||
\(212\) | 12.7279 | 0.874157 | ||||||||
\(213\) | 14.3923 | 0.986144 | ||||||||
\(214\) | 30.0526 | 2.05435 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.517638 | −0.0352208 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −22.9048 | −1.55131 | ||||||||
\(219\) | −10.9282 | −0.738460 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 16.0000 | 1.07628 | ||||||||
\(222\) | 1.46410 | 0.0982641 | ||||||||
\(223\) | −8.00000 | −0.535720 | −0.267860 | − | 0.963458i | \(-0.586316\pi\) | ||||
−0.267860 | + | 0.963458i | \(0.586316\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.732051 | −0.0486953 | ||||||||
\(227\) | −4.00000 | −0.265489 | −0.132745 | − | 0.991150i | \(-0.542379\pi\) | ||||
−0.132745 | + | 0.991150i | \(0.542379\pi\) | |||||||
\(228\) | −0.656339 | −0.0434671 | ||||||||
\(229\) | 23.2838 | 1.53863 | 0.769317 | − | 0.638867i | \(-0.220597\pi\) | ||||
0.769317 | + | 0.638867i | \(0.220597\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.62158 | −0.303421 | ||||||||
\(233\) | −0.378937 | −0.0248250 | −0.0124125 | − | 0.999923i | \(-0.503951\pi\) | ||||
−0.0124125 | + | 0.999923i | \(0.503951\pi\) | |||||||
\(234\) | −7.72741 | −0.505156 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 18.2832 | 1.19014 | ||||||||
\(237\) | −11.4641 | −0.744673 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.4641 | −1.00029 | −0.500145 | − | 0.865942i | \(-0.666720\pi\) | ||||
−0.500145 | + | 0.865942i | \(0.666720\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.55532 | 0.357850 | 0.178925 | − | 0.983863i | \(-0.442738\pi\) | ||||
0.178925 | + | 0.983863i | \(0.442738\pi\) | |||||||
\(242\) | 1.93185 | 0.124184 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 15.8338 | 1.01365 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −16.3923 | −1.04514 | ||||||||
\(247\) | 1.51575 | 0.0964448 | ||||||||
\(248\) | 3.80385 | 0.241545 | ||||||||
\(249\) | −6.00000 | −0.380235 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.04008 | 0.570605 | 0.285303 | − | 0.958438i | \(-0.407906\pi\) | ||||
0.285303 | + | 0.958438i | \(0.407906\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 21.8695 | 1.37493 | ||||||||
\(254\) | 5.46410 | 0.342848 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 19.3923 | 1.21202 | ||||||||
\(257\) | −3.46410 | −0.216085 | −0.108042 | − | 0.994146i | \(-0.534458\pi\) | ||||
−0.108042 | + | 0.994146i | \(0.534458\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.92820 | 0.552642 | ||||||||
\(262\) | 10.9282 | 0.675147 | ||||||||
\(263\) | −21.7680 | −1.34227 | −0.671136 | − | 0.741334i | \(-0.734194\pi\) | ||||
−0.671136 | + | 0.741334i | \(0.734194\pi\) | |||||||
\(264\) | 1.79315 | 0.110361 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.14110 | −0.253431 | ||||||||
\(268\) | 12.0716 | 0.737389 | ||||||||
\(269\) | 8.28221 | 0.504975 | 0.252488 | − | 0.967600i | \(-0.418751\pi\) | ||||
0.252488 | + | 0.967600i | \(0.418751\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.0053 | −0.790017 | −0.395009 | − | 0.918677i | \(-0.629258\pi\) | ||||
−0.395009 | + | 0.918677i | \(0.629258\pi\) | |||||||
\(272\) | 17.8564 | 1.08270 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.73205 | −0.527522 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −10.9348 | −0.658196 | ||||||||
\(277\) | −11.3137 | −0.679775 | −0.339887 | − | 0.940466i | \(-0.610389\pi\) | ||||
−0.339887 | + | 0.940466i | \(0.610389\pi\) | |||||||
\(278\) | 10.1962 | 0.611525 | ||||||||
\(279\) | −7.34847 | −0.439941 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.143594 | 0.00856607 | 0.00428304 | − | 0.999991i | \(-0.498637\pi\) | ||||
0.00428304 | + | 0.999991i | \(0.498637\pi\) | |||||||
\(282\) | −11.5911 | −0.690241 | ||||||||
\(283\) | −29.8564 | −1.77478 | −0.887390 | − | 0.461020i | \(-0.847484\pi\) | ||||
−0.887390 | + | 0.461020i | \(0.847484\pi\) | |||||||
\(284\) | 24.9282 | 1.47922 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 26.7685 | 1.58286 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −7.58871 | −0.447169 | ||||||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.07180 | −0.297314 | ||||||||
\(292\) | −18.9282 | −1.10769 | ||||||||
\(293\) | −4.53590 | −0.264990 | −0.132495 | − | 0.991184i | \(-0.542299\pi\) | ||||
−0.132495 | + | 0.991184i | \(0.542299\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.392305 | −0.0228023 | ||||||||
\(297\) | −3.46410 | −0.201008 | ||||||||
\(298\) | 40.4302 | 2.34206 | ||||||||
\(299\) | 25.2528 | 1.46041 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −24.2175 | −1.39356 | ||||||||
\(303\) | −12.6264 | −0.725367 | ||||||||
\(304\) | 1.69161 | 0.0970208 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −7.72741 | −0.441746 | ||||||||
\(307\) | 4.00000 | 0.228292 | 0.114146 | − | 0.993464i | \(-0.463587\pi\) | ||||
0.114146 | + | 0.993464i | \(0.463587\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 13.8564 | 0.788263 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.4548 | 0.876362 | 0.438181 | − | 0.898887i | \(-0.355623\pi\) | ||||
0.438181 | + | 0.898887i | \(0.355623\pi\) | |||||||
\(312\) | 2.07055 | 0.117222 | ||||||||
\(313\) | −10.9282 | −0.617699 | −0.308849 | − | 0.951111i | \(-0.599944\pi\) | ||||
−0.308849 | + | 0.951111i | \(0.599944\pi\) | |||||||
\(314\) | −36.5665 | −2.06357 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −19.8564 | −1.11701 | ||||||||
\(317\) | −29.2180 | −1.64105 | −0.820524 | − | 0.571613i | \(-0.806318\pi\) | ||||
−0.820524 | + | 0.571613i | \(0.806318\pi\) | |||||||
\(318\) | 14.1962 | 0.796081 | ||||||||
\(319\) | −30.9282 | −1.73165 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 15.5563 | 0.868271 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.51575 | 0.0843386 | ||||||||
\(324\) | 1.73205 | 0.0962250 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 32.3923 | 1.79404 | ||||||||
\(327\) | −11.8564 | −0.655661 | ||||||||
\(328\) | 4.39230 | 0.242524 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 32.7846 | 1.80201 | 0.901003 | − | 0.433814i | \(-0.142832\pi\) | ||||
0.901003 | + | 0.433814i | \(0.142832\pi\) | |||||||
\(332\) | −10.3923 | −0.570352 | ||||||||
\(333\) | 0.757875 | 0.0415313 | ||||||||
\(334\) | −9.79796 | −0.536120 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −27.5264 | −1.49946 | −0.749729 | − | 0.661745i | \(-0.769816\pi\) | ||||
−0.749729 | + | 0.661745i | \(0.769816\pi\) | |||||||
\(338\) | 5.79555 | 0.315237 | ||||||||
\(339\) | −0.378937 | −0.0205811 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 25.4558 | 1.37851 | ||||||||
\(342\) | −0.732051 | −0.0395848 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −30.9096 | −1.66171 | ||||||||
\(347\) | −11.4152 | −0.612802 | −0.306401 | − | 0.951902i | \(-0.599125\pi\) | ||||
−0.306401 | + | 0.951902i | \(0.599125\pi\) | |||||||
\(348\) | 15.4641 | 0.828963 | ||||||||
\(349\) | 7.82894 | 0.419074 | 0.209537 | − | 0.977801i | \(-0.432804\pi\) | ||||
0.209537 | + | 0.977801i | \(0.432804\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.00000 | −0.213504 | ||||||||
\(352\) | 26.2880 | 1.40116 | ||||||||
\(353\) | −4.53590 | −0.241422 | −0.120711 | − | 0.992688i | \(-0.538517\pi\) | ||||
−0.120711 | + | 0.992688i | \(0.538517\pi\) | |||||||
\(354\) | 20.3923 | 1.08384 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −7.17260 | −0.380147 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −20.0764 | −1.06107 | ||||||||
\(359\) | 8.53590 | 0.450507 | 0.225254 | − | 0.974300i | \(-0.427679\pi\) | ||||
0.225254 | + | 0.974300i | \(0.427679\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.8564 | −0.992442 | ||||||||
\(362\) | −6.73205 | −0.353829 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 17.6603 | 0.923116 | ||||||||
\(367\) | −4.00000 | −0.208798 | −0.104399 | − | 0.994535i | \(-0.533292\pi\) | ||||
−0.104399 | + | 0.994535i | \(0.533292\pi\) | |||||||
\(368\) | 28.1827 | 1.46913 | ||||||||
\(369\) | −8.48528 | −0.441726 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −12.7279 | −0.659912 | ||||||||
\(373\) | 26.7685 | 1.38602 | 0.693011 | − | 0.720927i | \(-0.256284\pi\) | ||||
0.693011 | + | 0.720927i | \(0.256284\pi\) | |||||||
\(374\) | 26.7685 | 1.38417 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.10583 | 0.160171 | ||||||||
\(377\) | −35.7128 | −1.83930 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.53590 | 0.232993 | 0.116497 | − | 0.993191i | \(-0.462834\pi\) | ||||
0.116497 | + | 0.993191i | \(0.462834\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.82843 | 0.144905 | ||||||||
\(382\) | −1.03528 | −0.0529693 | ||||||||
\(383\) | −3.85641 | −0.197053 | −0.0985266 | − | 0.995134i | \(-0.531413\pi\) | ||||
−0.0985266 | + | 0.995134i | \(0.531413\pi\) | |||||||
\(384\) | 4.10394 | 0.209428 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −31.3205 | −1.59417 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −8.78461 | −0.445971 | ||||||||
\(389\) | 24.9282 | 1.26391 | 0.631955 | − | 0.775005i | \(-0.282253\pi\) | ||||
0.631955 | + | 0.775005i | \(0.282253\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 25.2528 | 1.27709 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.65685 | 0.285351 | ||||||||
\(394\) | 22.1962 | 1.11823 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −6.00000 | −0.301511 | ||||||||
\(397\) | 31.7128 | 1.59162 | 0.795810 | − | 0.605546i | \(-0.207045\pi\) | ||||
0.795810 | + | 0.605546i | \(0.207045\pi\) | |||||||
\(398\) | −6.19615 | −0.310585 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.00000 | 0.0998752 | 0.0499376 | − | 0.998752i | \(-0.484098\pi\) | ||||
0.0499376 | + | 0.998752i | \(0.484098\pi\) | |||||||
\(402\) | 13.4641 | 0.671528 | ||||||||
\(403\) | 29.3939 | 1.46421 | ||||||||
\(404\) | −21.8695 | −1.08805 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.62536 | −0.130134 | ||||||||
\(408\) | 2.07055 | 0.102508 | ||||||||
\(409\) | 31.0112 | 1.53340 | 0.766702 | − | 0.642004i | \(-0.221897\pi\) | ||||
0.766702 | + | 0.642004i | \(0.221897\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.52004 | −0.222957 | ||||||||
\(412\) | 24.0000 | 1.18240 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −12.1962 | −0.599408 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 30.3548 | 1.48827 | ||||||||
\(417\) | 5.27792 | 0.258461 | ||||||||
\(418\) | 2.53590 | 0.124035 | ||||||||
\(419\) | 1.51575 | 0.0740492 | 0.0370246 | − | 0.999314i | \(-0.488212\pi\) | ||||
0.0370246 | + | 0.999314i | \(0.488212\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −28.7846 | −1.40288 | −0.701438 | − | 0.712730i | \(-0.747458\pi\) | ||||
−0.701438 | + | 0.712730i | \(0.747458\pi\) | |||||||
\(422\) | −25.2528 | −1.22929 | ||||||||
\(423\) | −6.00000 | −0.291730 | ||||||||
\(424\) | −3.80385 | −0.184731 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 27.8038 | 1.34710 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 26.9444 | 1.30241 | ||||||||
\(429\) | 13.8564 | 0.668994 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.67949 | 0.129067 | 0.0645333 | − | 0.997916i | \(-0.479444\pi\) | ||||
0.0645333 | + | 0.997916i | \(0.479444\pi\) | |||||||
\(432\) | −4.46410 | −0.214779 | ||||||||
\(433\) | −9.85641 | −0.473669 | −0.236834 | − | 0.971550i | \(-0.576110\pi\) | ||||
−0.236834 | + | 0.971550i | \(0.576110\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −20.5359 | −0.983491 | ||||||||
\(437\) | 2.39230 | 0.114439 | ||||||||
\(438\) | −21.1117 | −1.00875 | ||||||||
\(439\) | 1.69161 | 0.0807364 | 0.0403682 | − | 0.999185i | \(-0.487147\pi\) | ||||
0.0403682 | + | 0.999185i | \(0.487147\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 30.9096 | 1.47022 | ||||||||
\(443\) | −26.6670 | −1.26699 | −0.633493 | − | 0.773748i | \(-0.718380\pi\) | ||||
−0.633493 | + | 0.773748i | \(0.718380\pi\) | |||||||
\(444\) | 1.31268 | 0.0622969 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −15.4548 | −0.731807 | ||||||||
\(447\) | 20.9282 | 0.989870 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.14359 | 0.384320 | 0.192160 | − | 0.981364i | \(-0.438451\pi\) | ||||
0.192160 | + | 0.981364i | \(0.438451\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 29.3939 | 1.38410 | ||||||||
\(452\) | −0.656339 | −0.0308716 | ||||||||
\(453\) | −12.5359 | −0.588988 | ||||||||
\(454\) | −7.72741 | −0.362665 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.196152 | 0.00918568 | ||||||||
\(457\) | −12.0716 | −0.564685 | −0.282342 | − | 0.959314i | \(-0.591111\pi\) | ||||
−0.282342 | + | 0.959314i | \(0.591111\pi\) | |||||||
\(458\) | 44.9808 | 2.10181 | ||||||||
\(459\) | −4.00000 | −0.186704 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.8295 | −0.597527 | −0.298764 | − | 0.954327i | \(-0.596574\pi\) | ||||
−0.298764 | + | 0.954327i | \(0.596574\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.7675 | −0.779251 | −0.389626 | − | 0.920973i | \(-0.627396\pi\) | ||||
−0.389626 | + | 0.920973i | \(0.627396\pi\) | |||||||
\(464\) | −39.8564 | −1.85029 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.732051 | −0.0339116 | ||||||||
\(467\) | −17.8564 | −0.826296 | −0.413148 | − | 0.910664i | \(-0.635571\pi\) | ||||
−0.413148 | + | 0.910664i | \(0.635571\pi\) | |||||||
\(468\) | −6.92820 | −0.320256 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −18.9282 | −0.872166 | ||||||||
\(472\) | −5.46410 | −0.251506 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −22.1469 | −1.01724 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.34847 | 0.336463 | ||||||||
\(478\) | −29.8744 | −1.36642 | ||||||||
\(479\) | −13.9391 | −0.636892 | −0.318446 | − | 0.947941i | \(-0.603161\pi\) | ||||
−0.318446 | + | 0.947941i | \(0.603161\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.03150 | −0.138224 | ||||||||
\(482\) | 10.7321 | 0.488832 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.73205 | 0.0787296 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.93185 | 0.0876306 | ||||||||
\(487\) | −4.14110 | −0.187651 | −0.0938257 | − | 0.995589i | \(-0.529910\pi\) | ||||
−0.0938257 | + | 0.995589i | \(0.529910\pi\) | |||||||
\(488\) | −4.73205 | −0.214210 | ||||||||
\(489\) | 16.7675 | 0.758252 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.67949 | 0.301441 | 0.150721 | − | 0.988576i | \(-0.451841\pi\) | ||||
0.150721 | + | 0.988576i | \(0.451841\pi\) | |||||||
\(492\) | −14.6969 | −0.662589 | ||||||||
\(493\) | −35.7128 | −1.60842 | ||||||||
\(494\) | 2.92820 | 0.131746 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 32.8043 | 1.47296 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −11.5911 | −0.519410 | ||||||||
\(499\) | 16.2487 | 0.727392 | 0.363696 | − | 0.931518i | \(-0.381515\pi\) | ||||
0.363696 | + | 0.931518i | \(0.381515\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.07180 | −0.226591 | ||||||||
\(502\) | 17.4641 | 0.779461 | ||||||||
\(503\) | 3.85641 | 0.171949 | 0.0859743 | − | 0.996297i | \(-0.472600\pi\) | ||||
0.0859743 | + | 0.996297i | \(0.472600\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 42.2487 | 1.87818 | ||||||||
\(507\) | 3.00000 | 0.133235 | ||||||||
\(508\) | 4.89898 | 0.217357 | ||||||||
\(509\) | 42.2233 | 1.87152 | 0.935758 | − | 0.352642i | \(-0.114717\pi\) | ||||
0.935758 | + | 0.352642i | \(0.114717\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 29.2552 | 1.29291 | ||||||||
\(513\) | −0.378937 | −0.0167305 | ||||||||
\(514\) | −6.69213 | −0.295177 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 20.7846 | 0.914106 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −16.0000 | −0.702322 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 28.2843 | 1.23916 | 0.619578 | − | 0.784935i | \(-0.287304\pi\) | ||||
0.619578 | + | 0.784935i | \(0.287304\pi\) | |||||||
\(522\) | 17.2480 | 0.754923 | ||||||||
\(523\) | −11.7128 | −0.512166 | −0.256083 | − | 0.966655i | \(-0.582432\pi\) | ||||
−0.256083 | + | 0.966655i | \(0.582432\pi\) | |||||||
\(524\) | 9.79796 | 0.428026 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −42.0526 | −1.83358 | ||||||||
\(527\) | 29.3939 | 1.28042 | ||||||||
\(528\) | 15.4641 | 0.672989 | ||||||||
\(529\) | 16.8564 | 0.732887 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.5558 | 0.458084 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 33.9411 | 1.47015 | ||||||||
\(534\) | −8.00000 | −0.346194 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −3.60770 | −0.155829 | ||||||||
\(537\) | −10.3923 | −0.448461 | ||||||||
\(538\) | 16.0000 | 0.689809 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −42.6410 | −1.83328 | −0.916640 | − | 0.399713i | \(-0.869110\pi\) | ||||
−0.916640 | + | 0.399713i | \(0.869110\pi\) | |||||||
\(542\) | −25.1244 | −1.07918 | ||||||||
\(543\) | −3.48477 | −0.149546 | ||||||||
\(544\) | 30.3548 | 1.30145 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 29.5969 | 1.26547 | 0.632737 | − | 0.774367i | \(-0.281931\pi\) | ||||
0.632737 | + | 0.774367i | \(0.281931\pi\) | |||||||
\(548\) | −7.82894 | −0.334436 | ||||||||
\(549\) | 9.14162 | 0.390155 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.38323 | −0.144130 | ||||||||
\(552\) | 3.26795 | 0.139093 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −21.8564 | −0.928590 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9.14162 | 0.387691 | ||||||||
\(557\) | 13.7632 | 0.583165 | 0.291583 | − | 0.956546i | \(-0.405818\pi\) | ||||
0.291583 | + | 0.956546i | \(0.405818\pi\) | |||||||
\(558\) | −14.1962 | −0.600971 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 13.8564 | 0.585018 | ||||||||
\(562\) | 0.277401 | 0.0117015 | ||||||||
\(563\) | −31.8564 | −1.34259 | −0.671294 | − | 0.741191i | \(-0.734261\pi\) | ||||
−0.671294 | + | 0.741191i | \(0.734261\pi\) | |||||||
\(564\) | −10.3923 | −0.437595 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −57.6781 | −2.42439 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −7.45001 | −0.312595 | ||||||||
\(569\) | 11.8564 | 0.497046 | 0.248523 | − | 0.968626i | \(-0.420055\pi\) | ||||
0.248523 | + | 0.968626i | \(0.420055\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 39.7128 | 1.66193 | 0.830965 | − | 0.556325i | \(-0.187789\pi\) | ||||
0.830965 | + | 0.556325i | \(0.187789\pi\) | |||||||
\(572\) | 24.0000 | 1.00349 | ||||||||
\(573\) | −0.535898 | −0.0223875 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −5.73205 | −0.238835 | ||||||||
\(577\) | −4.00000 | −0.166522 | −0.0832611 | − | 0.996528i | \(-0.526534\pi\) | ||||
−0.0832611 | + | 0.996528i | \(0.526534\pi\) | |||||||
\(578\) | −1.93185 | −0.0803544 | ||||||||
\(579\) | −16.2127 | −0.673776 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −9.79796 | −0.406138 | ||||||||
\(583\) | −25.4558 | −1.05427 | ||||||||
\(584\) | 5.65685 | 0.234082 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −8.76268 | −0.361983 | ||||||||
\(587\) | 31.8564 | 1.31485 | 0.657427 | − | 0.753518i | \(-0.271645\pi\) | ||||
0.657427 | + | 0.753518i | \(0.271645\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.78461 | 0.114738 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11.4896 | 0.472618 | ||||||||
\(592\) | −3.38323 | −0.139050 | ||||||||
\(593\) | 9.32051 | 0.382747 | 0.191374 | − | 0.981517i | \(-0.438706\pi\) | ||||
0.191374 | + | 0.981517i | \(0.438706\pi\) | |||||||
\(594\) | −6.69213 | −0.274581 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 36.2487 | 1.48481 | ||||||||
\(597\) | −3.20736 | −0.131269 | ||||||||
\(598\) | 48.7846 | 1.99495 | ||||||||
\(599\) | −5.32051 | −0.217390 | −0.108695 | − | 0.994075i | \(-0.534667\pi\) | ||||
−0.108695 | + | 0.994075i | \(0.534667\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −33.6365 | −1.37206 | −0.686031 | − | 0.727572i | \(-0.740649\pi\) | ||||
−0.686031 | + | 0.727572i | \(0.740649\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.96953 | 0.283821 | ||||||||
\(604\) | −21.7128 | −0.883482 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −24.3923 | −0.990870 | ||||||||
\(607\) | 12.0000 | 0.487065 | 0.243532 | − | 0.969893i | \(-0.421694\pi\) | ||||
0.243532 | + | 0.969893i | \(0.421694\pi\) | |||||||
\(608\) | 2.87564 | 0.116623 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 24.0000 | 0.970936 | ||||||||
\(612\) | −6.92820 | −0.280056 | ||||||||
\(613\) | −9.79796 | −0.395736 | −0.197868 | − | 0.980229i | \(-0.563402\pi\) | ||||
−0.197868 | + | 0.980229i | \(0.563402\pi\) | |||||||
\(614\) | 7.72741 | 0.311853 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.4505 | 0.501239 | 0.250620 | − | 0.968086i | \(-0.419366\pi\) | ||||
0.250620 | + | 0.968086i | \(0.419366\pi\) | |||||||
\(618\) | 26.7685 | 1.07679 | ||||||||
\(619\) | −3.76217 | −0.151214 | −0.0756071 | − | 0.997138i | \(-0.524089\pi\) | ||||
−0.0756071 | + | 0.997138i | \(0.524089\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.31319 | −0.253340 | ||||||||
\(622\) | 29.8564 | 1.19713 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 17.8564 | 0.714828 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −21.1117 | −0.843792 | ||||||||
\(627\) | 1.31268 | 0.0524233 | ||||||||
\(628\) | −32.7846 | −1.30825 | ||||||||
\(629\) | −3.03150 | −0.120874 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.32051 | 0.371044 | 0.185522 | − | 0.982640i | \(-0.440602\pi\) | ||||
0.185522 | + | 0.982640i | \(0.440602\pi\) | |||||||
\(632\) | 5.93426 | 0.236052 | ||||||||
\(633\) | −13.0718 | −0.519557 | ||||||||
\(634\) | −56.4449 | −2.24171 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 12.7279 | 0.504695 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −59.7487 | −2.36547 | ||||||||
\(639\) | 14.3923 | 0.569351 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.0000 | 0.394976 | 0.197488 | − | 0.980305i | \(-0.436722\pi\) | ||||
0.197488 | + | 0.980305i | \(0.436722\pi\) | |||||||
\(642\) | 30.0526 | 1.18608 | ||||||||
\(643\) | 4.00000 | 0.157745 | 0.0788723 | − | 0.996885i | \(-0.474868\pi\) | ||||
0.0788723 | + | 0.996885i | \(0.474868\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.92820 | 0.115209 | ||||||||
\(647\) | 29.0718 | 1.14293 | 0.571465 | − | 0.820626i | \(-0.306375\pi\) | ||||
0.571465 | + | 0.820626i | \(0.306375\pi\) | |||||||
\(648\) | −0.517638 | −0.0203347 | ||||||||
\(649\) | −36.5665 | −1.43536 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 29.0421 | 1.13738 | ||||||||
\(653\) | −18.6622 | −0.730307 | −0.365154 | − | 0.930947i | \(-0.618984\pi\) | ||||
−0.365154 | + | 0.930947i | \(0.618984\pi\) | |||||||
\(654\) | −22.9048 | −0.895649 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 37.8792 | 1.47893 | ||||||||
\(657\) | −10.9282 | −0.426350 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10.3923 | −0.404827 | −0.202413 | − | 0.979300i | \(-0.564878\pi\) | ||||
−0.202413 | + | 0.979300i | \(0.564878\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23.2838 | −0.905633 | −0.452817 | − | 0.891604i | \(-0.649581\pi\) | ||||
−0.452817 | + | 0.891604i | \(0.649581\pi\) | |||||||
\(662\) | 63.3350 | 2.46158 | ||||||||
\(663\) | 16.0000 | 0.621389 | ||||||||
\(664\) | 3.10583 | 0.120530 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.46410 | 0.0567328 | ||||||||
\(667\) | −56.3655 | −2.18248 | ||||||||
\(668\) | −8.78461 | −0.339887 | ||||||||
\(669\) | −8.00000 | −0.309298 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −31.6675 | −1.22251 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.0716 | 0.465325 | 0.232663 | − | 0.972557i | \(-0.425256\pi\) | ||||
0.232663 | + | 0.972557i | \(0.425256\pi\) | |||||||
\(674\) | −53.1769 | −2.04830 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.19615 | 0.199852 | ||||||||
\(677\) | −39.1769 | −1.50569 | −0.752846 | − | 0.658197i | \(-0.771319\pi\) | ||||
−0.752846 | + | 0.658197i | \(0.771319\pi\) | |||||||
\(678\) | −0.732051 | −0.0281142 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.00000 | −0.153280 | ||||||||
\(682\) | 49.1769 | 1.88308 | ||||||||
\(683\) | −22.7290 | −0.869699 | −0.434850 | − | 0.900503i | \(-0.643198\pi\) | ||||
−0.434850 | + | 0.900503i | \(0.643198\pi\) | |||||||
\(684\) | −0.656339 | −0.0250957 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 23.2838 | 0.888331 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −29.3939 | −1.11982 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.03579 | −0.229612 | −0.114806 | − | 0.993388i | \(-0.536625\pi\) | ||||
−0.114806 | + | 0.993388i | \(0.536625\pi\) | |||||||
\(692\) | −27.7128 | −1.05348 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −22.0526 | −0.837104 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −4.62158 | −0.175180 | ||||||||
\(697\) | 33.9411 | 1.28561 | ||||||||
\(698\) | 15.1244 | 0.572465 | ||||||||
\(699\) | −0.378937 | −0.0143327 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −24.9282 | −0.941525 | −0.470763 | − | 0.882260i | \(-0.656021\pi\) | ||||
−0.470763 | + | 0.882260i | \(0.656021\pi\) | |||||||
\(702\) | −7.72741 | −0.291652 | ||||||||
\(703\) | −0.287187 | −0.0108315 | ||||||||
\(704\) | 19.8564 | 0.748366 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8.76268 | −0.329788 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 18.2832 | 0.687126 | ||||||||
\(709\) | 2.92820 | 0.109971 | 0.0549855 | − | 0.998487i | \(-0.482489\pi\) | ||||
0.0549855 | + | 0.998487i | \(0.482489\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −11.4641 | −0.429937 | ||||||||
\(712\) | 2.14359 | 0.0803346 | ||||||||
\(713\) | 46.3923 | 1.73741 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −18.0000 | −0.672692 | ||||||||
\(717\) | −15.4641 | −0.577517 | ||||||||
\(718\) | 16.4901 | 0.615405 | ||||||||
\(719\) | 14.6969 | 0.548103 | 0.274052 | − | 0.961715i | \(-0.411636\pi\) | ||||
0.274052 | + | 0.961715i | \(0.411636\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −36.4278 | −1.35570 | ||||||||
\(723\) | 5.55532 | 0.206605 | ||||||||
\(724\) | −6.03579 | −0.224318 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.93185 | 0.0716977 | ||||||||
\(727\) | −31.7128 | −1.17616 | −0.588082 | − | 0.808802i | \(-0.700117\pi\) | ||||
−0.588082 | + | 0.808802i | \(0.700117\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 15.8338 | 0.585232 | ||||||||
\(733\) | 9.85641 | 0.364055 | 0.182027 | − | 0.983293i | \(-0.441734\pi\) | ||||
0.182027 | + | 0.983293i | \(0.441734\pi\) | |||||||
\(734\) | −7.72741 | −0.285224 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 47.9090 | 1.76595 | ||||||||
\(737\) | −24.1432 | −0.889325 | ||||||||
\(738\) | −16.3923 | −0.603409 | ||||||||
\(739\) | 1.85641 | 0.0682890 | 0.0341445 | − | 0.999417i | \(-0.489129\pi\) | ||||
0.0341445 | + | 0.999417i | \(0.489129\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.51575 | 0.0556825 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 37.0197 | 1.35812 | 0.679061 | − | 0.734081i | \(-0.262387\pi\) | ||||
0.679061 | + | 0.734081i | \(0.262387\pi\) | |||||||
\(744\) | 3.80385 | 0.139456 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 51.7128 | 1.89334 | ||||||||
\(747\) | −6.00000 | −0.219529 | ||||||||
\(748\) | 24.0000 | 0.877527 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.78461 | 0.174593 | 0.0872964 | − | 0.996182i | \(-0.472177\pi\) | ||||
0.0872964 | + | 0.996182i | \(0.472177\pi\) | |||||||
\(752\) | 26.7846 | 0.976734 | ||||||||
\(753\) | 9.04008 | 0.329439 | ||||||||
\(754\) | −68.9919 | −2.51254 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −34.2929 | −1.24640 | −0.623198 | − | 0.782064i | \(-0.714167\pi\) | ||||
−0.623198 | + | 0.782064i | \(0.714167\pi\) | |||||||
\(758\) | 8.76268 | 0.318275 | ||||||||
\(759\) | 21.8695 | 0.793814 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 40.7076 | 1.47565 | 0.737824 | − | 0.674993i | \(-0.235853\pi\) | ||||
0.737824 | + | 0.674993i | \(0.235853\pi\) | |||||||
\(762\) | 5.46410 | 0.197944 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −0.928203 | −0.0335812 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −7.45001 | −0.269180 | ||||||||
\(767\) | −42.2233 | −1.52460 | ||||||||
\(768\) | 19.3923 | 0.699760 | ||||||||
\(769\) | 19.4944 | 0.702985 | 0.351493 | − | 0.936191i | \(-0.385674\pi\) | ||||
0.351493 | + | 0.936191i | \(0.385674\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.46410 | −0.124757 | ||||||||
\(772\) | −28.0812 | −1.01066 | ||||||||
\(773\) | −10.1436 | −0.364840 | −0.182420 | − | 0.983221i | \(-0.558393\pi\) | ||||
−0.182420 | + | 0.983221i | \(0.558393\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2.62536 | 0.0942448 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 48.1576 | 1.72653 | ||||||||
\(779\) | 3.21539 | 0.115203 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −49.8564 | −1.78400 | ||||||||
\(782\) | 48.7846 | 1.74453 | ||||||||
\(783\) | 8.92820 | 0.319068 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 10.9282 | 0.389796 | ||||||||
\(787\) | 18.1436 | 0.646749 | 0.323375 | − | 0.946271i | \(-0.395183\pi\) | ||||
0.323375 | + | 0.946271i | \(0.395183\pi\) | |||||||
\(788\) | 19.9005 | 0.708927 | ||||||||
\(789\) | −21.7680 | −0.774962 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.79315 | 0.0637168 | ||||||||
\(793\) | −36.5665 | −1.29851 | ||||||||
\(794\) | 61.2645 | 2.17419 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.55532 | −0.196903 | ||||||||
\(797\) | 37.8564 | 1.34094 | 0.670471 | − | 0.741935i | \(-0.266092\pi\) | ||||
0.670471 | + | 0.741935i | \(0.266092\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 24.0000 | 0.849059 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.14110 | −0.146319 | ||||||||
\(802\) | 3.86370 | 0.136432 | ||||||||
\(803\) | 37.8564 | 1.33592 | ||||||||
\(804\) | 12.0716 | 0.425732 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 56.7846 | 2.00015 | ||||||||
\(807\) | 8.28221 | 0.291548 | ||||||||
\(808\) | 6.53590 | 0.229932 | ||||||||
\(809\) | −33.7128 | −1.18528 | −0.592640 | − | 0.805468i | \(-0.701914\pi\) | ||||
−0.592640 | + | 0.805468i | \(0.701914\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8.66115 | −0.304134 | −0.152067 | − | 0.988370i | \(-0.548593\pi\) | ||||
−0.152067 | + | 0.988370i | \(0.548593\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −13.0053 | −0.456117 | ||||||||
\(814\) | −5.07180 | −0.177766 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 17.8564 | 0.625099 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 59.9090 | 2.09467 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −22.7846 | −0.795188 | −0.397594 | − | 0.917561i | \(-0.630155\pi\) | ||||
−0.397594 | + | 0.917561i | \(0.630155\pi\) | |||||||
\(822\) | −8.73205 | −0.304565 | ||||||||
\(823\) | −47.6771 | −1.66192 | −0.830960 | − | 0.556332i | \(-0.812208\pi\) | ||||
−0.830960 | + | 0.556332i | \(0.812208\pi\) | |||||||
\(824\) | −7.17260 | −0.249869 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 50.6071 | 1.75978 | 0.879890 | − | 0.475177i | \(-0.157616\pi\) | ||||
0.879890 | + | 0.475177i | \(0.157616\pi\) | |||||||
\(828\) | −10.9348 | −0.380010 | ||||||||
\(829\) | 35.9101 | 1.24721 | 0.623605 | − | 0.781739i | \(-0.285667\pi\) | ||||
0.623605 | + | 0.781739i | \(0.285667\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −11.3137 | −0.392468 | ||||||||
\(832\) | 22.9282 | 0.794892 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 10.1962 | 0.353064 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 2.27362 | 0.0786349 | ||||||||
\(837\) | −7.34847 | −0.254000 | ||||||||
\(838\) | 2.92820 | 0.101153 | ||||||||
\(839\) | −9.04008 | −0.312098 | −0.156049 | − | 0.987749i | \(-0.549876\pi\) | ||||
−0.156049 | + | 0.987749i | \(0.549876\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 50.7128 | 1.74872 | ||||||||
\(842\) | −55.6076 | −1.91636 | ||||||||
\(843\) | 0.143594 | 0.00494562 | ||||||||
\(844\) | −22.6410 | −0.779336 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −11.5911 | −0.398511 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −32.8043 | −1.12650 | ||||||||
\(849\) | −29.8564 | −1.02467 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.78461 | −0.164014 | ||||||||
\(852\) | 24.9282 | 0.854026 | ||||||||
\(853\) | −26.9282 | −0.922004 | −0.461002 | − | 0.887399i | \(-0.652510\pi\) | ||||
−0.461002 | + | 0.887399i | \(0.652510\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8.05256 | −0.275231 | ||||||||
\(857\) | −17.8564 | −0.609963 | −0.304982 | − | 0.952358i | \(-0.598650\pi\) | ||||
−0.304982 | + | 0.952358i | \(0.598650\pi\) | |||||||
\(858\) | 26.7685 | 0.913862 | ||||||||
\(859\) | 47.5013 | 1.62072 | 0.810361 | − | 0.585931i | \(-0.199271\pi\) | ||||
0.810361 | + | 0.585931i | \(0.199271\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 5.17638 | 0.176308 | ||||||||
\(863\) | 52.6776 | 1.79317 | 0.896584 | − | 0.442874i | \(-0.146041\pi\) | ||||
0.896584 | + | 0.442874i | \(0.146041\pi\) | |||||||
\(864\) | −7.58871 | −0.258173 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −19.0411 | −0.647043 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 39.7128 | 1.34716 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −27.8781 | −0.944614 | ||||||||
\(872\) | 6.13733 | 0.207836 | ||||||||
\(873\) | −5.07180 | −0.171654 | ||||||||
\(874\) | 4.62158 | 0.156327 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −18.9282 | −0.639525 | ||||||||
\(877\) | −33.9411 | −1.14611 | −0.573055 | − | 0.819517i | \(-0.694242\pi\) | ||||
−0.573055 | + | 0.819517i | \(0.694242\pi\) | |||||||
\(878\) | 3.26795 | 0.110288 | ||||||||
\(879\) | −4.53590 | −0.152992 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 10.0010 | 0.336943 | 0.168472 | − | 0.985707i | \(-0.446117\pi\) | ||||
0.168472 | + | 0.985707i | \(0.446117\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −29.3939 | −0.989183 | −0.494591 | − | 0.869126i | \(-0.664682\pi\) | ||||
−0.494591 | + | 0.869126i | \(0.664682\pi\) | |||||||
\(884\) | 27.7128 | 0.932083 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −51.5167 | −1.73074 | ||||||||
\(887\) | 41.7128 | 1.40058 | 0.700290 | − | 0.713859i | \(-0.253054\pi\) | ||||
0.700290 | + | 0.713859i | \(0.253054\pi\) | |||||||
\(888\) | −0.392305 | −0.0131649 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.46410 | −0.116052 | ||||||||
\(892\) | −13.8564 | −0.463947 | ||||||||
\(893\) | 2.27362 | 0.0760839 | ||||||||
\(894\) | 40.4302 | 1.35219 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 25.2528 | 0.843166 | ||||||||
\(898\) | 15.7322 | 0.524991 | ||||||||
\(899\) | −65.6086 | −2.18817 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −29.3939 | −0.979252 | ||||||||
\(902\) | 56.7846 | 1.89072 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.196152 | 0.00652393 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −24.2175 | −0.804572 | ||||||||
\(907\) | −52.0213 | −1.72734 | −0.863669 | − | 0.504059i | \(-0.831839\pi\) | ||||
−0.863669 | + | 0.504059i | \(0.831839\pi\) | |||||||
\(908\) | −6.92820 | −0.229920 | ||||||||
\(909\) | −12.6264 | −0.418791 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 30.3923 | 1.00694 | 0.503471 | − | 0.864012i | \(-0.332056\pi\) | ||||
0.503471 | + | 0.864012i | \(0.332056\pi\) | |||||||
\(912\) | 1.69161 | 0.0560150 | ||||||||
\(913\) | 20.7846 | 0.687870 | ||||||||
\(914\) | −23.3205 | −0.771374 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 40.3286 | 1.33250 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −7.72741 | −0.255042 | ||||||||
\(919\) | −22.9282 | −0.756332 | −0.378166 | − | 0.925738i | \(-0.623445\pi\) | ||||
−0.378166 | + | 0.925738i | \(0.623445\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.00000 | 0.131804 | ||||||||
\(922\) | −24.7846 | −0.816238 | ||||||||
\(923\) | −57.5692 | −1.89491 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −32.3923 | −1.06448 | ||||||||
\(927\) | 13.8564 | 0.455104 | ||||||||
\(928\) | −67.7535 | −2.22412 | ||||||||
\(929\) | −40.7076 | −1.33557 | −0.667786 | − | 0.744353i | \(-0.732758\pi\) | ||||
−0.667786 | + | 0.744353i | \(0.732758\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −0.656339 | −0.0214991 | ||||||||
\(933\) | 15.4548 | 0.505968 | ||||||||
\(934\) | −34.4959 | −1.12874 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.07055 | 0.0676781 | ||||||||
\(937\) | −24.7846 | −0.809678 | −0.404839 | − | 0.914388i | \(-0.632672\pi\) | ||||
−0.404839 | + | 0.914388i | \(0.632672\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −10.9282 | −0.356628 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −39.3949 | −1.28424 | −0.642119 | − | 0.766605i | \(-0.721944\pi\) | ||||
−0.642119 | + | 0.766605i | \(0.721944\pi\) | |||||||
\(942\) | −36.5665 | −1.19140 | ||||||||
\(943\) | 53.5692 | 1.74445 | ||||||||
\(944\) | −47.1223 | −1.53370 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 18.3848 | 0.597425 | 0.298712 | − | 0.954343i | \(-0.403443\pi\) | ||||
0.298712 | + | 0.954343i | \(0.403443\pi\) | |||||||
\(948\) | −19.8564 | −0.644906 | ||||||||
\(949\) | 43.7128 | 1.41898 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −29.2180 | −0.947459 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 19.6231 | 0.635655 | 0.317828 | − | 0.948148i | \(-0.397047\pi\) | ||||
0.317828 | + | 0.948148i | \(0.397047\pi\) | |||||||
\(954\) | 14.1962 | 0.459617 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −26.7846 | −0.866276 | ||||||||
\(957\) | −30.9282 | −0.999767 | ||||||||
\(958\) | −26.9282 | −0.870011 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23.0000 | 0.741935 | ||||||||
\(962\) | −5.85641 | −0.188818 | ||||||||
\(963\) | 15.5563 | 0.501296 | ||||||||
\(964\) | 9.62209 | 0.309907 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 29.5969 | 0.951774 | 0.475887 | − | 0.879507i | \(-0.342127\pi\) | ||||
0.475887 | + | 0.879507i | \(0.342127\pi\) | |||||||
\(968\) | −0.517638 | −0.0166375 | ||||||||
\(969\) | 1.51575 | 0.0486929 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −56.9203 | −1.82666 | −0.913329 | − | 0.407222i | \(-0.866498\pi\) | ||||
−0.913329 | + | 0.407222i | \(0.866498\pi\) | |||||||
\(972\) | 1.73205 | 0.0555556 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −8.00000 | −0.256337 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −40.8091 | −1.30627 | ||||||||
\(977\) | 50.5328 | 1.61669 | 0.808343 | − | 0.588712i | \(-0.200365\pi\) | ||||
0.808343 | + | 0.588712i | \(0.200365\pi\) | |||||||
\(978\) | 32.3923 | 1.03579 | ||||||||
\(979\) | 14.3452 | 0.458475 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11.8564 | −0.378546 | ||||||||
\(982\) | 12.9038 | 0.411776 | ||||||||
\(983\) | −16.7846 | −0.535346 | −0.267673 | − | 0.963510i | \(-0.586255\pi\) | ||||
−0.267673 | + | 0.963510i | \(0.586255\pi\) | |||||||
\(984\) | 4.39230 | 0.140022 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −68.9919 | −2.19715 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.62536 | 0.0835237 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −28.7846 | −0.914373 | −0.457187 | − | 0.889371i | \(-0.651143\pi\) | ||||
−0.457187 | + | 0.889371i | \(0.651143\pi\) | |||||||
\(992\) | 55.7654 | 1.77055 | ||||||||
\(993\) | 32.7846 | 1.04039 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −10.3923 | −0.329293 | ||||||||
\(997\) | −14.1436 | −0.447932 | −0.223966 | − | 0.974597i | \(-0.571900\pi\) | ||||
−0.223966 | + | 0.974597i | \(0.571900\pi\) | |||||||
\(998\) | 31.3901 | 0.993636 | ||||||||
\(999\) | 0.757875 | 0.0239781 |
(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 | 3675.2.a.bu.1.4 | 4 | ||
5.2 | odd | 4 | 735.2.d.f.589.7 | yes | 8 | ||
5.3 | odd | 4 | 735.2.d.f.589.2 | yes | 8 | ||
5.4 | even | 2 | 3675.2.a.bs.1.1 | 4 | |||
7.6 | odd | 2 | 3675.2.a.bs.1.4 | 4 | |||
15.2 | even | 4 | 2205.2.d.t.1324.2 | 8 | |||
15.8 | even | 4 | 2205.2.d.t.1324.8 | 8 | |||
35.2 | odd | 12 | 735.2.q.c.214.4 | 8 | |||
35.3 | even | 12 | 735.2.q.d.79.4 | 8 | |||
35.12 | even | 12 | 735.2.q.d.214.4 | 8 | |||
35.13 | even | 4 | 735.2.d.f.589.1 | ✓ | 8 | ||
35.17 | even | 12 | 735.2.q.c.79.1 | 8 | |||
35.18 | odd | 12 | 735.2.q.c.79.4 | 8 | |||
35.23 | odd | 12 | 735.2.q.d.214.1 | 8 | |||
35.27 | even | 4 | 735.2.d.f.589.8 | yes | 8 | ||
35.32 | odd | 12 | 735.2.q.d.79.1 | 8 | |||
35.33 | even | 12 | 735.2.q.c.214.1 | 8 | |||
35.34 | odd | 2 | inner | 3675.2.a.bu.1.1 | 4 | ||
105.62 | odd | 4 | 2205.2.d.t.1324.1 | 8 | |||
105.83 | odd | 4 | 2205.2.d.t.1324.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
735.2.d.f.589.1 | ✓ | 8 | 35.13 | even | 4 | ||
735.2.d.f.589.2 | yes | 8 | 5.3 | odd | 4 | ||
735.2.d.f.589.7 | yes | 8 | 5.2 | odd | 4 | ||
735.2.d.f.589.8 | yes | 8 | 35.27 | even | 4 | ||
735.2.q.c.79.1 | 8 | 35.17 | even | 12 | |||
735.2.q.c.79.4 | 8 | 35.18 | odd | 12 | |||
735.2.q.c.214.1 | 8 | 35.33 | even | 12 | |||
735.2.q.c.214.4 | 8 | 35.2 | odd | 12 | |||
735.2.q.d.79.1 | 8 | 35.32 | odd | 12 | |||
735.2.q.d.79.4 | 8 | 35.3 | even | 12 | |||
735.2.q.d.214.1 | 8 | 35.23 | odd | 12 | |||
735.2.q.d.214.4 | 8 | 35.12 | even | 12 | |||
2205.2.d.t.1324.1 | 8 | 105.62 | odd | 4 | |||
2205.2.d.t.1324.2 | 8 | 15.2 | even | 4 | |||
2205.2.d.t.1324.7 | 8 | 105.83 | odd | 4 | |||
2205.2.d.t.1324.8 | 8 | 15.8 | even | 4 | |||
3675.2.a.bs.1.1 | 4 | 5.4 | even | 2 | |||
3675.2.a.bs.1.4 | 4 | 7.6 | odd | 2 | |||
3675.2.a.bu.1.1 | 4 | 35.34 | odd | 2 | inner | ||
3675.2.a.bu.1.4 | 4 | 1.1 | even | 1 | trivial |