Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,2,Mod(1,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, 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("825.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.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: | \(6.58765816676\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 165) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.17009\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.53919 | −1.08837 | −0.544185 | − | 0.838965i | \(-0.683161\pi\) | ||||
−0.544185 | + | 0.838965i | \(0.683161\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0.369102 | 0.184551 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.53919 | −0.628371 | ||||||||
\(7\) | −0.290725 | −0.109884 | −0.0549418 | − | 0.998490i | \(-0.517497\pi\) | ||||
−0.0549418 | + | 0.998490i | \(0.517497\pi\) | |||||||
\(8\) | 2.51026 | 0.887511 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0.369102 | 0.106551 | ||||||||
\(13\) | −6.97107 | −1.93343 | −0.966714 | − | 0.255861i | \(-0.917641\pi\) | ||||
−0.966714 | + | 0.255861i | \(0.917641\pi\) | |||||||
\(14\) | 0.447480 | 0.119594 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.60197 | −1.15049 | ||||||||
\(17\) | −4.78765 | −1.16118 | −0.580588 | − | 0.814197i | \(-0.697177\pi\) | ||||
−0.580588 | + | 0.814197i | \(0.697177\pi\) | |||||||
\(18\) | −1.53919 | −0.362790 | ||||||||
\(19\) | 7.75872 | 1.77997 | 0.889987 | − | 0.455987i | \(-0.150714\pi\) | ||||
0.889987 | + | 0.455987i | \(0.150714\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.290725 | −0.0634413 | ||||||||
\(22\) | 1.53919 | 0.328156 | ||||||||
\(23\) | −4.00000 | −0.834058 | −0.417029 | − | 0.908893i | \(-0.636929\pi\) | ||||
−0.417029 | + | 0.908893i | \(0.636929\pi\) | |||||||
\(24\) | 2.51026 | 0.512405 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 10.7298 | 2.10429 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −0.107307 | −0.0202791 | ||||||||
\(29\) | −7.41855 | −1.37759 | −0.688795 | − | 0.724956i | \(-0.741860\pi\) | ||||
−0.688795 | + | 0.724956i | \(0.741860\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.34017 | 1.13873 | 0.569364 | − | 0.822085i | \(-0.307189\pi\) | ||||
0.569364 | + | 0.822085i | \(0.307189\pi\) | |||||||
\(32\) | 2.06278 | 0.364651 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | 7.36910 | 1.26379 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.369102 | 0.0615171 | ||||||||
\(37\) | 3.41855 | 0.562006 | 0.281003 | − | 0.959707i | \(-0.409333\pi\) | ||||
0.281003 | + | 0.959707i | \(0.409333\pi\) | |||||||
\(38\) | −11.9421 | −1.93727 | ||||||||
\(39\) | −6.97107 | −1.11626 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.41855 | −1.15858 | −0.579291 | − | 0.815120i | \(-0.696671\pi\) | ||||
−0.579291 | + | 0.815120i | \(0.696671\pi\) | |||||||
\(42\) | 0.447480 | 0.0690477 | ||||||||
\(43\) | −0.290725 | −0.0443351 | −0.0221675 | − | 0.999754i | \(-0.507057\pi\) | ||||
−0.0221675 | + | 0.999754i | \(0.507057\pi\) | |||||||
\(44\) | −0.369102 | −0.0556443 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.15676 | 0.907764 | ||||||||
\(47\) | −5.26180 | −0.767512 | −0.383756 | − | 0.923435i | \(-0.625370\pi\) | ||||
−0.383756 | + | 0.923435i | \(0.625370\pi\) | |||||||
\(48\) | −4.60197 | −0.664237 | ||||||||
\(49\) | −6.91548 | −0.987926 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.78765 | −0.670406 | ||||||||
\(52\) | −2.57304 | −0.356816 | ||||||||
\(53\) | −5.75872 | −0.791022 | −0.395511 | − | 0.918461i | \(-0.629432\pi\) | ||||
−0.395511 | + | 0.918461i | \(0.629432\pi\) | |||||||
\(54\) | −1.53919 | −0.209457 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.729794 | −0.0975229 | ||||||||
\(57\) | 7.75872 | 1.02767 | ||||||||
\(58\) | 11.4186 | 1.49933 | ||||||||
\(59\) | 3.60197 | 0.468936 | 0.234468 | − | 0.972124i | \(-0.424665\pi\) | ||||
0.234468 | + | 0.972124i | \(0.424665\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.68035 | −0.855331 | −0.427665 | − | 0.903937i | \(-0.640664\pi\) | ||||
−0.427665 | + | 0.903937i | \(0.640664\pi\) | |||||||
\(62\) | −9.75872 | −1.23936 | ||||||||
\(63\) | −0.290725 | −0.0366279 | ||||||||
\(64\) | 6.02893 | 0.753616 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.53919 | 0.189461 | ||||||||
\(67\) | −6.15676 | −0.752167 | −0.376084 | − | 0.926586i | \(-0.622729\pi\) | ||||
−0.376084 | + | 0.926586i | \(0.622729\pi\) | |||||||
\(68\) | −1.76713 | −0.214296 | ||||||||
\(69\) | −4.00000 | −0.481543 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.07838 | −0.602693 | −0.301346 | − | 0.953515i | \(-0.597436\pi\) | ||||
−0.301346 | + | 0.953515i | \(0.597436\pi\) | |||||||
\(72\) | 2.51026 | 0.295837 | ||||||||
\(73\) | 1.12783 | 0.132002 | 0.0660010 | − | 0.997820i | \(-0.478976\pi\) | ||||
0.0660010 | + | 0.997820i | \(0.478976\pi\) | |||||||
\(74\) | −5.26180 | −0.611671 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.86376 | 0.328496 | ||||||||
\(77\) | 0.290725 | 0.0331311 | ||||||||
\(78\) | 10.7298 | 1.21491 | ||||||||
\(79\) | −0.921622 | −0.103691 | −0.0518453 | − | 0.998655i | \(-0.516510\pi\) | ||||
−0.0518453 | + | 0.998655i | \(0.516510\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 11.4186 | 1.26097 | ||||||||
\(83\) | −1.70928 | −0.187617 | −0.0938087 | − | 0.995590i | \(-0.529904\pi\) | ||||
−0.0938087 | + | 0.995590i | \(0.529904\pi\) | |||||||
\(84\) | −0.107307 | −0.0117082 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.447480 | 0.0482530 | ||||||||
\(87\) | −7.41855 | −0.795352 | ||||||||
\(88\) | −2.51026 | −0.267595 | ||||||||
\(89\) | 4.34017 | 0.460057 | 0.230029 | − | 0.973184i | \(-0.426118\pi\) | ||||
0.230029 | + | 0.973184i | \(0.426118\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.02666 | 0.212452 | ||||||||
\(92\) | −1.47641 | −0.153926 | ||||||||
\(93\) | 6.34017 | 0.657445 | ||||||||
\(94\) | 8.09890 | 0.835337 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.06278 | 0.210532 | ||||||||
\(97\) | −4.68035 | −0.475217 | −0.237609 | − | 0.971361i | \(-0.576364\pi\) | ||||
−0.237609 | + | 0.971361i | \(0.576364\pi\) | |||||||
\(98\) | 10.6442 | 1.07523 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.58145 | −0.853886 | −0.426943 | − | 0.904279i | \(-0.640410\pi\) | ||||
−0.426943 | + | 0.904279i | \(0.640410\pi\) | |||||||
\(102\) | 7.36910 | 0.729650 | ||||||||
\(103\) | −6.73820 | −0.663935 | −0.331968 | − | 0.943291i | \(-0.607712\pi\) | ||||
−0.331968 | + | 0.943291i | \(0.607712\pi\) | |||||||
\(104\) | −17.4992 | −1.71594 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.86376 | 0.860925 | ||||||||
\(107\) | −12.2329 | −1.18260 | −0.591298 | − | 0.806453i | \(-0.701384\pi\) | ||||
−0.591298 | + | 0.806453i | \(0.701384\pi\) | |||||||
\(108\) | 0.369102 | 0.0355169 | ||||||||
\(109\) | −6.31351 | −0.604725 | −0.302362 | − | 0.953193i | \(-0.597775\pi\) | ||||
−0.302362 | + | 0.953193i | \(0.597775\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.41855 | 0.324474 | ||||||||
\(112\) | 1.33791 | 0.126420 | ||||||||
\(113\) | 16.4969 | 1.55190 | 0.775950 | − | 0.630794i | \(-0.217271\pi\) | ||||
0.775950 | + | 0.630794i | \(0.217271\pi\) | |||||||
\(114\) | −11.9421 | −1.11848 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.73820 | −0.254236 | ||||||||
\(117\) | −6.97107 | −0.644476 | ||||||||
\(118\) | −5.54411 | −0.510377 | ||||||||
\(119\) | 1.39189 | 0.127594 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 10.2823 | 0.930917 | ||||||||
\(123\) | −7.41855 | −0.668908 | ||||||||
\(124\) | 2.34017 | 0.210154 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.447480 | 0.0398647 | ||||||||
\(127\) | −4.87217 | −0.432336 | −0.216168 | − | 0.976356i | \(-0.569356\pi\) | ||||
−0.216168 | + | 0.976356i | \(0.569356\pi\) | |||||||
\(128\) | −13.4052 | −1.18487 | ||||||||
\(129\) | −0.290725 | −0.0255969 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.68035 | −0.758405 | −0.379203 | − | 0.925314i | \(-0.623802\pi\) | ||||
−0.379203 | + | 0.925314i | \(0.623802\pi\) | |||||||
\(132\) | −0.369102 | −0.0321262 | ||||||||
\(133\) | −2.25565 | −0.195590 | ||||||||
\(134\) | 9.47641 | 0.818637 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −12.0183 | −1.03056 | ||||||||
\(137\) | 12.5958 | 1.07613 | 0.538067 | − | 0.842902i | \(-0.319155\pi\) | ||||
0.538067 | + | 0.842902i | \(0.319155\pi\) | |||||||
\(138\) | 6.15676 | 0.524098 | ||||||||
\(139\) | −9.91548 | −0.841020 | −0.420510 | − | 0.907288i | \(-0.638149\pi\) | ||||
−0.420510 | + | 0.907288i | \(0.638149\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.26180 | −0.443123 | ||||||||
\(142\) | 7.81658 | 0.655953 | ||||||||
\(143\) | 6.97107 | 0.582950 | ||||||||
\(144\) | −4.60197 | −0.383497 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.73594 | −0.143667 | ||||||||
\(147\) | −6.91548 | −0.570379 | ||||||||
\(148\) | 1.26180 | 0.103719 | ||||||||
\(149\) | −1.26180 | −0.103370 | −0.0516851 | − | 0.998663i | \(-0.516459\pi\) | ||||
−0.0516851 | + | 0.998663i | \(0.516459\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.60197 | 0.130366 | 0.0651832 | − | 0.997873i | \(-0.479237\pi\) | ||||
0.0651832 | + | 0.997873i | \(0.479237\pi\) | |||||||
\(152\) | 19.4764 | 1.57975 | ||||||||
\(153\) | −4.78765 | −0.387059 | ||||||||
\(154\) | −0.447480 | −0.0360590 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.57304 | −0.206008 | ||||||||
\(157\) | 7.10504 | 0.567044 | 0.283522 | − | 0.958966i | \(-0.408497\pi\) | ||||
0.283522 | + | 0.958966i | \(0.408497\pi\) | |||||||
\(158\) | 1.41855 | 0.112854 | ||||||||
\(159\) | −5.75872 | −0.456696 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.16290 | 0.0916492 | ||||||||
\(162\) | −1.53919 | −0.120930 | ||||||||
\(163\) | 22.9360 | 1.79649 | 0.898243 | − | 0.439499i | \(-0.144844\pi\) | ||||
0.898243 | + | 0.439499i | \(0.144844\pi\) | |||||||
\(164\) | −2.73820 | −0.213818 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.63090 | 0.204197 | ||||||||
\(167\) | −4.81432 | −0.372543 | −0.186271 | − | 0.982498i | \(-0.559640\pi\) | ||||
−0.186271 | + | 0.982498i | \(0.559640\pi\) | |||||||
\(168\) | −0.729794 | −0.0563049 | ||||||||
\(169\) | 35.5958 | 2.73814 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.75872 | 0.593324 | ||||||||
\(172\) | −0.107307 | −0.00818209 | ||||||||
\(173\) | 12.8865 | 0.979746 | 0.489873 | − | 0.871794i | \(-0.337043\pi\) | ||||
0.489873 | + | 0.871794i | \(0.337043\pi\) | |||||||
\(174\) | 11.4186 | 0.865638 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.60197 | 0.346886 | ||||||||
\(177\) | 3.60197 | 0.270741 | ||||||||
\(178\) | −6.68035 | −0.500713 | ||||||||
\(179\) | 1.84324 | 0.137771 | 0.0688853 | − | 0.997625i | \(-0.478056\pi\) | ||||
0.0688853 | + | 0.997625i | \(0.478056\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.2823 | 0.764278 | 0.382139 | − | 0.924105i | \(-0.375187\pi\) | ||||
0.382139 | + | 0.924105i | \(0.375187\pi\) | |||||||
\(182\) | −3.11942 | −0.231226 | ||||||||
\(183\) | −6.68035 | −0.493825 | ||||||||
\(184\) | −10.0410 | −0.740235 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −9.75872 | −0.715544 | ||||||||
\(187\) | 4.78765 | 0.350108 | ||||||||
\(188\) | −1.94214 | −0.141645 | ||||||||
\(189\) | −0.290725 | −0.0211471 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.5174 | −0.833373 | −0.416687 | − | 0.909050i | \(-0.636809\pi\) | ||||
−0.416687 | + | 0.909050i | \(0.636809\pi\) | |||||||
\(192\) | 6.02893 | 0.435101 | ||||||||
\(193\) | −3.86603 | −0.278283 | −0.139141 | − | 0.990273i | \(-0.544434\pi\) | ||||
−0.139141 | + | 0.990273i | \(0.544434\pi\) | |||||||
\(194\) | 7.20394 | 0.517212 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.55252 | −0.182323 | ||||||||
\(197\) | 8.57304 | 0.610804 | 0.305402 | − | 0.952224i | \(-0.401209\pi\) | ||||
0.305402 | + | 0.952224i | \(0.401209\pi\) | |||||||
\(198\) | 1.53919 | 0.109385 | ||||||||
\(199\) | 8.31351 | 0.589329 | 0.294665 | − | 0.955601i | \(-0.404792\pi\) | ||||
0.294665 | + | 0.955601i | \(0.404792\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.15676 | −0.434264 | ||||||||
\(202\) | 13.2085 | 0.929345 | ||||||||
\(203\) | 2.15676 | 0.151375 | ||||||||
\(204\) | −1.76713 | −0.123724 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 10.3714 | 0.722608 | ||||||||
\(207\) | −4.00000 | −0.278019 | ||||||||
\(208\) | 32.0806 | 2.22439 | ||||||||
\(209\) | −7.75872 | −0.536682 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 25.9155 | 1.78410 | 0.892048 | − | 0.451941i | \(-0.149268\pi\) | ||||
0.892048 | + | 0.451941i | \(0.149268\pi\) | |||||||
\(212\) | −2.12556 | −0.145984 | ||||||||
\(213\) | −5.07838 | −0.347965 | ||||||||
\(214\) | 18.8287 | 1.28710 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.51026 | 0.170802 | ||||||||
\(217\) | −1.84324 | −0.125128 | ||||||||
\(218\) | 9.71769 | 0.658165 | ||||||||
\(219\) | 1.12783 | 0.0762114 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 33.3751 | 2.24505 | ||||||||
\(222\) | −5.26180 | −0.353149 | ||||||||
\(223\) | 9.62863 | 0.644781 | 0.322390 | − | 0.946607i | \(-0.395514\pi\) | ||||
0.322390 | + | 0.946607i | \(0.395514\pi\) | |||||||
\(224\) | −0.599701 | −0.0400692 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −25.3919 | −1.68904 | ||||||||
\(227\) | 18.3896 | 1.22056 | 0.610281 | − | 0.792185i | \(-0.291057\pi\) | ||||
0.610281 | + | 0.792185i | \(0.291057\pi\) | |||||||
\(228\) | 2.86376 | 0.189657 | ||||||||
\(229\) | 17.1506 | 1.13334 | 0.566672 | − | 0.823943i | \(-0.308231\pi\) | ||||
0.566672 | + | 0.823943i | \(0.308231\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.290725 | 0.0191283 | ||||||||
\(232\) | −18.6225 | −1.22263 | ||||||||
\(233\) | 4.10731 | 0.269079 | 0.134539 | − | 0.990908i | \(-0.457045\pi\) | ||||
0.134539 | + | 0.990908i | \(0.457045\pi\) | |||||||
\(234\) | 10.7298 | 0.701429 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.32950 | 0.0865428 | ||||||||
\(237\) | −0.921622 | −0.0598658 | ||||||||
\(238\) | −2.14238 | −0.138870 | ||||||||
\(239\) | −4.36683 | −0.282467 | −0.141234 | − | 0.989976i | \(-0.545107\pi\) | ||||
−0.141234 | + | 0.989976i | \(0.545107\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.20394 | −0.335215 | −0.167608 | − | 0.985854i | \(-0.553604\pi\) | ||||
−0.167608 | + | 0.985854i | \(0.553604\pi\) | |||||||
\(242\) | −1.53919 | −0.0989428 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −2.46573 | −0.157852 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 11.4186 | 0.728020 | ||||||||
\(247\) | −54.0866 | −3.44145 | ||||||||
\(248\) | 15.9155 | 1.01063 | ||||||||
\(249\) | −1.70928 | −0.108321 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.28231 | −0.522775 | −0.261388 | − | 0.965234i | \(-0.584180\pi\) | ||||
−0.261388 | + | 0.965234i | \(0.584180\pi\) | |||||||
\(252\) | −0.107307 | −0.00675972 | ||||||||
\(253\) | 4.00000 | 0.251478 | ||||||||
\(254\) | 7.49920 | 0.470541 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8.57531 | 0.535957 | ||||||||
\(257\) | −11.0205 | −0.687441 | −0.343721 | − | 0.939072i | \(-0.611687\pi\) | ||||
−0.343721 | + | 0.939072i | \(0.611687\pi\) | |||||||
\(258\) | 0.447480 | 0.0278589 | ||||||||
\(259\) | −0.993857 | −0.0617553 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.41855 | −0.459197 | ||||||||
\(262\) | 13.3607 | 0.825426 | ||||||||
\(263\) | 2.97107 | 0.183204 | 0.0916020 | − | 0.995796i | \(-0.470801\pi\) | ||||
0.0916020 | + | 0.995796i | \(0.470801\pi\) | |||||||
\(264\) | −2.51026 | −0.154496 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 3.47187 | 0.212874 | ||||||||
\(267\) | 4.34017 | 0.265614 | ||||||||
\(268\) | −2.27247 | −0.138813 | ||||||||
\(269\) | −15.8432 | −0.965980 | −0.482990 | − | 0.875626i | \(-0.660449\pi\) | ||||
−0.482990 | + | 0.875626i | \(0.660449\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.28231 | −0.381623 | −0.190812 | − | 0.981627i | \(-0.561112\pi\) | ||||
−0.190812 | + | 0.981627i | \(0.561112\pi\) | |||||||
\(272\) | 22.0326 | 1.33592 | ||||||||
\(273\) | 2.02666 | 0.122659 | ||||||||
\(274\) | −19.3874 | −1.17123 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.47641 | −0.0888694 | ||||||||
\(277\) | −5.12783 | −0.308101 | −0.154051 | − | 0.988063i | \(-0.549232\pi\) | ||||
−0.154051 | + | 0.988063i | \(0.549232\pi\) | |||||||
\(278\) | 15.2618 | 0.915342 | ||||||||
\(279\) | 6.34017 | 0.379576 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 21.8888 | 1.30578 | 0.652889 | − | 0.757454i | \(-0.273557\pi\) | ||||
0.652889 | + | 0.757454i | \(0.273557\pi\) | |||||||
\(282\) | 8.09890 | 0.482282 | ||||||||
\(283\) | −25.9649 | −1.54345 | −0.771727 | − | 0.635954i | \(-0.780607\pi\) | ||||
−0.771727 | + | 0.635954i | \(0.780607\pi\) | |||||||
\(284\) | −1.87444 | −0.111228 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −10.7298 | −0.634466 | ||||||||
\(287\) | 2.15676 | 0.127309 | ||||||||
\(288\) | 2.06278 | 0.121550 | ||||||||
\(289\) | 5.92162 | 0.348331 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.68035 | −0.274367 | ||||||||
\(292\) | 0.416283 | 0.0243611 | ||||||||
\(293\) | −10.4163 | −0.608526 | −0.304263 | − | 0.952588i | \(-0.598410\pi\) | ||||
−0.304263 | + | 0.952588i | \(0.598410\pi\) | |||||||
\(294\) | 10.6442 | 0.620784 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 8.58145 | 0.498787 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | 1.94214 | 0.112505 | ||||||||
\(299\) | 27.8843 | 1.61259 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.0845208 | 0.00487170 | ||||||||
\(302\) | −2.46573 | −0.141887 | ||||||||
\(303\) | −8.58145 | −0.492991 | ||||||||
\(304\) | −35.7054 | −2.04785 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 7.36910 | 0.421264 | ||||||||
\(307\) | 29.0700 | 1.65911 | 0.829555 | − | 0.558425i | \(-0.188594\pi\) | ||||
0.829555 | + | 0.558425i | \(0.188594\pi\) | |||||||
\(308\) | 0.107307 | 0.00611439 | ||||||||
\(309\) | −6.73820 | −0.383323 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.44521 | 0.308770 | 0.154385 | − | 0.988011i | \(-0.450660\pi\) | ||||
0.154385 | + | 0.988011i | \(0.450660\pi\) | |||||||
\(312\) | −17.4992 | −0.990697 | ||||||||
\(313\) | −25.0928 | −1.41833 | −0.709163 | − | 0.705044i | \(-0.750927\pi\) | ||||
−0.709163 | + | 0.705044i | \(0.750927\pi\) | |||||||
\(314\) | −10.9360 | −0.617154 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.340173 | −0.0191362 | ||||||||
\(317\) | −21.1773 | −1.18943 | −0.594717 | − | 0.803935i | \(-0.702736\pi\) | ||||
−0.594717 | + | 0.803935i | \(0.702736\pi\) | |||||||
\(318\) | 8.86376 | 0.497055 | ||||||||
\(319\) | 7.41855 | 0.415359 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.2329 | −0.682772 | ||||||||
\(322\) | −1.78992 | −0.0997484 | ||||||||
\(323\) | −37.1461 | −2.06686 | ||||||||
\(324\) | 0.369102 | 0.0205057 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −35.3028 | −1.95524 | ||||||||
\(327\) | −6.31351 | −0.349138 | ||||||||
\(328\) | −18.6225 | −1.02825 | ||||||||
\(329\) | 1.52973 | 0.0843369 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.70701 | −0.368650 | −0.184325 | − | 0.982865i | \(-0.559010\pi\) | ||||
−0.184325 | + | 0.982865i | \(0.559010\pi\) | |||||||
\(332\) | −0.630898 | −0.0346250 | ||||||||
\(333\) | 3.41855 | 0.187335 | ||||||||
\(334\) | 7.41014 | 0.405465 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.33791 | 0.0729887 | ||||||||
\(337\) | −23.7503 | −1.29376 | −0.646881 | − | 0.762591i | \(-0.723927\pi\) | ||||
−0.646881 | + | 0.762591i | \(0.723927\pi\) | |||||||
\(338\) | −54.7887 | −2.98011 | ||||||||
\(339\) | 16.4969 | 0.895990 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.34017 | −0.343340 | ||||||||
\(342\) | −11.9421 | −0.645757 | ||||||||
\(343\) | 4.04557 | 0.218440 | ||||||||
\(344\) | −0.729794 | −0.0393479 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −19.8348 | −1.06633 | ||||||||
\(347\) | 31.1689 | 1.67323 | 0.836616 | − | 0.547790i | \(-0.184531\pi\) | ||||
0.836616 | + | 0.547790i | \(0.184531\pi\) | |||||||
\(348\) | −2.73820 | −0.146783 | ||||||||
\(349\) | 11.0472 | 0.591342 | 0.295671 | − | 0.955290i | \(-0.404457\pi\) | ||||
0.295671 | + | 0.955290i | \(0.404457\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.97107 | −0.372088 | ||||||||
\(352\) | −2.06278 | −0.109947 | ||||||||
\(353\) | 27.4329 | 1.46011 | 0.730054 | − | 0.683390i | \(-0.239495\pi\) | ||||
0.730054 | + | 0.683390i | \(0.239495\pi\) | |||||||
\(354\) | −5.54411 | −0.294666 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.60197 | 0.0849041 | ||||||||
\(357\) | 1.39189 | 0.0736666 | ||||||||
\(358\) | −2.83710 | −0.149945 | ||||||||
\(359\) | −19.1506 | −1.01073 | −0.505365 | − | 0.862905i | \(-0.668642\pi\) | ||||
−0.505365 | + | 0.862905i | \(0.668642\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 41.1978 | 2.16830 | ||||||||
\(362\) | −15.8264 | −0.831818 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | 0.748046 | 0.0392083 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 10.2823 | 0.537465 | ||||||||
\(367\) | 14.5692 | 0.760504 | 0.380252 | − | 0.924883i | \(-0.375837\pi\) | ||||
0.380252 | + | 0.924883i | \(0.375837\pi\) | |||||||
\(368\) | 18.4079 | 0.959577 | ||||||||
\(369\) | −7.41855 | −0.386194 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.67420 | 0.0869203 | ||||||||
\(372\) | 2.34017 | 0.121332 | ||||||||
\(373\) | 8.81432 | 0.456388 | 0.228194 | − | 0.973616i | \(-0.426718\pi\) | ||||
0.228194 | + | 0.973616i | \(0.426718\pi\) | |||||||
\(374\) | −7.36910 | −0.381047 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −13.2085 | −0.681175 | ||||||||
\(377\) | 51.7152 | 2.66347 | ||||||||
\(378\) | 0.447480 | 0.0230159 | ||||||||
\(379\) | −23.5174 | −1.20801 | −0.604005 | − | 0.796980i | \(-0.706429\pi\) | ||||
−0.604005 | + | 0.796980i | \(0.706429\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.87217 | −0.249609 | ||||||||
\(382\) | 17.7275 | 0.907019 | ||||||||
\(383\) | 19.3028 | 0.986329 | 0.493164 | − | 0.869936i | \(-0.335840\pi\) | ||||
0.493164 | + | 0.869936i | \(0.335840\pi\) | |||||||
\(384\) | −13.4052 | −0.684082 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.95055 | 0.302875 | ||||||||
\(387\) | −0.290725 | −0.0147784 | ||||||||
\(388\) | −1.72753 | −0.0877019 | ||||||||
\(389\) | −20.0410 | −1.01612 | −0.508060 | − | 0.861321i | \(-0.669637\pi\) | ||||
−0.508060 | + | 0.861321i | \(0.669637\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 19.1506 | 0.968488 | ||||||||
\(392\) | −17.3596 | −0.876795 | ||||||||
\(393\) | −8.68035 | −0.437866 | ||||||||
\(394\) | −13.1955 | −0.664781 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.369102 | −0.0185481 | ||||||||
\(397\) | 33.3607 | 1.67433 | 0.837163 | − | 0.546954i | \(-0.184213\pi\) | ||||
0.837163 | + | 0.546954i | \(0.184213\pi\) | |||||||
\(398\) | −12.7961 | −0.641409 | ||||||||
\(399\) | −2.25565 | −0.112924 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −37.6475 | −1.88003 | −0.940014 | − | 0.341135i | \(-0.889189\pi\) | ||||
−0.940014 | + | 0.341135i | \(0.889189\pi\) | |||||||
\(402\) | 9.47641 | 0.472640 | ||||||||
\(403\) | −44.1978 | −2.20165 | ||||||||
\(404\) | −3.16743 | −0.157586 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.31965 | −0.164752 | ||||||||
\(407\) | −3.41855 | −0.169451 | ||||||||
\(408\) | −12.0183 | −0.594992 | ||||||||
\(409\) | −25.2039 | −1.24625 | −0.623127 | − | 0.782120i | \(-0.714138\pi\) | ||||
−0.623127 | + | 0.782120i | \(0.714138\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.5958 | 0.621306 | ||||||||
\(412\) | −2.48709 | −0.122530 | ||||||||
\(413\) | −1.04718 | −0.0515284 | ||||||||
\(414\) | 6.15676 | 0.302588 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −14.3798 | −0.705027 | ||||||||
\(417\) | −9.91548 | −0.485563 | ||||||||
\(418\) | 11.9421 | 0.584109 | ||||||||
\(419\) | 17.8432 | 0.871700 | 0.435850 | − | 0.900019i | \(-0.356448\pi\) | ||||
0.435850 | + | 0.900019i | \(0.356448\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.8120 | −0.575684 | −0.287842 | − | 0.957678i | \(-0.592938\pi\) | ||||
−0.287842 | + | 0.957678i | \(0.592938\pi\) | |||||||
\(422\) | −39.8888 | −1.94176 | ||||||||
\(423\) | −5.26180 | −0.255837 | ||||||||
\(424\) | −14.4559 | −0.702040 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 7.81658 | 0.378715 | ||||||||
\(427\) | 1.94214 | 0.0939868 | ||||||||
\(428\) | −4.51518 | −0.218249 | ||||||||
\(429\) | 6.97107 | 0.336566 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.6803 | 0.803464 | 0.401732 | − | 0.915757i | \(-0.368408\pi\) | ||||
0.401732 | + | 0.915757i | \(0.368408\pi\) | |||||||
\(432\) | −4.60197 | −0.221412 | ||||||||
\(433\) | 28.3135 | 1.36066 | 0.680330 | − | 0.732906i | \(-0.261836\pi\) | ||||
0.680330 | + | 0.732906i | \(0.261836\pi\) | |||||||
\(434\) | 2.83710 | 0.136185 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.33033 | −0.111603 | ||||||||
\(437\) | −31.0349 | −1.48460 | ||||||||
\(438\) | −1.73594 | −0.0829463 | ||||||||
\(439\) | −27.4452 | −1.30989 | −0.654944 | − | 0.755677i | \(-0.727308\pi\) | ||||
−0.654944 | + | 0.755677i | \(0.727308\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.91548 | −0.329309 | ||||||||
\(442\) | −51.3705 | −2.44345 | ||||||||
\(443\) | −0.412408 | −0.0195941 | −0.00979704 | − | 0.999952i | \(-0.503119\pi\) | ||||
−0.00979704 | + | 0.999952i | \(0.503119\pi\) | |||||||
\(444\) | 1.26180 | 0.0598822 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −14.8203 | −0.701761 | ||||||||
\(447\) | −1.26180 | −0.0596809 | ||||||||
\(448\) | −1.75276 | −0.0828100 | ||||||||
\(449\) | 1.33403 | 0.0629568 | 0.0314784 | − | 0.999504i | \(-0.489978\pi\) | ||||
0.0314784 | + | 0.999504i | \(0.489978\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.41855 | 0.349326 | ||||||||
\(452\) | 6.08906 | 0.286405 | ||||||||
\(453\) | 1.60197 | 0.0752670 | ||||||||
\(454\) | −28.3051 | −1.32842 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 19.4764 | 0.912066 | ||||||||
\(457\) | −11.6514 | −0.545030 | −0.272515 | − | 0.962151i | \(-0.587855\pi\) | ||||
−0.272515 | + | 0.962151i | \(0.587855\pi\) | |||||||
\(458\) | −26.3980 | −1.23350 | ||||||||
\(459\) | −4.78765 | −0.223469 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.05786 | −0.0958440 | −0.0479220 | − | 0.998851i | \(-0.515260\pi\) | ||||
−0.0479220 | + | 0.998851i | \(0.515260\pi\) | |||||||
\(462\) | −0.447480 | −0.0208187 | ||||||||
\(463\) | −28.7792 | −1.33748 | −0.668742 | − | 0.743494i | \(-0.733167\pi\) | ||||
−0.668742 | + | 0.743494i | \(0.733167\pi\) | |||||||
\(464\) | 34.1399 | 1.58491 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.32192 | −0.292857 | ||||||||
\(467\) | −1.84324 | −0.0852952 | −0.0426476 | − | 0.999090i | \(-0.513579\pi\) | ||||
−0.0426476 | + | 0.999090i | \(0.513579\pi\) | |||||||
\(468\) | −2.57304 | −0.118939 | ||||||||
\(469\) | 1.78992 | 0.0826509 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.10504 | 0.327383 | ||||||||
\(472\) | 9.04187 | 0.416186 | ||||||||
\(473\) | 0.290725 | 0.0133675 | ||||||||
\(474\) | 1.41855 | 0.0651562 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.513749 | 0.0235477 | ||||||||
\(477\) | −5.75872 | −0.263674 | ||||||||
\(478\) | 6.72138 | 0.307429 | ||||||||
\(479\) | 26.8371 | 1.22622 | 0.613109 | − | 0.789998i | \(-0.289919\pi\) | ||||
0.613109 | + | 0.789998i | \(0.289919\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −23.8310 | −1.08660 | ||||||||
\(482\) | 8.00984 | 0.364838 | ||||||||
\(483\) | 1.16290 | 0.0529137 | ||||||||
\(484\) | 0.369102 | 0.0167774 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.53919 | −0.0698190 | ||||||||
\(487\) | −28.5646 | −1.29439 | −0.647193 | − | 0.762326i | \(-0.724057\pi\) | ||||
−0.647193 | + | 0.762326i | \(0.724057\pi\) | |||||||
\(488\) | −16.7694 | −0.759115 | ||||||||
\(489\) | 22.9360 | 1.03720 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 25.9877 | 1.17281 | 0.586405 | − | 0.810018i | \(-0.300543\pi\) | ||||
0.586405 | + | 0.810018i | \(0.300543\pi\) | |||||||
\(492\) | −2.73820 | −0.123448 | ||||||||
\(493\) | 35.5174 | 1.59963 | ||||||||
\(494\) | 83.2495 | 3.74557 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −29.1773 | −1.31010 | ||||||||
\(497\) | 1.47641 | 0.0662260 | ||||||||
\(498\) | 2.63090 | 0.117893 | ||||||||
\(499\) | −27.5174 | −1.23185 | −0.615925 | − | 0.787805i | \(-0.711218\pi\) | ||||
−0.615925 | + | 0.787805i | \(0.711218\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.81432 | −0.215088 | ||||||||
\(502\) | 12.7480 | 0.568973 | ||||||||
\(503\) | −22.6576 | −1.01025 | −0.505125 | − | 0.863046i | \(-0.668554\pi\) | ||||
−0.505125 | + | 0.863046i | \(0.668554\pi\) | |||||||
\(504\) | −0.729794 | −0.0325076 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −6.15676 | −0.273701 | ||||||||
\(507\) | 35.5958 | 1.58087 | ||||||||
\(508\) | −1.79833 | −0.0797880 | ||||||||
\(509\) | −27.8432 | −1.23413 | −0.617065 | − | 0.786912i | \(-0.711678\pi\) | ||||
−0.617065 | + | 0.786912i | \(0.711678\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.327887 | −0.0145049 | ||||||||
\(512\) | 13.6114 | 0.601546 | ||||||||
\(513\) | 7.75872 | 0.342556 | ||||||||
\(514\) | 16.9627 | 0.748191 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.107307 | −0.00472393 | ||||||||
\(517\) | 5.26180 | 0.231413 | ||||||||
\(518\) | 1.52973 | 0.0672126 | ||||||||
\(519\) | 12.8865 | 0.565657 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 29.7009 | 1.30122 | 0.650609 | − | 0.759413i | \(-0.274514\pi\) | ||||
0.650609 | + | 0.759413i | \(0.274514\pi\) | |||||||
\(522\) | 11.4186 | 0.499776 | ||||||||
\(523\) | −24.7565 | −1.08252 | −0.541262 | − | 0.840854i | \(-0.682053\pi\) | ||||
−0.541262 | + | 0.840854i | \(0.682053\pi\) | |||||||
\(524\) | −3.20394 | −0.139965 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.57304 | −0.199394 | ||||||||
\(527\) | −30.3545 | −1.32226 | ||||||||
\(528\) | 4.60197 | 0.200275 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.60197 | 0.156312 | ||||||||
\(532\) | −0.832567 | −0.0360963 | ||||||||
\(533\) | 51.7152 | 2.24004 | ||||||||
\(534\) | −6.68035 | −0.289087 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −15.4551 | −0.667557 | ||||||||
\(537\) | 1.84324 | 0.0795419 | ||||||||
\(538\) | 24.3857 | 1.05134 | ||||||||
\(539\) | 6.91548 | 0.297871 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.5236 | −0.538431 | −0.269216 | − | 0.963080i | \(-0.586764\pi\) | ||||
−0.269216 | + | 0.963080i | \(0.586764\pi\) | |||||||
\(542\) | 9.66967 | 0.415348 | ||||||||
\(543\) | 10.2823 | 0.441256 | ||||||||
\(544\) | −9.87587 | −0.423425 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −3.11942 | −0.133499 | ||||||||
\(547\) | 14.2784 | 0.610502 | 0.305251 | − | 0.952272i | \(-0.401260\pi\) | ||||
0.305251 | + | 0.952272i | \(0.401260\pi\) | |||||||
\(548\) | 4.64915 | 0.198602 | ||||||||
\(549\) | −6.68035 | −0.285110 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −57.5585 | −2.45207 | ||||||||
\(552\) | −10.0410 | −0.427375 | ||||||||
\(553\) | 0.267938 | 0.0113939 | ||||||||
\(554\) | 7.89269 | 0.335328 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.65983 | −0.155211 | ||||||||
\(557\) | 3.57918 | 0.151655 | 0.0758274 | − | 0.997121i | \(-0.475840\pi\) | ||||
0.0758274 | + | 0.997121i | \(0.475840\pi\) | |||||||
\(558\) | −9.75872 | −0.413120 | ||||||||
\(559\) | 2.02666 | 0.0857187 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.78765 | 0.202135 | ||||||||
\(562\) | −33.6910 | −1.42117 | ||||||||
\(563\) | −28.9588 | −1.22047 | −0.610234 | − | 0.792222i | \(-0.708924\pi\) | ||||
−0.610234 | + | 0.792222i | \(0.708924\pi\) | |||||||
\(564\) | −1.94214 | −0.0817789 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 39.9649 | 1.67985 | ||||||||
\(567\) | −0.290725 | −0.0122093 | ||||||||
\(568\) | −12.7480 | −0.534896 | ||||||||
\(569\) | −25.8264 | −1.08270 | −0.541350 | − | 0.840797i | \(-0.682087\pi\) | ||||
−0.541350 | + | 0.840797i | \(0.682087\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.1194 | 0.716425 | 0.358213 | − | 0.933640i | \(-0.383386\pi\) | ||||
0.358213 | + | 0.933640i | \(0.383386\pi\) | |||||||
\(572\) | 2.57304 | 0.107584 | ||||||||
\(573\) | −11.5174 | −0.481148 | ||||||||
\(574\) | −3.31965 | −0.138560 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 6.02893 | 0.251205 | ||||||||
\(577\) | −22.5692 | −0.939567 | −0.469783 | − | 0.882782i | \(-0.655668\pi\) | ||||
−0.469783 | + | 0.882782i | \(0.655668\pi\) | |||||||
\(578\) | −9.11450 | −0.379113 | ||||||||
\(579\) | −3.86603 | −0.160667 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.496928 | 0.0206161 | ||||||||
\(582\) | 7.20394 | 0.298613 | ||||||||
\(583\) | 5.75872 | 0.238502 | ||||||||
\(584\) | 2.83114 | 0.117153 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 16.0326 | 0.662302 | ||||||||
\(587\) | −3.63317 | −0.149957 | −0.0749784 | − | 0.997185i | \(-0.523889\pi\) | ||||
−0.0749784 | + | 0.997185i | \(0.523889\pi\) | |||||||
\(588\) | −2.55252 | −0.105264 | ||||||||
\(589\) | 49.1917 | 2.02691 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.57304 | 0.352648 | ||||||||
\(592\) | −15.7321 | −0.646584 | ||||||||
\(593\) | −12.3051 | −0.505310 | −0.252655 | − | 0.967556i | \(-0.581304\pi\) | ||||
−0.252655 | + | 0.967556i | \(0.581304\pi\) | |||||||
\(594\) | 1.53919 | 0.0631537 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.465732 | −0.0190771 | ||||||||
\(597\) | 8.31351 | 0.340249 | ||||||||
\(598\) | −42.9192 | −1.75510 | ||||||||
\(599\) | 19.6865 | 0.804368 | 0.402184 | − | 0.915559i | \(-0.368251\pi\) | ||||
0.402184 | + | 0.915559i | \(0.368251\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25.8843 | 1.05584 | 0.527921 | − | 0.849294i | \(-0.322972\pi\) | ||||
0.527921 | + | 0.849294i | \(0.322972\pi\) | |||||||
\(602\) | −0.130094 | −0.00530222 | ||||||||
\(603\) | −6.15676 | −0.250722 | ||||||||
\(604\) | 0.591290 | 0.0240593 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 13.2085 | 0.536557 | ||||||||
\(607\) | 41.5357 | 1.68588 | 0.842941 | − | 0.538006i | \(-0.180822\pi\) | ||||
0.842941 | + | 0.538006i | \(0.180822\pi\) | |||||||
\(608\) | 16.0045 | 0.649070 | ||||||||
\(609\) | 2.15676 | 0.0873961 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 36.6803 | 1.48393 | ||||||||
\(612\) | −1.76713 | −0.0714322 | ||||||||
\(613\) | 20.6453 | 0.833855 | 0.416927 | − | 0.908940i | \(-0.363107\pi\) | ||||
0.416927 | + | 0.908940i | \(0.363107\pi\) | |||||||
\(614\) | −44.7442 | −1.80573 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.729794 | 0.0294042 | ||||||||
\(617\) | −8.69472 | −0.350036 | −0.175018 | − | 0.984565i | \(-0.555998\pi\) | ||||
−0.175018 | + | 0.984565i | \(0.555998\pi\) | |||||||
\(618\) | 10.3714 | 0.417198 | ||||||||
\(619\) | 2.65368 | 0.106661 | 0.0533303 | − | 0.998577i | \(-0.483016\pi\) | ||||
0.0533303 | + | 0.998577i | \(0.483016\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.00000 | −0.160514 | ||||||||
\(622\) | −8.38121 | −0.336056 | ||||||||
\(623\) | −1.26180 | −0.0505528 | ||||||||
\(624\) | 32.0806 | 1.28425 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 38.6225 | 1.54367 | ||||||||
\(627\) | −7.75872 | −0.309854 | ||||||||
\(628\) | 2.62249 | 0.104649 | ||||||||
\(629\) | −16.3668 | −0.652588 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.6393 | −0.423544 | −0.211772 | − | 0.977319i | \(-0.567923\pi\) | ||||
−0.211772 | + | 0.977319i | \(0.567923\pi\) | |||||||
\(632\) | −2.31351 | −0.0920265 | ||||||||
\(633\) | 25.9155 | 1.03005 | ||||||||
\(634\) | 32.5958 | 1.29455 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −2.12556 | −0.0842839 | ||||||||
\(637\) | 48.2083 | 1.91008 | ||||||||
\(638\) | −11.4186 | −0.452065 | ||||||||
\(639\) | −5.07838 | −0.200898 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −35.8576 | −1.41629 | −0.708145 | − | 0.706067i | \(-0.750468\pi\) | ||||
−0.708145 | + | 0.706067i | \(0.750468\pi\) | |||||||
\(642\) | 18.8287 | 0.743109 | ||||||||
\(643\) | −12.2146 | −0.481697 | −0.240849 | − | 0.970563i | \(-0.577426\pi\) | ||||
−0.240849 | + | 0.970563i | \(0.577426\pi\) | |||||||
\(644\) | 0.429229 | 0.0169140 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 57.1748 | 2.24951 | ||||||||
\(647\) | −25.9421 | −1.01989 | −0.509945 | − | 0.860207i | \(-0.670334\pi\) | ||||
−0.509945 | + | 0.860207i | \(0.670334\pi\) | |||||||
\(648\) | 2.51026 | 0.0986123 | ||||||||
\(649\) | −3.60197 | −0.141390 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.84324 | −0.0722424 | ||||||||
\(652\) | 8.46573 | 0.331544 | ||||||||
\(653\) | 14.3402 | 0.561174 | 0.280587 | − | 0.959829i | \(-0.409471\pi\) | ||||
0.280587 | + | 0.959829i | \(0.409471\pi\) | |||||||
\(654\) | 9.71769 | 0.379992 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 34.1399 | 1.33294 | ||||||||
\(657\) | 1.12783 | 0.0440007 | ||||||||
\(658\) | −2.35455 | −0.0917899 | ||||||||
\(659\) | 6.52359 | 0.254123 | 0.127062 | − | 0.991895i | \(-0.459445\pi\) | ||||
0.127062 | + | 0.991895i | \(0.459445\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.16290 | 0.123022 | 0.0615112 | − | 0.998106i | \(-0.480408\pi\) | ||||
0.0615112 | + | 0.998106i | \(0.480408\pi\) | |||||||
\(662\) | 10.3234 | 0.401228 | ||||||||
\(663\) | 33.3751 | 1.29618 | ||||||||
\(664\) | −4.29072 | −0.166512 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5.26180 | −0.203890 | ||||||||
\(667\) | 29.6742 | 1.14899 | ||||||||
\(668\) | −1.77698 | −0.0687532 | ||||||||
\(669\) | 9.62863 | 0.372264 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.68035 | 0.257892 | ||||||||
\(672\) | −0.599701 | −0.0231340 | ||||||||
\(673\) | 18.4885 | 0.712680 | 0.356340 | − | 0.934356i | \(-0.384024\pi\) | ||||
0.356340 | + | 0.934356i | \(0.384024\pi\) | |||||||
\(674\) | 36.5562 | 1.40809 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 13.1385 | 0.505327 | ||||||||
\(677\) | −15.0966 | −0.580211 | −0.290105 | − | 0.956995i | \(-0.593690\pi\) | ||||
−0.290105 | + | 0.956995i | \(0.593690\pi\) | |||||||
\(678\) | −25.3919 | −0.975170 | ||||||||
\(679\) | 1.36069 | 0.0522186 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 18.3896 | 0.704692 | ||||||||
\(682\) | 9.75872 | 0.373681 | ||||||||
\(683\) | 12.4657 | 0.476988 | 0.238494 | − | 0.971144i | \(-0.423346\pi\) | ||||
0.238494 | + | 0.971144i | \(0.423346\pi\) | |||||||
\(684\) | 2.86376 | 0.109499 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −6.22690 | −0.237744 | ||||||||
\(687\) | 17.1506 | 0.654337 | ||||||||
\(688\) | 1.33791 | 0.0510072 | ||||||||
\(689\) | 40.1445 | 1.52938 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −30.7214 | −1.16870 | −0.584348 | − | 0.811503i | \(-0.698650\pi\) | ||||
−0.584348 | + | 0.811503i | \(0.698650\pi\) | |||||||
\(692\) | 4.75646 | 0.180813 | ||||||||
\(693\) | 0.290725 | 0.0110437 | ||||||||
\(694\) | −47.9748 | −1.82110 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −18.6225 | −0.705884 | ||||||||
\(697\) | 35.5174 | 1.34532 | ||||||||
\(698\) | −17.0037 | −0.643599 | ||||||||
\(699\) | 4.10731 | 0.155353 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.9955 | 0.679679 | 0.339840 | − | 0.940483i | \(-0.389627\pi\) | ||||
0.339840 | + | 0.940483i | \(0.389627\pi\) | |||||||
\(702\) | 10.7298 | 0.404970 | ||||||||
\(703\) | 26.5236 | 1.00036 | ||||||||
\(704\) | −6.02893 | −0.227224 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −42.2245 | −1.58914 | ||||||||
\(707\) | 2.49484 | 0.0938281 | ||||||||
\(708\) | 1.32950 | 0.0499655 | ||||||||
\(709\) | 23.5897 | 0.885929 | 0.442965 | − | 0.896539i | \(-0.353927\pi\) | ||||
0.442965 | + | 0.896539i | \(0.353927\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.921622 | −0.0345635 | ||||||||
\(712\) | 10.8950 | 0.408306 | ||||||||
\(713\) | −25.3607 | −0.949765 | ||||||||
\(714\) | −2.14238 | −0.0801765 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.680346 | 0.0254257 | ||||||||
\(717\) | −4.36683 | −0.163082 | ||||||||
\(718\) | 29.4764 | 1.10005 | ||||||||
\(719\) | 24.5646 | 0.916106 | 0.458053 | − | 0.888925i | \(-0.348547\pi\) | ||||
0.458053 | + | 0.888925i | \(0.348547\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.95896 | 0.0729556 | ||||||||
\(722\) | −63.4112 | −2.35992 | ||||||||
\(723\) | −5.20394 | −0.193536 | ||||||||
\(724\) | 3.79523 | 0.141048 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.53919 | −0.0571247 | ||||||||
\(727\) | −8.51130 | −0.315667 | −0.157833 | − | 0.987466i | \(-0.550451\pi\) | ||||
−0.157833 | + | 0.987466i | \(0.550451\pi\) | |||||||
\(728\) | 5.08745 | 0.188553 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.39189 | 0.0514809 | ||||||||
\(732\) | −2.46573 | −0.0911361 | ||||||||
\(733\) | 29.8615 | 1.10296 | 0.551480 | − | 0.834188i | \(-0.314063\pi\) | ||||
0.551480 | + | 0.834188i | \(0.314063\pi\) | |||||||
\(734\) | −22.4247 | −0.827711 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8.25112 | −0.304140 | ||||||||
\(737\) | 6.15676 | 0.226787 | ||||||||
\(738\) | 11.4186 | 0.420323 | ||||||||
\(739\) | −36.7526 | −1.35197 | −0.675983 | − | 0.736917i | \(-0.736281\pi\) | ||||
−0.675983 | + | 0.736917i | \(0.736281\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −54.0866 | −1.98692 | ||||||||
\(742\) | −2.57691 | −0.0946015 | ||||||||
\(743\) | 2.17501 | 0.0797933 | 0.0398966 | − | 0.999204i | \(-0.487297\pi\) | ||||
0.0398966 | + | 0.999204i | \(0.487297\pi\) | |||||||
\(744\) | 15.9155 | 0.583490 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −13.5669 | −0.496719 | ||||||||
\(747\) | −1.70928 | −0.0625391 | ||||||||
\(748\) | 1.76713 | 0.0646128 | ||||||||
\(749\) | 3.55640 | 0.129948 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −44.4580 | −1.62229 | −0.811147 | − | 0.584842i | \(-0.801157\pi\) | ||||
−0.811147 | + | 0.584842i | \(0.801157\pi\) | |||||||
\(752\) | 24.2146 | 0.883016 | ||||||||
\(753\) | −8.28231 | −0.301824 | ||||||||
\(754\) | −79.5995 | −2.89884 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.107307 | −0.00390272 | ||||||||
\(757\) | 26.4247 | 0.960422 | 0.480211 | − | 0.877153i | \(-0.340560\pi\) | ||||
0.480211 | + | 0.877153i | \(0.340560\pi\) | |||||||
\(758\) | 36.1978 | 1.31476 | ||||||||
\(759\) | 4.00000 | 0.145191 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −27.6163 | −1.00109 | −0.500546 | − | 0.865710i | \(-0.666867\pi\) | ||||
−0.500546 | + | 0.865710i | \(0.666867\pi\) | |||||||
\(762\) | 7.49920 | 0.271667 | ||||||||
\(763\) | 1.83549 | 0.0664493 | ||||||||
\(764\) | −4.25112 | −0.153800 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −29.7107 | −1.07349 | ||||||||
\(767\) | −25.1096 | −0.906654 | ||||||||
\(768\) | 8.57531 | 0.309435 | ||||||||
\(769\) | 27.8432 | 1.00405 | 0.502027 | − | 0.864852i | \(-0.332588\pi\) | ||||
0.502027 | + | 0.864852i | \(0.332588\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.0205 | −0.396894 | ||||||||
\(772\) | −1.42696 | −0.0513575 | ||||||||
\(773\) | 18.0267 | 0.648374 | 0.324187 | − | 0.945993i | \(-0.394909\pi\) | ||||
0.324187 | + | 0.945993i | \(0.394909\pi\) | |||||||
\(774\) | 0.447480 | 0.0160843 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −11.7489 | −0.421760 | ||||||||
\(777\) | −0.993857 | −0.0356544 | ||||||||
\(778\) | 30.8469 | 1.10592 | ||||||||
\(779\) | −57.5585 | −2.06225 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.07838 | 0.181719 | ||||||||
\(782\) | −29.4764 | −1.05407 | ||||||||
\(783\) | −7.41855 | −0.265117 | ||||||||
\(784\) | 31.8248 | 1.13660 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 13.3607 | 0.476560 | ||||||||
\(787\) | −35.6391 | −1.27040 | −0.635199 | − | 0.772349i | \(-0.719082\pi\) | ||||
−0.635199 | + | 0.772349i | \(0.719082\pi\) | |||||||
\(788\) | 3.16433 | 0.112725 | ||||||||
\(789\) | 2.97107 | 0.105773 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.79606 | −0.170528 | ||||||||
\(792\) | −2.51026 | −0.0891982 | ||||||||
\(793\) | 46.5692 | 1.65372 | ||||||||
\(794\) | −51.3484 | −1.82229 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.06854 | 0.108761 | ||||||||
\(797\) | 4.97948 | 0.176382 | 0.0881911 | − | 0.996104i | \(-0.471891\pi\) | ||||
0.0881911 | + | 0.996104i | \(0.471891\pi\) | |||||||
\(798\) | 3.47187 | 0.122903 | ||||||||
\(799\) | 25.1917 | 0.891217 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.34017 | 0.153352 | ||||||||
\(802\) | 57.9467 | 2.04617 | ||||||||
\(803\) | −1.12783 | −0.0398001 | ||||||||
\(804\) | −2.27247 | −0.0801439 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 68.0288 | 2.39621 | ||||||||
\(807\) | −15.8432 | −0.557709 | ||||||||
\(808\) | −21.5417 | −0.757833 | ||||||||
\(809\) | 31.6697 | 1.11345 | 0.556723 | − | 0.830698i | \(-0.312058\pi\) | ||||
0.556723 | + | 0.830698i | \(0.312058\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.7998 | −0.765493 | −0.382747 | − | 0.923853i | \(-0.625022\pi\) | ||||
−0.382747 | + | 0.923853i | \(0.625022\pi\) | |||||||
\(812\) | 0.796064 | 0.0279364 | ||||||||
\(813\) | −6.28231 | −0.220330 | ||||||||
\(814\) | 5.26180 | 0.184426 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 22.0326 | 0.771296 | ||||||||
\(817\) | −2.25565 | −0.0789153 | ||||||||
\(818\) | 38.7936 | 1.35639 | ||||||||
\(819\) | 2.02666 | 0.0708173 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10.9360 | −0.381669 | −0.190834 | − | 0.981622i | \(-0.561119\pi\) | ||||
−0.190834 | + | 0.981622i | \(0.561119\pi\) | |||||||
\(822\) | −19.3874 | −0.676212 | ||||||||
\(823\) | −45.9709 | −1.60244 | −0.801222 | − | 0.598367i | \(-0.795817\pi\) | ||||
−0.801222 | + | 0.598367i | \(0.795817\pi\) | |||||||
\(824\) | −16.9146 | −0.589249 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.61181 | 0.0560820 | ||||||||
\(827\) | 22.9711 | 0.798782 | 0.399391 | − | 0.916781i | \(-0.369222\pi\) | ||||
0.399391 | + | 0.916781i | \(0.369222\pi\) | |||||||
\(828\) | −1.47641 | −0.0513088 | ||||||||
\(829\) | −48.1543 | −1.67247 | −0.836234 | − | 0.548373i | \(-0.815248\pi\) | ||||
−0.836234 | + | 0.548373i | \(0.815248\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.12783 | −0.177882 | ||||||||
\(832\) | −42.0281 | −1.45706 | ||||||||
\(833\) | 33.1089 | 1.14716 | ||||||||
\(834\) | 15.2618 | 0.528473 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2.86376 | −0.0990453 | ||||||||
\(837\) | 6.34017 | 0.219148 | ||||||||
\(838\) | −27.4641 | −0.948732 | ||||||||
\(839\) | −17.9278 | −0.618935 | −0.309468 | − | 0.950910i | \(-0.600151\pi\) | ||||
−0.309468 | + | 0.950910i | \(0.600151\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26.0349 | 0.897755 | ||||||||
\(842\) | 18.1810 | 0.626558 | ||||||||
\(843\) | 21.8888 | 0.753891 | ||||||||
\(844\) | 9.56547 | 0.329257 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 8.09890 | 0.278446 | ||||||||
\(847\) | −0.290725 | −0.00998942 | ||||||||
\(848\) | 26.5015 | 0.910064 | ||||||||
\(849\) | −25.9649 | −0.891114 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −13.6742 | −0.468746 | ||||||||
\(852\) | −1.87444 | −0.0642173 | ||||||||
\(853\) | 9.54799 | 0.326917 | 0.163458 | − | 0.986550i | \(-0.447735\pi\) | ||||
0.163458 | + | 0.986550i | \(0.447735\pi\) | |||||||
\(854\) | −2.98932 | −0.102292 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −30.7077 | −1.04957 | ||||||||
\(857\) | −10.5776 | −0.361323 | −0.180662 | − | 0.983545i | \(-0.557824\pi\) | ||||
−0.180662 | + | 0.983545i | \(0.557824\pi\) | |||||||
\(858\) | −10.7298 | −0.366309 | ||||||||
\(859\) | −31.3340 | −1.06910 | −0.534552 | − | 0.845136i | \(-0.679520\pi\) | ||||
−0.534552 | + | 0.845136i | \(0.679520\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.15676 | 0.0735020 | ||||||||
\(862\) | −25.6742 | −0.874467 | ||||||||
\(863\) | −56.7792 | −1.93279 | −0.966394 | − | 0.257066i | \(-0.917244\pi\) | ||||
−0.966394 | + | 0.257066i | \(0.917244\pi\) | |||||||
\(864\) | 2.06278 | 0.0701772 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −43.5798 | −1.48090 | ||||||||
\(867\) | 5.92162 | 0.201109 | ||||||||
\(868\) | −0.680346 | −0.0230924 | ||||||||
\(869\) | 0.921622 | 0.0312639 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 42.9192 | 1.45426 | ||||||||
\(872\) | −15.8486 | −0.536700 | ||||||||
\(873\) | −4.68035 | −0.158406 | ||||||||
\(874\) | 47.7686 | 1.61580 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.416283 | 0.0140649 | ||||||||
\(877\) | −5.87832 | −0.198497 | −0.0992483 | − | 0.995063i | \(-0.531644\pi\) | ||||
−0.0992483 | + | 0.995063i | \(0.531644\pi\) | |||||||
\(878\) | 42.2434 | 1.42564 | ||||||||
\(879\) | −10.4163 | −0.351333 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.21008 | 0.276605 | 0.138302 | − | 0.990390i | \(-0.455835\pi\) | ||||
0.138302 | + | 0.990390i | \(0.455835\pi\) | |||||||
\(882\) | 10.6442 | 0.358410 | ||||||||
\(883\) | 27.0349 | 0.909797 | 0.454898 | − | 0.890543i | \(-0.349676\pi\) | ||||
0.454898 | + | 0.890543i | \(0.349676\pi\) | |||||||
\(884\) | 12.3188 | 0.414327 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.634773 | 0.0213256 | ||||||||
\(887\) | 48.7442 | 1.63667 | 0.818335 | − | 0.574742i | \(-0.194898\pi\) | ||||
0.818335 | + | 0.574742i | \(0.194898\pi\) | |||||||
\(888\) | 8.58145 | 0.287975 | ||||||||
\(889\) | 1.41646 | 0.0475066 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | 3.55395 | 0.118995 | ||||||||
\(893\) | −40.8248 | −1.36615 | ||||||||
\(894\) | 1.94214 | 0.0649549 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 3.89723 | 0.130197 | ||||||||
\(897\) | 27.8843 | 0.931029 | ||||||||
\(898\) | −2.05332 | −0.0685203 | ||||||||
\(899\) | −47.0349 | −1.56870 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 27.5708 | 0.918516 | ||||||||
\(902\) | −11.4186 | −0.380196 | ||||||||
\(903\) | 0.0845208 | 0.00281268 | ||||||||
\(904\) | 41.4116 | 1.37733 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −2.46573 | −0.0819184 | ||||||||
\(907\) | 32.4657 | 1.07801 | 0.539003 | − | 0.842304i | \(-0.318801\pi\) | ||||
0.539003 | + | 0.842304i | \(0.318801\pi\) | |||||||
\(908\) | 6.78765 | 0.225256 | ||||||||
\(909\) | −8.58145 | −0.284629 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.84939 | −0.160667 | −0.0803337 | − | 0.996768i | \(-0.525599\pi\) | ||||
−0.0803337 | + | 0.996768i | \(0.525599\pi\) | |||||||
\(912\) | −35.7054 | −1.18232 | ||||||||
\(913\) | 1.70928 | 0.0565688 | ||||||||
\(914\) | 17.9337 | 0.593195 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 6.33033 | 0.209160 | ||||||||
\(917\) | 2.52359 | 0.0833363 | ||||||||
\(918\) | 7.36910 | 0.243217 | ||||||||
\(919\) | −14.3980 | −0.474947 | −0.237474 | − | 0.971394i | \(-0.576319\pi\) | ||||
−0.237474 | + | 0.971394i | \(0.576319\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 29.0700 | 0.957888 | ||||||||
\(922\) | 3.16743 | 0.104314 | ||||||||
\(923\) | 35.4017 | 1.16526 | ||||||||
\(924\) | 0.107307 | 0.00353015 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 44.2967 | 1.45568 | ||||||||
\(927\) | −6.73820 | −0.221312 | ||||||||
\(928\) | −15.3028 | −0.502340 | ||||||||
\(929\) | −11.1629 | −0.366243 | −0.183121 | − | 0.983090i | \(-0.558620\pi\) | ||||
−0.183121 | + | 0.983090i | \(0.558620\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −53.6553 | −1.75848 | ||||||||
\(932\) | 1.51602 | 0.0496588 | ||||||||
\(933\) | 5.44521 | 0.178268 | ||||||||
\(934\) | 2.83710 | 0.0928328 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −17.4992 | −0.571979 | ||||||||
\(937\) | −48.6453 | −1.58917 | −0.794586 | − | 0.607152i | \(-0.792312\pi\) | ||||
−0.794586 | + | 0.607152i | \(0.792312\pi\) | |||||||
\(938\) | −2.75503 | −0.0899548 | ||||||||
\(939\) | −25.0928 | −0.818871 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16.4124 | 0.535029 | 0.267515 | − | 0.963554i | \(-0.413798\pi\) | ||||
0.267515 | + | 0.963554i | \(0.413798\pi\) | |||||||
\(942\) | −10.9360 | −0.356314 | ||||||||
\(943\) | 29.6742 | 0.966325 | ||||||||
\(944\) | −16.5761 | −0.539508 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.447480 | −0.0145488 | ||||||||
\(947\) | 45.7198 | 1.48569 | 0.742847 | − | 0.669462i | \(-0.233475\pi\) | ||||
0.742847 | + | 0.669462i | \(0.233475\pi\) | |||||||
\(948\) | −0.340173 | −0.0110483 | ||||||||
\(949\) | −7.86216 | −0.255216 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −21.1773 | −0.686720 | ||||||||
\(952\) | 3.49400 | 0.113241 | ||||||||
\(953\) | 26.4619 | 0.857184 | 0.428592 | − | 0.903498i | \(-0.359010\pi\) | ||||
0.428592 | + | 0.903498i | \(0.359010\pi\) | |||||||
\(954\) | 8.86376 | 0.286975 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.61181 | −0.0521296 | ||||||||
\(957\) | 7.41855 | 0.239808 | ||||||||
\(958\) | −41.3074 | −1.33458 | ||||||||
\(959\) | −3.66192 | −0.118249 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.19779 | 0.296703 | ||||||||
\(962\) | 36.6803 | 1.18262 | ||||||||
\(963\) | −12.2329 | −0.394199 | ||||||||
\(964\) | −1.92079 | −0.0618643 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.78992 | −0.0575897 | ||||||||
\(967\) | −50.5464 | −1.62546 | −0.812731 | − | 0.582639i | \(-0.802020\pi\) | ||||
−0.812731 | + | 0.582639i | \(0.802020\pi\) | |||||||
\(968\) | 2.51026 | 0.0806828 | ||||||||
\(969\) | −37.1461 | −1.19330 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −57.3074 | −1.83908 | −0.919540 | − | 0.392995i | \(-0.871439\pi\) | ||||
−0.919540 | + | 0.392995i | \(0.871439\pi\) | |||||||
\(972\) | 0.369102 | 0.0118390 | ||||||||
\(973\) | 2.88267 | 0.0924143 | ||||||||
\(974\) | 43.9664 | 1.40877 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 30.7427 | 0.984051 | ||||||||
\(977\) | 45.7875 | 1.46487 | 0.732436 | − | 0.680836i | \(-0.238384\pi\) | ||||
0.732436 | + | 0.680836i | \(0.238384\pi\) | |||||||
\(978\) | −35.3028 | −1.12886 | ||||||||
\(979\) | −4.34017 | −0.138713 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.31351 | −0.201575 | ||||||||
\(982\) | −40.0000 | −1.27645 | ||||||||
\(983\) | −55.0805 | −1.75679 | −0.878397 | − | 0.477932i | \(-0.841387\pi\) | ||||
−0.878397 | + | 0.477932i | \(0.841387\pi\) | |||||||
\(984\) | −18.6225 | −0.593663 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −54.6681 | −1.74099 | ||||||||
\(987\) | 1.52973 | 0.0486920 | ||||||||
\(988\) | −19.9635 | −0.635123 | ||||||||
\(989\) | 1.16290 | 0.0369780 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 40.6947 | 1.29271 | 0.646355 | − | 0.763037i | \(-0.276292\pi\) | ||||
0.646355 | + | 0.763037i | \(0.276292\pi\) | |||||||
\(992\) | 13.0784 | 0.415239 | ||||||||
\(993\) | −6.70701 | −0.212840 | ||||||||
\(994\) | −2.27247 | −0.0720785 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −0.630898 | −0.0199908 | ||||||||
\(997\) | 32.7610 | 1.03755 | 0.518775 | − | 0.854911i | \(-0.326388\pi\) | ||||
0.518775 | + | 0.854911i | \(0.326388\pi\) | |||||||
\(998\) | 42.3545 | 1.34071 | ||||||||
\(999\) | 3.41855 | 0.108158 |
(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 | 825.2.a.h.1.2 | 3 | ||
3.2 | odd | 2 | 2475.2.a.be.1.2 | 3 | |||
5.2 | odd | 4 | 165.2.c.a.34.2 | ✓ | 6 | ||
5.3 | odd | 4 | 165.2.c.a.34.5 | yes | 6 | ||
5.4 | even | 2 | 825.2.a.n.1.2 | 3 | |||
11.10 | odd | 2 | 9075.2.a.ck.1.2 | 3 | |||
15.2 | even | 4 | 495.2.c.d.199.5 | 6 | |||
15.8 | even | 4 | 495.2.c.d.199.2 | 6 | |||
15.14 | odd | 2 | 2475.2.a.y.1.2 | 3 | |||
20.3 | even | 4 | 2640.2.d.i.529.3 | 6 | |||
20.7 | even | 4 | 2640.2.d.i.529.6 | 6 | |||
55.32 | even | 4 | 1815.2.c.d.364.5 | 6 | |||
55.43 | even | 4 | 1815.2.c.d.364.2 | 6 | |||
55.54 | odd | 2 | 9075.2.a.cc.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.c.a.34.2 | ✓ | 6 | 5.2 | odd | 4 | ||
165.2.c.a.34.5 | yes | 6 | 5.3 | odd | 4 | ||
495.2.c.d.199.2 | 6 | 15.8 | even | 4 | |||
495.2.c.d.199.5 | 6 | 15.2 | even | 4 | |||
825.2.a.h.1.2 | 3 | 1.1 | even | 1 | trivial | ||
825.2.a.n.1.2 | 3 | 5.4 | even | 2 | |||
1815.2.c.d.364.2 | 6 | 55.43 | even | 4 | |||
1815.2.c.d.364.5 | 6 | 55.32 | even | 4 | |||
2475.2.a.y.1.2 | 3 | 15.14 | odd | 2 | |||
2475.2.a.be.1.2 | 3 | 3.2 | odd | 2 | |||
2640.2.d.i.529.3 | 6 | 20.3 | even | 4 | |||
2640.2.d.i.529.6 | 6 | 20.7 | even | 4 | |||
9075.2.a.cc.1.2 | 3 | 55.54 | odd | 2 | |||
9075.2.a.ck.1.2 | 3 | 11.10 | odd | 2 |