Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4028,2,Mod(1,4028)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4028, 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("4028.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4028 = 2^{2} \cdot 19 \cdot 53 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4028.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.1637419342\) |
Analytic rank: | \(1\) |
Dimension: | \(19\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{19} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{19} - 5 x^{18} - 27 x^{17} + 161 x^{16} + 253 x^{15} - 2103 x^{14} - 683 x^{13} + 14442 x^{12} - 4144 x^{11} - 56325 x^{10} + 37245 x^{9} + 124233 x^{8} - 117486 x^{7} + \cdots - 4088 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Root | \(-0.440747\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4028.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.440747 | 0.254466 | 0.127233 | − | 0.991873i | \(-0.459390\pi\) | ||||
0.127233 | + | 0.991873i | \(0.459390\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.359379 | 0.160719 | 0.0803597 | − | 0.996766i | \(-0.474393\pi\) | ||||
0.0803597 | + | 0.996766i | \(0.474393\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.921983 | 0.348477 | 0.174238 | − | 0.984704i | \(-0.444254\pi\) | ||||
0.174238 | + | 0.984704i | \(0.444254\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.80574 | −0.935247 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.53021 | 0.461375 | 0.230688 | − | 0.973028i | \(-0.425902\pi\) | ||||
0.230688 | + | 0.973028i | \(0.425902\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.01271 | −0.558225 | −0.279112 | − | 0.960258i | \(-0.590040\pi\) | ||||
−0.279112 | + | 0.960258i | \(0.590040\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.158396 | 0.0408975 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.43213 | −0.347343 | −0.173672 | − | 0.984804i | \(-0.555563\pi\) | ||||
−0.173672 | + | 0.984804i | \(0.555563\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.406362 | 0.0886754 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.72144 | 0.984488 | 0.492244 | − | 0.870457i | \(-0.336177\pi\) | ||||
0.492244 | + | 0.870457i | \(0.336177\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.87085 | −0.974169 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.55887 | −0.492454 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.88231 | −1.46371 | −0.731854 | − | 0.681462i | \(-0.761345\pi\) | ||||
−0.731854 | + | 0.681462i | \(0.761345\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.20119 | 0.215739 | 0.107870 | − | 0.994165i | \(-0.465597\pi\) | ||||
0.107870 | + | 0.994165i | \(0.465597\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.674435 | 0.117404 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.331342 | 0.0560070 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.80918 | −1.44822 | −0.724110 | − | 0.689685i | \(-0.757749\pi\) | ||||
−0.724110 | + | 0.689685i | \(0.757749\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.887096 | −0.142049 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.83669 | −0.755364 | −0.377682 | − | 0.925935i | \(-0.623279\pi\) | ||||
−0.377682 | + | 0.925935i | \(0.623279\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.59135 | 0.852673 | 0.426336 | − | 0.904565i | \(-0.359804\pi\) | ||||
0.426336 | + | 0.904565i | \(0.359804\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00833 | −0.150312 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.1547 | 1.77294 | 0.886470 | − | 0.462786i | \(-0.153150\pi\) | ||||
0.886470 | + | 0.462786i | \(0.153150\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.14995 | −0.878564 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.631208 | −0.0883869 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.00000 | −0.137361 | ||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.549925 | 0.0741519 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.440747 | 0.0583784 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −12.3656 | −1.60987 | −0.804934 | − | 0.593364i | \(-0.797800\pi\) | ||||
−0.804934 | + | 0.593364i | \(0.797800\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.555852 | −0.0711696 | −0.0355848 | − | 0.999367i | \(-0.511329\pi\) | ||||
−0.0355848 | + | 0.999367i | \(0.511329\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.58685 | −0.325912 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.723326 | −0.0897175 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.72210 | 0.699066 | 0.349533 | − | 0.936924i | \(-0.386340\pi\) | ||||
0.349533 | + | 0.936924i | \(0.386340\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.08096 | 0.250518 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.58675 | −1.01906 | −0.509530 | − | 0.860453i | \(-0.670181\pi\) | ||||
−0.509530 | + | 0.860453i | \(0.670181\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.9477 | 1.39837 | 0.699184 | − | 0.714941i | \(-0.253547\pi\) | ||||
0.699184 | + | 0.714941i | \(0.253547\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.14681 | −0.247893 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.41083 | 0.160779 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.0735 | −1.24587 | −0.622933 | − | 0.782275i | \(-0.714059\pi\) | ||||
−0.622933 | + | 0.782275i | \(0.714059\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.28941 | 0.809935 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.92651 | −0.540755 | −0.270377 | − | 0.962754i | \(-0.587148\pi\) | ||||
−0.270377 | + | 0.962754i | \(0.587148\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.514679 | −0.0558247 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.47411 | −0.372463 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.1645 | −1.07744 | −0.538718 | − | 0.842486i | \(-0.681091\pi\) | ||||
−0.538718 | + | 0.842486i | \(0.681091\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.85568 | −0.194528 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.529419 | 0.0548982 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.359379 | 0.0368715 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.927087 | 0.0941314 | 0.0470657 | − | 0.998892i | \(-0.485013\pi\) | ||||
0.0470657 | + | 0.998892i | \(0.485013\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.29337 | −0.431500 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.84479 | 0.681082 | 0.340541 | − | 0.940230i | \(-0.389390\pi\) | ||||
0.340541 | + | 0.940230i | \(0.389390\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.55724 | −0.547571 | −0.273785 | − | 0.961791i | \(-0.588276\pi\) | ||||
−0.273785 | + | 0.961791i | \(0.588276\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.146038 | 0.0142518 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.3781 | −1.00329 | −0.501644 | − | 0.865074i | \(-0.667271\pi\) | ||||
−0.501644 | + | 0.865074i | \(0.667271\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.79003 | 0.363019 | 0.181510 | − | 0.983389i | \(-0.441902\pi\) | ||||
0.181510 | + | 0.983389i | \(0.441902\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.88262 | −0.368522 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.8505 | −1.02073 | −0.510363 | − | 0.859959i | \(-0.670489\pi\) | ||||
−0.510363 | + | 0.859959i | \(0.670489\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.69679 | 0.158226 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.64714 | 0.522078 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.32040 | −0.121041 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.65846 | −0.787133 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.13176 | −0.192214 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.54738 | −0.317287 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.26100 | −0.289367 | −0.144684 | − | 0.989478i | \(-0.546216\pi\) | ||||
−0.144684 | + | 0.989478i | \(0.546216\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.46437 | 0.216976 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.2967 | −0.986995 | −0.493497 | − | 0.869747i | \(-0.664282\pi\) | ||||
−0.493497 | + | 0.869747i | \(0.664282\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.921983 | 0.0799461 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.919603 | −0.0791469 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.5333 | 1.15623 | 0.578116 | − | 0.815955i | \(-0.303788\pi\) | ||||
0.578116 | + | 0.815955i | \(0.303788\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.58140 | −0.727865 | −0.363932 | − | 0.931425i | \(-0.618566\pi\) | ||||
−0.363932 | + | 0.931425i | \(0.618566\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.35714 | 0.451152 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.07986 | −0.257551 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.83274 | −0.235246 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.71057 | −0.223564 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.3601 | −1.01258 | −0.506288 | − | 0.862364i | \(-0.668983\pi\) | ||||
−0.506288 | + | 0.862364i | \(0.668983\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.64754 | 0.622348 | 0.311174 | − | 0.950353i | \(-0.399278\pi\) | ||||
0.311174 | + | 0.950353i | \(0.399278\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.01819 | 0.324852 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.431681 | 0.0346735 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.2352 | −1.45533 | −0.727664 | − | 0.685934i | \(-0.759394\pi\) | ||||
−0.727664 | + | 0.685934i | \(0.759394\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.440747 | −0.0349535 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.35309 | 0.343071 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.1390 | 1.10745 | 0.553727 | − | 0.832698i | \(-0.313205\pi\) | ||||
0.553727 | + | 0.832698i | \(0.313205\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.242378 | 0.0188691 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.3568 | 0.801430 | 0.400715 | − | 0.916203i | \(-0.368762\pi\) | ||||
0.400715 | + | 0.916203i | \(0.368762\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.94901 | −0.688385 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.80574 | −0.214560 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.44245 | −0.641867 | −0.320934 | − | 0.947102i | \(-0.603997\pi\) | ||||
−0.320934 | + | 0.947102i | \(0.603997\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.49084 | −0.339475 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.45012 | −0.409656 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.7966 | 0.956459 | 0.478230 | − | 0.878235i | \(-0.341279\pi\) | ||||
0.478230 | + | 0.878235i | \(0.341279\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.19453 | −0.163118 | −0.0815592 | − | 0.996668i | \(-0.525990\pi\) | ||||
−0.0815592 | + | 0.996668i | \(0.525990\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.244990 | −0.0181102 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.16584 | −0.232757 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.19146 | −0.160255 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.35923 | −0.171609 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 17.3246 | 1.25357 | 0.626783 | − | 0.779194i | \(-0.284371\pi\) | ||||
0.626783 | + | 0.779194i | \(0.284371\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.4183 | 1.46974 | 0.734870 | − | 0.678208i | \(-0.237243\pi\) | ||||
0.734870 | + | 0.678208i | \(0.237243\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.318804 | −0.0228300 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 26.2928 | 1.87328 | 0.936641 | − | 0.350292i | \(-0.113918\pi\) | ||||
0.936641 | + | 0.350292i | \(0.113918\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.20666 | 0.0855381 | 0.0427690 | − | 0.999085i | \(-0.486382\pi\) | ||||
0.0427690 | + | 0.999085i | \(0.486382\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.52200 | 0.177888 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.26735 | −0.510068 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.73821 | −0.121402 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −13.2471 | −0.920740 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.53021 | 0.105847 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.02684 | −0.346062 | −0.173031 | − | 0.984916i | \(-0.555356\pi\) | ||||
−0.173031 | + | 0.984916i | \(0.555356\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.78459 | −0.259316 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.00942 | 0.137041 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.10747 | 0.0751801 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.26590 | 0.355837 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.88246 | 0.193895 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.9145 | −0.864816 | −0.432408 | − | 0.901678i | \(-0.642336\pi\) | ||||
−0.432408 | + | 0.901678i | \(0.642336\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 13.6663 | 0.911089 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −19.7954 | −1.31386 | −0.656932 | − | 0.753950i | \(-0.728146\pi\) | ||||
−0.656932 | + | 0.753950i | \(0.728146\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −19.2426 | −1.27159 | −0.635793 | − | 0.771859i | \(-0.719327\pi\) | ||||
−0.635793 | + | 0.771859i | \(0.719327\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.621818 | 0.0409126 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −23.0287 | −1.50866 | −0.754329 | − | 0.656497i | \(-0.772038\pi\) | ||||
−0.754329 | + | 0.656497i | \(0.772038\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.36814 | 0.284946 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.88062 | −0.317030 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.1442 | 1.23834 | 0.619168 | − | 0.785259i | \(-0.287470\pi\) | ||||
0.619168 | + | 0.785259i | \(0.287470\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.20557 | 0.0776577 | 0.0388288 | − | 0.999246i | \(-0.487637\pi\) | ||||
0.0388288 | + | 0.999246i | \(0.487637\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 10.8894 | 0.698554 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.21016 | −0.141202 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.01271 | −0.128066 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.17135 | −0.137603 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.7902 | 1.18603 | 0.593015 | − | 0.805191i | \(-0.297937\pi\) | ||||
0.593015 | + | 0.805191i | \(0.297937\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.22479 | 0.454218 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.226843 | −0.0142055 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.178596 | 0.0111405 | 0.00557027 | − | 0.999984i | \(-0.498227\pi\) | ||||
0.00557027 | + | 0.999984i | \(0.498227\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.12191 | −0.504671 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 22.1157 | 1.36893 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −21.3040 | −1.31366 | −0.656831 | − | 0.754038i | \(-0.728103\pi\) | ||||
−0.656831 | + | 0.754038i | \(0.728103\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.359379 | −0.0220765 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.47998 | −0.274170 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.90158 | −0.237883 | −0.118942 | − | 0.992901i | \(-0.537950\pi\) | ||||
−0.118942 | + | 0.992901i | \(0.537950\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −23.3838 | −1.42047 | −0.710233 | − | 0.703967i | \(-0.751410\pi\) | ||||
−0.710233 | + | 0.703967i | \(0.751410\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.817887 | −0.0495008 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −7.45341 | −0.449457 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.2607 | −0.796756 | −0.398378 | − | 0.917221i | \(-0.630427\pi\) | ||||
−0.398378 | + | 0.917221i | \(0.630427\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.37022 | −0.201770 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.2247 | −0.848572 | −0.424286 | − | 0.905528i | \(-0.639475\pi\) | ||||
−0.424286 | + | 0.905528i | \(0.639475\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −21.6460 | −1.28672 | −0.643359 | − | 0.765564i | \(-0.722460\pi\) | ||||
−0.643359 | + | 0.765564i | \(0.722460\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.158396 | 0.00938254 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.45934 | −0.263227 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.9490 | −0.879353 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.408611 | 0.0239532 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.95564 | 0.172670 | 0.0863352 | − | 0.996266i | \(-0.472484\pi\) | ||||
0.0863352 | + | 0.996266i | \(0.472484\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.44395 | −0.258737 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.91560 | −0.227206 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −9.50288 | −0.549566 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.15513 | 0.297137 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.01682 | 0.173312 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.199762 | −0.0114383 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.1312 | 1.03480 | 0.517401 | − | 0.855743i | \(-0.326900\pi\) | ||||
0.517401 | + | 0.855743i | \(0.326900\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.44934 | −0.139338 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.2849 | 0.696611 | 0.348306 | − | 0.937381i | \(-0.386757\pi\) | ||||
0.348306 | + | 0.937381i | \(0.386757\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.05996 | 0.116436 | 0.0582178 | − | 0.998304i | \(-0.481458\pi\) | ||||
0.0582178 | + | 0.998304i | \(0.481458\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.929659 | −0.0523803 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 25.2374 | 1.41747 | 0.708737 | − | 0.705473i | \(-0.249265\pi\) | ||||
0.708737 | + | 0.705473i | \(0.249265\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.0616 | −0.675318 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.57411 | −0.255302 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.43213 | −0.0796860 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.80359 | 0.543805 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.67045 | 0.0923759 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 11.2064 | 0.617828 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.76350 | −0.206861 | −0.103430 | − | 0.994637i | \(-0.532982\pi\) | ||||
−0.103430 | + | 0.994637i | \(0.532982\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 24.7163 | 1.35444 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.05640 | 0.112353 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.78046 | −0.205935 | −0.102967 | − | 0.994685i | \(-0.532834\pi\) | ||||
−0.102967 | + | 0.994685i | \(0.532834\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.78231 | −0.259739 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.83806 | 0.0995367 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.1240 | −0.654636 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.747855 | 0.0402632 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −13.3465 | −0.716480 | −0.358240 | − | 0.933630i | \(-0.616623\pi\) | ||||
−0.358240 | + | 0.933630i | \(0.616623\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 28.6206 | 1.53203 | 0.766013 | − | 0.642825i | \(-0.222238\pi\) | ||||
0.766013 | + | 0.642825i | \(0.222238\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.15025 | 0.274900 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −15.0178 | −0.799316 | −0.399658 | − | 0.916664i | \(-0.630871\pi\) | ||||
−0.399658 | + | 0.916664i | \(0.630871\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.08590 | −0.163783 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.581963 | −0.0308008 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −17.3904 | −0.917831 | −0.458915 | − | 0.888480i | \(-0.651762\pi\) | ||||
−0.458915 | + | 0.888480i | \(0.651762\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.81620 | −0.200298 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.29375 | 0.224745 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −24.2681 | −1.26678 | −0.633391 | − | 0.773832i | \(-0.718338\pi\) | ||||
−0.633391 | + | 0.773832i | \(0.718338\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 13.5705 | 0.706452 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.921983 | −0.0478670 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.60524 | −0.0831162 | −0.0415581 | − | 0.999136i | \(-0.513232\pi\) | ||||
−0.0415581 | + | 0.999136i | \(0.513232\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.56350 | −0.0807387 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 15.8648 | 0.817078 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.4231 | 1.35726 | 0.678632 | − | 0.734478i | \(-0.262573\pi\) | ||||
0.678632 | + | 0.734478i | \(0.262573\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.43728 | −0.0736340 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.550870 | 0.0281481 | 0.0140741 | − | 0.999901i | \(-0.495520\pi\) | ||||
0.0140741 | + | 0.999901i | \(0.495520\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.507022 | 0.0258402 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −15.6879 | −0.797460 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.0445884 | 0.00226072 | 0.00113036 | − | 0.999999i | \(-0.499640\pi\) | ||||
0.00113036 | + | 0.999999i | \(0.499640\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.76172 | −0.341955 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.97898 | −0.251156 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.97959 | −0.200235 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.31886 | 0.467700 | 0.233850 | − | 0.972273i | \(-0.424868\pi\) | ||||
0.233850 | + | 0.972273i | \(0.424868\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.406362 | 0.0203435 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 30.6347 | 1.52982 | 0.764912 | − | 0.644135i | \(-0.222782\pi\) | ||||
0.764912 | + | 0.644135i | \(0.222782\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.41764 | −0.120431 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.61966 | 0.130172 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −13.4799 | −0.668173 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.1673 | 0.552187 | 0.276094 | − | 0.961131i | \(-0.410960\pi\) | ||||
0.276094 | + | 0.961131i | \(0.410960\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.96478 | 0.294221 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −11.4009 | −0.561002 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.77049 | −0.0869097 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.78223 | −0.185217 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.61049 | −0.274090 | −0.137045 | − | 0.990565i | \(-0.543761\pi\) | ||||
−0.137045 | + | 0.990565i | \(0.543761\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −30.9216 | −1.50703 | −0.753514 | − | 0.657432i | \(-0.771643\pi\) | ||||
−0.753514 | + | 0.657432i | \(0.771643\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −34.1029 | −1.65814 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.97569 | 0.338371 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.512486 | −0.0248009 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.35744 | −0.0655379 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.56872 | 0.220067 | 0.110034 | − | 0.993928i | \(-0.464904\pi\) | ||||
0.110034 | + | 0.993928i | \(0.464904\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.13191 | 0.294681 | 0.147340 | − | 0.989086i | \(-0.452929\pi\) | ||||
0.147340 | + | 0.989086i | \(0.452929\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.24852 | −0.0598620 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.72144 | 0.225857 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.89651 | −0.185970 | −0.0929851 | − | 0.995668i | \(-0.529641\pi\) | ||||
−0.0929851 | + | 0.995668i | \(0.529641\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 17.2552 | 0.821675 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 26.4701 | 1.25763 | 0.628817 | − | 0.777554i | \(-0.283540\pi\) | ||||
0.628817 | + | 0.777554i | \(0.283540\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.65291 | −0.173165 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5.44767 | −0.257666 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −30.8885 | −1.45772 | −0.728860 | − | 0.684663i | \(-0.759949\pi\) | ||||
−0.728860 | + | 0.684663i | \(0.759949\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.40114 | −0.348506 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.37063 | 0.158366 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.666894 | −0.0312645 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −32.6517 | −1.52738 | −0.763692 | − | 0.645581i | \(-0.776615\pi\) | ||||
−0.763692 | + | 0.645581i | \(0.776615\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.66463 | 0.171050 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.48479 | −0.0691536 | −0.0345768 | − | 0.999402i | \(-0.511008\pi\) | ||||
−0.0345768 | + | 0.999402i | \(0.511008\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 31.5195 | 1.46483 | 0.732417 | − | 0.680856i | \(-0.238392\pi\) | ||||
0.732417 | + | 0.680856i | \(0.238392\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.190262 | 0.00882321 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 15.4017 | 0.712704 | 0.356352 | − | 0.934352i | \(-0.384020\pi\) | ||||
0.356352 | + | 0.934352i | \(0.384020\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.27568 | 0.243608 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.03712 | −0.370331 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.55593 | 0.393402 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.87085 | −0.223490 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.80574 | 0.128466 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 19.6443 | 0.897571 | 0.448786 | − | 0.893639i | \(-0.351857\pi\) | ||||
0.448786 | + | 0.893639i | \(0.351857\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 17.7303 | 0.808432 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.91861 | 0.0872998 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.333176 | 0.0151287 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14.4698 | −0.655689 | −0.327845 | − | 0.944732i | \(-0.606322\pi\) | ||||
−0.327845 | + | 0.944732i | \(0.606322\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.23174 | 0.281809 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.920419 | 0.0415379 | 0.0207690 | − | 0.999784i | \(-0.493389\pi\) | ||||
0.0207690 | + | 0.999784i | \(0.493389\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.2885 | 0.508409 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.54295 | −0.0693504 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7.91684 | −0.355119 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 33.5889 | 1.50364 | 0.751822 | − | 0.659366i | \(-0.229175\pi\) | ||||
0.751822 | + | 0.659366i | \(0.229175\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.56472 | 0.203936 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 30.3472 | 1.35312 | 0.676558 | − | 0.736390i | \(-0.263471\pi\) | ||||
0.676558 | + | 0.736390i | \(0.263471\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.45988 | 0.109463 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.94425 | −0.175170 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −29.0923 | −1.28949 | −0.644746 | − | 0.764396i | \(-0.723037\pi\) | ||||
−0.644746 | + | 0.764396i | \(0.723037\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.0155 | 0.487299 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.55887 | −0.112977 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.99716 | −0.0880052 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 18.5992 | 0.817990 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.72099 | −0.163333 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.33543 | 0.321371 | 0.160685 | − | 0.987006i | \(-0.448630\pi\) | ||||
0.160685 | + | 0.987006i | \(0.448630\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −23.0612 | −1.00840 | −0.504198 | − | 0.863588i | \(-0.668212\pi\) | ||||
−0.504198 | + | 0.863588i | \(0.668212\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.97932 | −0.0863848 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.72026 | −0.0749355 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.708008 | −0.0307830 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 34.6948 | 1.50563 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.73484 | 0.421663 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.72967 | −0.161248 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.64005 | 0.243386 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −9.41070 | −0.405348 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −35.3976 | −1.52186 | −0.760932 | − | 0.648832i | \(-0.775258\pi\) | ||||
−0.760932 | + | 0.648832i | \(0.775258\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.967235 | −0.0415080 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.36206 | 0.0583442 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.7707 | −0.674308 | −0.337154 | − | 0.941449i | \(-0.609464\pi\) | ||||
−0.337154 | + | 0.941449i | \(0.609464\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.55958 | 0.0665611 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.88231 | −0.335798 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.2096 | −0.434155 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.39533 | −0.0592286 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7.59077 | −0.321631 | −0.160816 | − | 0.986984i | \(-0.551412\pi\) | ||||
−0.160816 | + | 0.986984i | \(0.551412\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11.2538 | −0.475983 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.965880 | −0.0407795 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 21.7641 | 0.917246 | 0.458623 | − | 0.888631i | \(-0.348343\pi\) | ||||
0.458623 | + | 0.888631i | \(0.348343\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.89943 | −0.164050 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 6.72071 | 0.282243 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 42.6803 | 1.78925 | 0.894626 | − | 0.446816i | \(-0.147442\pi\) | ||||
0.894626 | + | 0.446816i | \(0.147442\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.565043 | −0.0236463 | −0.0118231 | − | 0.999930i | \(-0.503764\pi\) | ||||
−0.0118231 | + | 0.999930i | \(0.503764\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7.63578 | 0.318989 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −22.9974 | −0.959058 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10.4967 | −0.436982 | −0.218491 | − | 0.975839i | \(-0.570113\pi\) | ||||
−0.218491 | + | 0.975839i | \(0.570113\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.99930 | 0.373998 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.54216 | −0.188440 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.53021 | −0.0633747 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.02946 | 0.0839080 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −36.4173 | −1.50310 | −0.751551 | − | 0.659675i | \(-0.770694\pi\) | ||||
−0.751551 | + | 0.659675i | \(0.770694\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.20119 | 0.0494940 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11.5885 | 0.476686 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 23.7587 | 0.975652 | 0.487826 | − | 0.872941i | \(-0.337790\pi\) | ||||
0.487826 | + | 0.872941i | \(0.337790\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.474525 | −0.0194536 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.531834 | 0.0217665 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −41.8619 | −1.71043 | −0.855216 | − | 0.518272i | \(-0.826575\pi\) | ||||
−0.855216 | + | 0.518272i | \(0.826575\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 38.0135 | 1.55060 | 0.775301 | − | 0.631591i | \(-0.217598\pi\) | ||||
0.775301 | + | 0.631591i | \(0.217598\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −16.0547 | −0.653799 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.11167 | −0.126507 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.78146 | 0.275251 | 0.137625 | − | 0.990484i | \(-0.456053\pi\) | ||||
0.137625 | + | 0.990484i | \(0.456053\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.20307 | −0.129795 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −24.4638 | −0.989699 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.09545 | 0.0846343 | 0.0423171 | − | 0.999104i | \(-0.486526\pi\) | ||||
0.0423171 | + | 0.999104i | \(0.486526\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.766110 | −0.0308925 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.8431 | 0.476784 | 0.238392 | − | 0.971169i | \(-0.423380\pi\) | ||||
0.238392 | + | 0.971169i | \(0.423380\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15.7568 | −0.633319 | −0.316660 | − | 0.948539i | \(-0.602561\pi\) | ||||
−0.316660 | + | 0.948539i | \(0.602561\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −12.0815 | −0.484815 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9.37150 | −0.375461 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.0794 | 0.923175 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.674435 | 0.0269343 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 12.6159 | 0.503029 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.53885 | 0.260307 | 0.130154 | − | 0.991494i | \(-0.458453\pi\) | ||||
0.130154 | + | 0.991494i | \(0.458453\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.21557 | −0.0880608 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.17194 | −0.0465069 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12.3780 | 0.490436 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 24.0922 | 0.953073 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.27237 | 0.0897533 | 0.0448766 | − | 0.998993i | \(-0.485711\pi\) | ||||
0.0448766 | + | 0.998993i | \(0.485711\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18.6275 | −0.734597 | −0.367298 | − | 0.930103i | \(-0.619717\pi\) | ||||
−0.367298 | + | 0.930103i | \(0.619717\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.885645 | 0.0348722 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 45.6415 | 1.79435 | 0.897177 | − | 0.441671i | \(-0.145614\pi\) | ||||
0.897177 | + | 0.441671i | \(0.145614\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −18.9220 | −0.742753 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.488116 | 0.0191308 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.43679 | 0.369290 | 0.184645 | − | 0.982805i | \(-0.440886\pi\) | ||||
0.184645 | + | 0.982805i | \(0.440886\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.05979 | −0.158629 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −33.5221 | −1.30782 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 32.9355 | 1.28298 | 0.641492 | − | 0.767130i | \(-0.278316\pi\) | ||||
0.641492 | + | 0.767130i | \(0.278316\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.5298 | 0.565142 | 0.282571 | − | 0.959246i | \(-0.408813\pi\) | ||||
0.282571 | + | 0.959246i | \(0.408813\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.27044 | 0.0493397 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.331342 | 0.0128489 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −37.2158 | −1.44100 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5.69201 | −0.220066 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.850569 | −0.0328359 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.80750 | 0.378051 | 0.189026 | − | 0.981972i | \(-0.439467\pi\) | ||||
0.189026 | + | 0.981972i | \(0.439467\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 12.4638 | 0.479733 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 19.0133 | 0.730740 | 0.365370 | − | 0.930862i | \(-0.380943\pi\) | ||||
0.365370 | + | 0.930862i | \(0.380943\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.854758 | 0.0328026 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.72475 | −0.334333 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 21.7869 | 0.833653 | 0.416827 | − | 0.908986i | \(-0.363142\pi\) | ||||
0.416827 | + | 0.908986i | \(0.363142\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.86360 | 0.185829 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8.48113 | −0.323575 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.01271 | 0.0766781 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 43.2260 | 1.64439 | 0.822197 | − | 0.569204i | \(-0.192748\pi\) | ||||
0.822197 | + | 0.569204i | \(0.192748\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.95841 | −0.150368 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.08398 | −0.116982 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.92678 | 0.262370 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −10.1498 | −0.383902 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23.1213 | 0.873278 | 0.436639 | − | 0.899637i | \(-0.356169\pi\) | ||||
0.436639 | + | 0.899637i | \(0.356169\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.80918 | −0.332244 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.92524 | 0.0725089 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.31078 | 0.237341 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.2482 | −0.422434 | −0.211217 | − | 0.977439i | \(-0.567743\pi\) | ||||
−0.211217 | + | 0.977439i | \(0.567743\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 31.0694 | 1.16519 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.67133 | 0.212393 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.10684 | −0.0413934 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8.43776 | 0.315114 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8.44443 | −0.314924 | −0.157462 | − | 0.987525i | \(-0.550331\pi\) | ||||
−0.157462 | + | 0.987525i | \(0.550331\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.12368 | −0.190816 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.531352 | 0.0197612 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 38.3935 | 1.42590 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.64131 | −0.135049 | −0.0675244 | − | 0.997718i | \(-0.521510\pi\) | ||||
−0.0675244 | + | 0.997718i | \(0.521510\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −17.0688 | −0.632177 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.00755 | −0.296170 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17.6292 | 0.651150 | 0.325575 | − | 0.945516i | \(-0.394442\pi\) | ||||
0.325575 | + | 0.945516i | \(0.394442\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.974124 | −0.0359311 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.75600 | 0.322532 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 50.6494 | 1.86317 | 0.931585 | − | 0.363524i | \(-0.118426\pi\) | ||||
0.931585 | + | 0.363524i | \(0.118426\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.887096 | −0.0325883 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 35.3412 | 1.29654 | 0.648272 | − | 0.761409i | \(-0.275492\pi\) | ||||
0.648272 | + | 0.761409i | \(0.275492\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.44195 | −0.162741 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 13.8225 | 0.505739 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.56842 | −0.349622 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.86347 | −0.213961 | −0.106981 | − | 0.994261i | \(-0.534118\pi\) | ||||
−0.106981 | + | 0.994261i | \(0.534118\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.28175 | 0.301804 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.74837 | 0.100023 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −23.4695 | −0.853013 | −0.426507 | − | 0.904484i | \(-0.640256\pi\) | ||||
−0.426507 | + | 0.904484i | \(0.640256\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.18431 | 0.115583 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 39.0176 | 1.41439 | 0.707193 | − | 0.707021i | \(-0.249961\pi\) | ||||
0.707193 | + | 0.707021i | \(0.249961\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.49435 | 0.126504 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.44406 | 0.0522099 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 24.8884 | 0.898668 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 46.2642 | 1.66833 | 0.834165 | − | 0.551515i | \(-0.185950\pi\) | ||||
0.834165 | + | 0.551515i | \(0.185950\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.0787159 | 0.00283488 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 26.0579 | 0.937239 | 0.468620 | − | 0.883400i | \(-0.344752\pi\) | ||||
0.468620 | + | 0.883400i | \(0.344752\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.85079 | −0.210167 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.57971 | −0.128421 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.83669 | −0.173292 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.1395 | −0.470169 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 20.1698 | 0.720809 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.55336 | −0.233899 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −38.0168 | −1.35515 | −0.677577 | − | 0.735452i | \(-0.736970\pi\) | ||||
−0.677577 | + | 0.735452i | \(0.736970\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9.38969 | −0.334282 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.0039 | −0.355699 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.11877 | 0.0397286 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.158396 | −0.00561771 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −25.3162 | −0.896748 | −0.448374 | − | 0.893846i | \(-0.647997\pi\) | ||||
−0.448374 | + | 0.893846i | \(0.647997\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −17.4071 | −0.615818 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 28.5190 | 1.00767 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 18.2824 | 0.645173 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.56441 | 0.0551382 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.71961 | −0.0605331 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 25.7411 | 0.905008 | 0.452504 | − | 0.891762i | \(-0.350531\pi\) | ||||
0.452504 | + | 0.891762i | \(0.350531\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −37.0055 | −1.29944 | −0.649720 | − | 0.760174i | \(-0.725114\pi\) | ||||
−0.649720 | + | 0.760174i | \(0.725114\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −10.3064 | −0.361460 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.08128 | 0.177989 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.59135 | 0.195617 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.20656 | 0.181932 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12.6894 | −0.442862 | −0.221431 | − | 0.975176i | \(-0.571073\pi\) | ||||
−0.221431 | + | 0.975176i | \(0.571073\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17.4609 | −0.608647 | −0.304324 | − | 0.952569i | \(-0.598430\pi\) | ||||
−0.304324 | + | 0.952569i | \(0.598430\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.28507 | −0.114371 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.17174 | 0.318933 | 0.159466 | − | 0.987203i | \(-0.449023\pi\) | ||||
0.159466 | + | 0.987203i | \(0.449023\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.1335 | 0.629804 | 0.314902 | − | 0.949124i | \(-0.398028\pi\) | ||||
0.314902 | + | 0.949124i | \(0.398028\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.84460 | −0.202747 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.80754 | 0.305163 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.72201 | 0.128805 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.07367 | −0.106242 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 21.0714 | 0.727464 | 0.363732 | − | 0.931504i | \(-0.381502\pi\) | ||||
0.363732 | + | 0.931504i | \(0.381502\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 33.1308 | 1.14244 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −6.26948 | −0.215933 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.21609 | −0.110637 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.98295 | −0.274298 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −9.54040 | −0.327426 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −41.5920 | −1.42576 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.07429 | 0.207980 | 0.103990 | − | 0.994578i | \(-0.466839\pi\) | ||||
0.103990 | + | 0.994578i | \(0.466839\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.00833 | −0.0344840 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 46.7400 | 1.59661 | 0.798304 | − | 0.602254i | \(-0.205731\pi\) | ||||
0.798304 | + | 0.602254i | \(0.205731\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −38.7867 | −1.32339 | −0.661693 | − | 0.749775i | \(-0.730162\pi\) | ||||
−0.661693 | + | 0.749775i | \(0.730162\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.96544 | −0.0669822 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 30.4822 | 1.03763 | 0.518813 | − | 0.854887i | \(-0.326374\pi\) | ||||
0.518813 | + | 0.854887i | \(0.326374\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.03404 | −0.103161 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6.58873 | −0.223765 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −16.9448 | −0.574811 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11.5169 | −0.390236 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.60117 | −0.0880361 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.27062 | −0.110567 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.57576 | 0.323350 | 0.161675 | − | 0.986844i | \(-0.448310\pi\) | ||||
0.161675 | + | 0.986844i | \(0.448310\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.30269 | 0.0439387 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.84025 | −0.129381 | −0.0646907 | − | 0.997905i | \(-0.520606\pi\) | ||||
−0.0646907 | + | 0.997905i | \(0.520606\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.42465 | 0.249859 | 0.124930 | − | 0.992166i | \(-0.460129\pi\) | ||||
0.124930 | + | 0.992166i | \(0.460129\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.95866 | −0.0658397 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12.1102 | 0.406621 | 0.203310 | − | 0.979114i | \(-0.434830\pi\) | ||||
0.203310 | + | 0.979114i | \(0.434830\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.00659 | −0.100838 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 11.1543 | 0.373684 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12.1547 | 0.406740 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.59882 | 0.153721 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.18837 | −0.139846 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.46811 | −0.315779 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.43213 | 0.0477112 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.27211 | 0.0756111 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.788670 | −0.0262163 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 29.8920 | 0.992549 | 0.496275 | − | 0.868166i | \(-0.334701\pi\) | ||||
0.496275 | + | 0.868166i | \(0.334701\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −19.2047 | −0.636980 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −44.2395 | −1.46572 | −0.732860 | − | 0.680379i | \(-0.761815\pi\) | ||||
−0.732860 | + | 0.680379i | \(0.761815\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.53858 | −0.249491 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.0880445 | −0.00291066 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −10.4153 | −0.343945 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −36.0167 | −1.18808 | −0.594040 | − | 0.804436i | \(-0.702468\pi\) | ||||
−0.594040 | + | 0.804436i | \(0.702468\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.99128 | 0.263322 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 17.2826 | 0.568864 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 42.9082 | 1.41081 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 15.5922 | 0.512114 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −53.6285 | −1.75949 | −0.879747 | − | 0.475442i | \(-0.842288\pi\) | ||||
−0.879747 | + | 0.475442i | \(0.842288\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.14995 | −0.201556 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5.41453 | 0.177264 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.787565 | −0.0257561 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −53.6935 | −1.75409 | −0.877044 | − | 0.480410i | \(-0.840488\pi\) | ||||
−0.877044 | + | 0.480410i | \(0.840488\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.907920 | 0.0296289 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14.2431 | −0.464313 | −0.232156 | − | 0.972678i | \(-0.574578\pi\) | ||||
−0.232156 | + | 0.972678i | \(0.574578\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −22.8361 | −0.743647 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.847859 | −0.0275808 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 35.6890 | 1.15974 | 0.579869 | − | 0.814710i | \(-0.303104\pi\) | ||||
0.579869 | + | 0.814710i | \(0.303104\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −24.0472 | −0.780604 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 11.1233 | 0.360699 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −42.8183 | −1.38702 | −0.693511 | − | 0.720446i | \(-0.743937\pi\) | ||||
−0.693511 | + | 0.720446i | \(0.743937\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.22611 | 0.201472 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5.31611 | −0.171845 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 12.4775 | 0.402920 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.5572 | −0.953457 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 29.1182 | 0.938322 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.33790 | 0.236216 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.60778 | 0.0517027 | 0.0258514 | − | 0.999666i | \(-0.491770\pi\) | ||||
0.0258514 | + | 0.999666i | \(0.491770\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.631208 | −0.0202773 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −16.6691 | −0.534938 | −0.267469 | − | 0.963566i | \(-0.586187\pi\) | ||||
−0.267469 | + | 0.963566i | \(0.586187\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.91190 | −0.253644 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.32091 | 0.138380 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −52.8780 | −1.69172 | −0.845859 | − | 0.533407i | \(-0.820911\pi\) | ||||
−0.845859 | + | 0.533407i | \(0.820911\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −15.5538 | −0.497102 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.6339 | −0.339513 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.20251 | 0.165934 | 0.0829672 | − | 0.996552i | \(-0.473560\pi\) | ||||
0.0829672 | + | 0.996552i | \(0.473560\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.44907 | 0.301073 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4.93919 | 0.157216 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 26.3992 | 0.839446 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 47.2436 | 1.50074 | 0.750372 | − | 0.661016i | \(-0.229875\pi\) | ||||
0.750372 | + | 0.661016i | \(0.229875\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.65875 | −0.0526389 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.433650 | 0.0137476 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.6048 | 0.652562 | 0.326281 | − | 0.945273i | \(-0.394205\pi\) | ||||
0.326281 | + | 0.945273i | \(0.394205\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 22.5415 | 0.713182 |
(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 | 4028.2.a.c.1.12 | ✓ | 19 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4028.2.a.c.1.12 | ✓ | 19 | 1.1 | even | 1 | trivial |