Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8015,2,Mod(1,8015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8015, 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("8015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8015 = 5 \cdot 7 \cdot 229 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8015.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: | \(64.0000972201\) |
Analytic rank: | \(0\) |
Dimension: | \(62\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.37 | ||
Character | \(\chi\) | \(=\) | 8015.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.609593 | 0.431047 | 0.215524 | − | 0.976499i | \(-0.430854\pi\) | ||||
0.215524 | + | 0.976499i | \(0.430854\pi\) | |||||||
\(3\) | 2.28126 | 1.31709 | 0.658543 | − | 0.752543i | \(-0.271173\pi\) | ||||
0.658543 | + | 0.752543i | \(0.271173\pi\) | |||||||
\(4\) | −1.62840 | −0.814198 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 1.39064 | 0.567726 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −2.21184 | −0.782005 | ||||||||
\(9\) | 2.20414 | 0.734714 | ||||||||
\(10\) | −0.609593 | −0.192770 | ||||||||
\(11\) | 3.79775 | 1.14507 | 0.572533 | − | 0.819882i | \(-0.305961\pi\) | ||||
0.572533 | + | 0.819882i | \(0.305961\pi\) | |||||||
\(12\) | −3.71480 | −1.07237 | ||||||||
\(13\) | 6.31536 | 1.75157 | 0.875783 | − | 0.482706i | \(-0.160346\pi\) | ||||
0.875783 | + | 0.482706i | \(0.160346\pi\) | |||||||
\(14\) | −0.609593 | −0.162920 | ||||||||
\(15\) | −2.28126 | −0.589019 | ||||||||
\(16\) | 1.90847 | 0.477117 | ||||||||
\(17\) | 2.30733 | 0.559610 | 0.279805 | − | 0.960057i | \(-0.409730\pi\) | ||||
0.279805 | + | 0.960057i | \(0.409730\pi\) | |||||||
\(18\) | 1.34363 | 0.316697 | ||||||||
\(19\) | −2.08034 | −0.477262 | −0.238631 | − | 0.971110i | \(-0.576699\pi\) | ||||
−0.238631 | + | 0.971110i | \(0.576699\pi\) | |||||||
\(20\) | 1.62840 | 0.364121 | ||||||||
\(21\) | −2.28126 | −0.497812 | ||||||||
\(22\) | 2.31508 | 0.493577 | ||||||||
\(23\) | 0.263969 | 0.0550414 | 0.0275207 | − | 0.999621i | \(-0.491239\pi\) | ||||
0.0275207 | + | 0.999621i | \(0.491239\pi\) | |||||||
\(24\) | −5.04579 | −1.02997 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 3.84980 | 0.755007 | ||||||||
\(27\) | −1.81556 | −0.349404 | ||||||||
\(28\) | 1.62840 | 0.307738 | ||||||||
\(29\) | 5.74574 | 1.06696 | 0.533479 | − | 0.845813i | \(-0.320884\pi\) | ||||
0.533479 | + | 0.845813i | \(0.320884\pi\) | |||||||
\(30\) | −1.39064 | −0.253895 | ||||||||
\(31\) | −4.16265 | −0.747635 | −0.373817 | − | 0.927502i | \(-0.621951\pi\) | ||||
−0.373817 | + | 0.927502i | \(0.621951\pi\) | |||||||
\(32\) | 5.58708 | 0.987665 | ||||||||
\(33\) | 8.66366 | 1.50815 | ||||||||
\(34\) | 1.40653 | 0.241218 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | −3.58922 | −0.598203 | ||||||||
\(37\) | 1.78740 | 0.293846 | 0.146923 | − | 0.989148i | \(-0.453063\pi\) | ||||
0.146923 | + | 0.989148i | \(0.453063\pi\) | |||||||
\(38\) | −1.26816 | −0.205723 | ||||||||
\(39\) | 14.4070 | 2.30696 | ||||||||
\(40\) | 2.21184 | 0.349723 | ||||||||
\(41\) | −11.8375 | −1.84871 | −0.924356 | − | 0.381531i | \(-0.875397\pi\) | ||||
−0.924356 | + | 0.381531i | \(0.875397\pi\) | |||||||
\(42\) | −1.39064 | −0.214580 | ||||||||
\(43\) | 3.06067 | 0.466748 | 0.233374 | − | 0.972387i | \(-0.425023\pi\) | ||||
0.233374 | + | 0.972387i | \(0.425023\pi\) | |||||||
\(44\) | −6.18425 | −0.932311 | ||||||||
\(45\) | −2.20414 | −0.328574 | ||||||||
\(46\) | 0.160914 | 0.0237254 | ||||||||
\(47\) | 3.53800 | 0.516071 | 0.258035 | − | 0.966135i | \(-0.416925\pi\) | ||||
0.258035 | + | 0.966135i | \(0.416925\pi\) | |||||||
\(48\) | 4.35371 | 0.628405 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0.609593 | 0.0862094 | ||||||||
\(51\) | 5.26362 | 0.737054 | ||||||||
\(52\) | −10.2839 | −1.42612 | ||||||||
\(53\) | −10.1754 | −1.39769 | −0.698847 | − | 0.715271i | \(-0.746303\pi\) | ||||
−0.698847 | + | 0.715271i | \(0.746303\pi\) | |||||||
\(54\) | −1.10675 | −0.150610 | ||||||||
\(55\) | −3.79775 | −0.512089 | ||||||||
\(56\) | 2.21184 | 0.295570 | ||||||||
\(57\) | −4.74579 | −0.628595 | ||||||||
\(58\) | 3.50256 | 0.459909 | ||||||||
\(59\) | 6.39001 | 0.831908 | 0.415954 | − | 0.909386i | \(-0.363448\pi\) | ||||
0.415954 | + | 0.909386i | \(0.363448\pi\) | |||||||
\(60\) | 3.71480 | 0.479578 | ||||||||
\(61\) | 0.234512 | 0.0300262 | 0.0150131 | − | 0.999887i | \(-0.495221\pi\) | ||||
0.0150131 | + | 0.999887i | \(0.495221\pi\) | |||||||
\(62\) | −2.53752 | −0.322266 | ||||||||
\(63\) | −2.20414 | −0.277696 | ||||||||
\(64\) | −0.411098 | −0.0513873 | ||||||||
\(65\) | −6.31536 | −0.783324 | ||||||||
\(66\) | 5.28130 | 0.650084 | ||||||||
\(67\) | −13.7050 | −1.67433 | −0.837164 | − | 0.546953i | \(-0.815788\pi\) | ||||
−0.837164 | + | 0.546953i | \(0.815788\pi\) | |||||||
\(68\) | −3.75725 | −0.455633 | ||||||||
\(69\) | 0.602182 | 0.0724942 | ||||||||
\(70\) | 0.609593 | 0.0728603 | ||||||||
\(71\) | −1.07440 | −0.127508 | −0.0637541 | − | 0.997966i | \(-0.520307\pi\) | ||||
−0.0637541 | + | 0.997966i | \(0.520307\pi\) | |||||||
\(72\) | −4.87522 | −0.574550 | ||||||||
\(73\) | 13.5549 | 1.58648 | 0.793241 | − | 0.608907i | \(-0.208392\pi\) | ||||
0.793241 | + | 0.608907i | \(0.208392\pi\) | |||||||
\(74\) | 1.08958 | 0.126662 | ||||||||
\(75\) | 2.28126 | 0.263417 | ||||||||
\(76\) | 3.38762 | 0.388586 | ||||||||
\(77\) | −3.79775 | −0.432794 | ||||||||
\(78\) | 8.78238 | 0.994409 | ||||||||
\(79\) | −0.238780 | −0.0268648 | −0.0134324 | − | 0.999910i | \(-0.504276\pi\) | ||||
−0.0134324 | + | 0.999910i | \(0.504276\pi\) | |||||||
\(80\) | −1.90847 | −0.213373 | ||||||||
\(81\) | −10.7542 | −1.19491 | ||||||||
\(82\) | −7.21607 | −0.796882 | ||||||||
\(83\) | 0.663084 | 0.0727830 | 0.0363915 | − | 0.999338i | \(-0.488414\pi\) | ||||
0.0363915 | + | 0.999338i | \(0.488414\pi\) | |||||||
\(84\) | 3.71480 | 0.405317 | ||||||||
\(85\) | −2.30733 | −0.250265 | ||||||||
\(86\) | 1.86576 | 0.201191 | ||||||||
\(87\) | 13.1075 | 1.40527 | ||||||||
\(88\) | −8.40004 | −0.895447 | ||||||||
\(89\) | 16.2882 | 1.72655 | 0.863276 | − | 0.504733i | \(-0.168409\pi\) | ||||
0.863276 | + | 0.504733i | \(0.168409\pi\) | |||||||
\(90\) | −1.34363 | −0.141631 | ||||||||
\(91\) | −6.31536 | −0.662029 | ||||||||
\(92\) | −0.429846 | −0.0448146 | ||||||||
\(93\) | −9.49609 | −0.984699 | ||||||||
\(94\) | 2.15674 | 0.222451 | ||||||||
\(95\) | 2.08034 | 0.213438 | ||||||||
\(96\) | 12.7456 | 1.30084 | ||||||||
\(97\) | 0.859629 | 0.0872821 | 0.0436411 | − | 0.999047i | \(-0.486104\pi\) | ||||
0.0436411 | + | 0.999047i | \(0.486104\pi\) | |||||||
\(98\) | 0.609593 | 0.0615782 | ||||||||
\(99\) | 8.37079 | 0.841296 | ||||||||
\(100\) | −1.62840 | −0.162840 | ||||||||
\(101\) | 0.661812 | 0.0658528 | 0.0329264 | − | 0.999458i | \(-0.489517\pi\) | ||||
0.0329264 | + | 0.999458i | \(0.489517\pi\) | |||||||
\(102\) | 3.20866 | 0.317705 | ||||||||
\(103\) | −1.19785 | −0.118027 | −0.0590136 | − | 0.998257i | \(-0.518796\pi\) | ||||
−0.0590136 | + | 0.998257i | \(0.518796\pi\) | |||||||
\(104\) | −13.9686 | −1.36973 | ||||||||
\(105\) | 2.28126 | 0.222628 | ||||||||
\(106\) | −6.20283 | −0.602472 | ||||||||
\(107\) | 9.72768 | 0.940410 | 0.470205 | − | 0.882557i | \(-0.344180\pi\) | ||||
0.470205 | + | 0.882557i | \(0.344180\pi\) | |||||||
\(108\) | 2.95644 | 0.284484 | ||||||||
\(109\) | 17.7364 | 1.69884 | 0.849421 | − | 0.527716i | \(-0.176951\pi\) | ||||
0.849421 | + | 0.527716i | \(0.176951\pi\) | |||||||
\(110\) | −2.31508 | −0.220734 | ||||||||
\(111\) | 4.07751 | 0.387021 | ||||||||
\(112\) | −1.90847 | −0.180333 | ||||||||
\(113\) | 12.3006 | 1.15714 | 0.578571 | − | 0.815632i | \(-0.303611\pi\) | ||||
0.578571 | + | 0.815632i | \(0.303611\pi\) | |||||||
\(114\) | −2.89300 | −0.270954 | ||||||||
\(115\) | −0.263969 | −0.0246152 | ||||||||
\(116\) | −9.35635 | −0.868715 | ||||||||
\(117\) | 13.9200 | 1.28690 | ||||||||
\(118\) | 3.89530 | 0.358592 | ||||||||
\(119\) | −2.30733 | −0.211513 | ||||||||
\(120\) | 5.04579 | 0.460615 | ||||||||
\(121\) | 3.42293 | 0.311176 | ||||||||
\(122\) | 0.142957 | 0.0129427 | ||||||||
\(123\) | −27.0045 | −2.43491 | ||||||||
\(124\) | 6.77845 | 0.608723 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −1.34363 | −0.119700 | ||||||||
\(127\) | 19.4000 | 1.72147 | 0.860737 | − | 0.509050i | \(-0.170003\pi\) | ||||
0.860737 | + | 0.509050i | \(0.170003\pi\) | |||||||
\(128\) | −11.4248 | −1.00982 | ||||||||
\(129\) | 6.98219 | 0.614747 | ||||||||
\(130\) | −3.84980 | −0.337649 | ||||||||
\(131\) | 19.4521 | 1.69954 | 0.849771 | − | 0.527152i | \(-0.176740\pi\) | ||||
0.849771 | + | 0.527152i | \(0.176740\pi\) | |||||||
\(132\) | −14.1079 | −1.22793 | ||||||||
\(133\) | 2.08034 | 0.180388 | ||||||||
\(134\) | −8.35444 | −0.721714 | ||||||||
\(135\) | 1.81556 | 0.156258 | ||||||||
\(136\) | −5.10345 | −0.437618 | ||||||||
\(137\) | 1.65064 | 0.141023 | 0.0705117 | − | 0.997511i | \(-0.477537\pi\) | ||||
0.0705117 | + | 0.997511i | \(0.477537\pi\) | |||||||
\(138\) | 0.367086 | 0.0312484 | ||||||||
\(139\) | 19.0852 | 1.61879 | 0.809393 | − | 0.587267i | \(-0.199796\pi\) | ||||
0.809393 | + | 0.587267i | \(0.199796\pi\) | |||||||
\(140\) | −1.62840 | −0.137625 | ||||||||
\(141\) | 8.07110 | 0.679709 | ||||||||
\(142\) | −0.654948 | −0.0549620 | ||||||||
\(143\) | 23.9842 | 2.00566 | ||||||||
\(144\) | 4.20654 | 0.350545 | ||||||||
\(145\) | −5.74574 | −0.477158 | ||||||||
\(146\) | 8.26298 | 0.683849 | ||||||||
\(147\) | 2.28126 | 0.188155 | ||||||||
\(148\) | −2.91059 | −0.239249 | ||||||||
\(149\) | −2.28925 | −0.187543 | −0.0937713 | − | 0.995594i | \(-0.529892\pi\) | ||||
−0.0937713 | + | 0.995594i | \(0.529892\pi\) | |||||||
\(150\) | 1.39064 | 0.113545 | ||||||||
\(151\) | −3.43002 | −0.279131 | −0.139566 | − | 0.990213i | \(-0.544571\pi\) | ||||
−0.139566 | + | 0.990213i | \(0.544571\pi\) | |||||||
\(152\) | 4.60138 | 0.373222 | ||||||||
\(153\) | 5.08569 | 0.411153 | ||||||||
\(154\) | −2.31508 | −0.186555 | ||||||||
\(155\) | 4.16265 | 0.334352 | ||||||||
\(156\) | −23.4603 | −1.87832 | ||||||||
\(157\) | 4.74723 | 0.378870 | 0.189435 | − | 0.981893i | \(-0.439334\pi\) | ||||
0.189435 | + | 0.981893i | \(0.439334\pi\) | |||||||
\(158\) | −0.145558 | −0.0115800 | ||||||||
\(159\) | −23.2126 | −1.84088 | ||||||||
\(160\) | −5.58708 | −0.441697 | ||||||||
\(161\) | −0.263969 | −0.0208037 | ||||||||
\(162\) | −6.55567 | −0.515062 | ||||||||
\(163\) | −3.02512 | −0.236946 | −0.118473 | − | 0.992957i | \(-0.537800\pi\) | ||||
−0.118473 | + | 0.992957i | \(0.537800\pi\) | |||||||
\(164\) | 19.2762 | 1.50522 | ||||||||
\(165\) | −8.66366 | −0.674465 | ||||||||
\(166\) | 0.404211 | 0.0313729 | ||||||||
\(167\) | 8.65634 | 0.669848 | 0.334924 | − | 0.942245i | \(-0.391289\pi\) | ||||
0.334924 | + | 0.942245i | \(0.391289\pi\) | |||||||
\(168\) | 5.04579 | 0.389291 | ||||||||
\(169\) | 26.8837 | 2.06798 | ||||||||
\(170\) | −1.40653 | −0.107876 | ||||||||
\(171\) | −4.58536 | −0.350652 | ||||||||
\(172\) | −4.98399 | −0.380026 | ||||||||
\(173\) | −13.1499 | −0.999768 | −0.499884 | − | 0.866092i | \(-0.666624\pi\) | ||||
−0.499884 | + | 0.866092i | \(0.666624\pi\) | |||||||
\(174\) | 7.99025 | 0.605740 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 7.24790 | 0.546331 | ||||||||
\(177\) | 14.5773 | 1.09569 | ||||||||
\(178\) | 9.92920 | 0.744225 | ||||||||
\(179\) | 11.6213 | 0.868619 | 0.434310 | − | 0.900764i | \(-0.356992\pi\) | ||||
0.434310 | + | 0.900764i | \(0.356992\pi\) | |||||||
\(180\) | 3.58922 | 0.267525 | ||||||||
\(181\) | 7.67898 | 0.570774 | 0.285387 | − | 0.958412i | \(-0.407878\pi\) | ||||
0.285387 | + | 0.958412i | \(0.407878\pi\) | |||||||
\(182\) | −3.84980 | −0.285366 | ||||||||
\(183\) | 0.534983 | 0.0395471 | ||||||||
\(184\) | −0.583859 | −0.0430426 | ||||||||
\(185\) | −1.78740 | −0.131412 | ||||||||
\(186\) | −5.78875 | −0.424452 | ||||||||
\(187\) | 8.76267 | 0.640790 | ||||||||
\(188\) | −5.76127 | −0.420184 | ||||||||
\(189\) | 1.81556 | 0.132062 | ||||||||
\(190\) | 1.26816 | 0.0920019 | ||||||||
\(191\) | −11.6654 | −0.844075 | −0.422038 | − | 0.906578i | \(-0.638685\pi\) | ||||
−0.422038 | + | 0.906578i | \(0.638685\pi\) | |||||||
\(192\) | −0.937822 | −0.0676815 | ||||||||
\(193\) | −7.62481 | −0.548846 | −0.274423 | − | 0.961609i | \(-0.588487\pi\) | ||||
−0.274423 | + | 0.961609i | \(0.588487\pi\) | |||||||
\(194\) | 0.524024 | 0.0376227 | ||||||||
\(195\) | −14.4070 | −1.03170 | ||||||||
\(196\) | −1.62840 | −0.116314 | ||||||||
\(197\) | 1.98744 | 0.141600 | 0.0707998 | − | 0.997491i | \(-0.477445\pi\) | ||||
0.0707998 | + | 0.997491i | \(0.477445\pi\) | |||||||
\(198\) | 5.10277 | 0.362638 | ||||||||
\(199\) | −20.2140 | −1.43293 | −0.716466 | − | 0.697622i | \(-0.754241\pi\) | ||||
−0.716466 | + | 0.697622i | \(0.754241\pi\) | |||||||
\(200\) | −2.21184 | −0.156401 | ||||||||
\(201\) | −31.2646 | −2.20523 | ||||||||
\(202\) | 0.403436 | 0.0283856 | ||||||||
\(203\) | −5.74574 | −0.403272 | ||||||||
\(204\) | −8.57126 | −0.600108 | ||||||||
\(205\) | 11.8375 | 0.826769 | ||||||||
\(206\) | −0.730198 | −0.0508753 | ||||||||
\(207\) | 0.581826 | 0.0404397 | ||||||||
\(208\) | 12.0527 | 0.835702 | ||||||||
\(209\) | −7.90061 | −0.546497 | ||||||||
\(210\) | 1.39064 | 0.0959632 | ||||||||
\(211\) | 0.669141 | 0.0460656 | 0.0230328 | − | 0.999735i | \(-0.492668\pi\) | ||||
0.0230328 | + | 0.999735i | \(0.492668\pi\) | |||||||
\(212\) | 16.5695 | 1.13800 | ||||||||
\(213\) | −2.45099 | −0.167939 | ||||||||
\(214\) | 5.92992 | 0.405361 | ||||||||
\(215\) | −3.06067 | −0.208736 | ||||||||
\(216\) | 4.01573 | 0.273236 | ||||||||
\(217\) | 4.16265 | 0.282579 | ||||||||
\(218\) | 10.8120 | 0.732281 | ||||||||
\(219\) | 30.9223 | 2.08953 | ||||||||
\(220\) | 6.18425 | 0.416942 | ||||||||
\(221\) | 14.5716 | 0.980193 | ||||||||
\(222\) | 2.48562 | 0.166824 | ||||||||
\(223\) | 8.37637 | 0.560923 | 0.280461 | − | 0.959865i | \(-0.409513\pi\) | ||||
0.280461 | + | 0.959865i | \(0.409513\pi\) | |||||||
\(224\) | −5.58708 | −0.373302 | ||||||||
\(225\) | 2.20414 | 0.146943 | ||||||||
\(226\) | 7.49834 | 0.498782 | ||||||||
\(227\) | −3.34665 | −0.222125 | −0.111062 | − | 0.993813i | \(-0.535425\pi\) | ||||
−0.111062 | + | 0.993813i | \(0.535425\pi\) | |||||||
\(228\) | 7.72803 | 0.511801 | ||||||||
\(229\) | 1.00000 | 0.0660819 | ||||||||
\(230\) | −0.160914 | −0.0106103 | ||||||||
\(231\) | −8.66366 | −0.570027 | ||||||||
\(232\) | −12.7087 | −0.834366 | ||||||||
\(233\) | −14.0456 | −0.920158 | −0.460079 | − | 0.887878i | \(-0.652179\pi\) | ||||
−0.460079 | + | 0.887878i | \(0.652179\pi\) | |||||||
\(234\) | 8.48550 | 0.554715 | ||||||||
\(235\) | −3.53800 | −0.230794 | ||||||||
\(236\) | −10.4055 | −0.677338 | ||||||||
\(237\) | −0.544719 | −0.0353833 | ||||||||
\(238\) | −1.40653 | −0.0911719 | ||||||||
\(239\) | 25.2062 | 1.63045 | 0.815225 | − | 0.579144i | \(-0.196613\pi\) | ||||
0.815225 | + | 0.579144i | \(0.196613\pi\) | |||||||
\(240\) | −4.35371 | −0.281031 | ||||||||
\(241\) | 6.11985 | 0.394214 | 0.197107 | − | 0.980382i | \(-0.436845\pi\) | ||||
0.197107 | + | 0.980382i | \(0.436845\pi\) | |||||||
\(242\) | 2.08659 | 0.134131 | ||||||||
\(243\) | −19.0864 | −1.22439 | ||||||||
\(244\) | −0.381879 | −0.0244473 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | −16.4617 | −1.04956 | ||||||||
\(247\) | −13.1381 | −0.835956 | ||||||||
\(248\) | 9.20714 | 0.584654 | ||||||||
\(249\) | 1.51267 | 0.0958614 | ||||||||
\(250\) | −0.609593 | −0.0385540 | ||||||||
\(251\) | −20.6471 | −1.30323 | −0.651617 | − | 0.758548i | \(-0.725909\pi\) | ||||
−0.651617 | + | 0.758548i | \(0.725909\pi\) | |||||||
\(252\) | 3.58922 | 0.226100 | ||||||||
\(253\) | 1.00249 | 0.0630260 | ||||||||
\(254\) | 11.8261 | 0.742036 | ||||||||
\(255\) | −5.26362 | −0.329621 | ||||||||
\(256\) | −6.14225 | −0.383891 | ||||||||
\(257\) | −1.24330 | −0.0775547 | −0.0387773 | − | 0.999248i | \(-0.512346\pi\) | ||||
−0.0387773 | + | 0.999248i | \(0.512346\pi\) | |||||||
\(258\) | 4.25629 | 0.264985 | ||||||||
\(259\) | −1.78740 | −0.111063 | ||||||||
\(260\) | 10.2839 | 0.637781 | ||||||||
\(261\) | 12.6644 | 0.783909 | ||||||||
\(262\) | 11.8579 | 0.732583 | ||||||||
\(263\) | 17.0619 | 1.05208 | 0.526042 | − | 0.850459i | \(-0.323676\pi\) | ||||
0.526042 | + | 0.850459i | \(0.323676\pi\) | |||||||
\(264\) | −19.1627 | −1.17938 | ||||||||
\(265\) | 10.1754 | 0.625068 | ||||||||
\(266\) | 1.26816 | 0.0777558 | ||||||||
\(267\) | 37.1577 | 2.27402 | ||||||||
\(268\) | 22.3171 | 1.36323 | ||||||||
\(269\) | 14.6943 | 0.895927 | 0.447963 | − | 0.894052i | \(-0.352150\pi\) | ||||
0.447963 | + | 0.894052i | \(0.352150\pi\) | |||||||
\(270\) | 1.10675 | 0.0673546 | ||||||||
\(271\) | −29.4092 | −1.78648 | −0.893242 | − | 0.449576i | \(-0.851575\pi\) | ||||
−0.893242 | + | 0.449576i | \(0.851575\pi\) | |||||||
\(272\) | 4.40347 | 0.267000 | ||||||||
\(273\) | −14.4070 | −0.871949 | ||||||||
\(274\) | 1.00622 | 0.0607877 | ||||||||
\(275\) | 3.79775 | 0.229013 | ||||||||
\(276\) | −0.980591 | −0.0590247 | ||||||||
\(277\) | 5.58984 | 0.335861 | 0.167930 | − | 0.985799i | \(-0.446292\pi\) | ||||
0.167930 | + | 0.985799i | \(0.446292\pi\) | |||||||
\(278\) | 11.6342 | 0.697773 | ||||||||
\(279\) | −9.17508 | −0.549298 | ||||||||
\(280\) | −2.21184 | −0.132183 | ||||||||
\(281\) | 11.8748 | 0.708389 | 0.354195 | − | 0.935172i | \(-0.384755\pi\) | ||||
0.354195 | + | 0.935172i | \(0.384755\pi\) | |||||||
\(282\) | 4.92008 | 0.292987 | ||||||||
\(283\) | 23.0995 | 1.37312 | 0.686561 | − | 0.727072i | \(-0.259119\pi\) | ||||
0.686561 | + | 0.727072i | \(0.259119\pi\) | |||||||
\(284\) | 1.74955 | 0.103817 | ||||||||
\(285\) | 4.74579 | 0.281116 | ||||||||
\(286\) | 14.6206 | 0.864533 | ||||||||
\(287\) | 11.8375 | 0.698748 | ||||||||
\(288\) | 12.3147 | 0.725652 | ||||||||
\(289\) | −11.6762 | −0.686837 | ||||||||
\(290\) | −3.50256 | −0.205678 | ||||||||
\(291\) | 1.96104 | 0.114958 | ||||||||
\(292\) | −22.0728 | −1.29171 | ||||||||
\(293\) | −4.47880 | −0.261654 | −0.130827 | − | 0.991405i | \(-0.541763\pi\) | ||||
−0.130827 | + | 0.991405i | \(0.541763\pi\) | |||||||
\(294\) | 1.39064 | 0.0811037 | ||||||||
\(295\) | −6.39001 | −0.372041 | ||||||||
\(296\) | −3.95344 | −0.229789 | ||||||||
\(297\) | −6.89503 | −0.400090 | ||||||||
\(298\) | −1.39551 | −0.0808397 | ||||||||
\(299\) | 1.66706 | 0.0964085 | ||||||||
\(300\) | −3.71480 | −0.214474 | ||||||||
\(301\) | −3.06067 | −0.176414 | ||||||||
\(302\) | −2.09091 | −0.120319 | ||||||||
\(303\) | 1.50976 | 0.0867337 | ||||||||
\(304\) | −3.97026 | −0.227710 | ||||||||
\(305\) | −0.234512 | −0.0134281 | ||||||||
\(306\) | 3.10020 | 0.177226 | ||||||||
\(307\) | −11.0768 | −0.632187 | −0.316094 | − | 0.948728i | \(-0.602371\pi\) | ||||
−0.316094 | + | 0.948728i | \(0.602371\pi\) | |||||||
\(308\) | 6.18425 | 0.352380 | ||||||||
\(309\) | −2.73260 | −0.155452 | ||||||||
\(310\) | 2.53752 | 0.144122 | ||||||||
\(311\) | −13.7160 | −0.777762 | −0.388881 | − | 0.921288i | \(-0.627138\pi\) | ||||
−0.388881 | + | 0.921288i | \(0.627138\pi\) | |||||||
\(312\) | −31.8660 | −1.80406 | ||||||||
\(313\) | 19.9914 | 1.12998 | 0.564989 | − | 0.825098i | \(-0.308880\pi\) | ||||
0.564989 | + | 0.825098i | \(0.308880\pi\) | |||||||
\(314\) | 2.89388 | 0.163311 | ||||||||
\(315\) | 2.20414 | 0.124189 | ||||||||
\(316\) | 0.388828 | 0.0218733 | ||||||||
\(317\) | 21.3063 | 1.19668 | 0.598341 | − | 0.801242i | \(-0.295827\pi\) | ||||
0.598341 | + | 0.801242i | \(0.295827\pi\) | |||||||
\(318\) | −14.1503 | −0.793507 | ||||||||
\(319\) | 21.8209 | 1.22174 | ||||||||
\(320\) | 0.411098 | 0.0229811 | ||||||||
\(321\) | 22.1914 | 1.23860 | ||||||||
\(322\) | −0.160914 | −0.00896737 | ||||||||
\(323\) | −4.80003 | −0.267081 | ||||||||
\(324\) | 17.5121 | 0.972893 | ||||||||
\(325\) | 6.31536 | 0.350313 | ||||||||
\(326\) | −1.84409 | −0.102135 | ||||||||
\(327\) | 40.4614 | 2.23752 | ||||||||
\(328\) | 26.1828 | 1.44570 | ||||||||
\(329\) | −3.53800 | −0.195056 | ||||||||
\(330\) | −5.28130 | −0.290726 | ||||||||
\(331\) | −0.788224 | −0.0433247 | −0.0216624 | − | 0.999765i | \(-0.506896\pi\) | ||||
−0.0216624 | + | 0.999765i | \(0.506896\pi\) | |||||||
\(332\) | −1.07976 | −0.0592598 | ||||||||
\(333\) | 3.93968 | 0.215893 | ||||||||
\(334\) | 5.27684 | 0.288736 | ||||||||
\(335\) | 13.7050 | 0.748782 | ||||||||
\(336\) | −4.35371 | −0.237515 | ||||||||
\(337\) | 0.0861554 | 0.00469318 | 0.00234659 | − | 0.999997i | \(-0.499253\pi\) | ||||
0.00234659 | + | 0.999997i | \(0.499253\pi\) | |||||||
\(338\) | 16.3881 | 0.891397 | ||||||||
\(339\) | 28.0608 | 1.52405 | ||||||||
\(340\) | 3.75725 | 0.203765 | ||||||||
\(341\) | −15.8087 | −0.856091 | ||||||||
\(342\) | −2.79520 | −0.151147 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −6.76973 | −0.364999 | ||||||||
\(345\) | −0.602182 | −0.0324204 | ||||||||
\(346\) | −8.01608 | −0.430947 | ||||||||
\(347\) | −34.3437 | −1.84367 | −0.921834 | − | 0.387585i | \(-0.873309\pi\) | ||||
−0.921834 | + | 0.387585i | \(0.873309\pi\) | |||||||
\(348\) | −21.3443 | −1.14417 | ||||||||
\(349\) | 16.6826 | 0.893001 | 0.446501 | − | 0.894783i | \(-0.352670\pi\) | ||||
0.446501 | + | 0.894783i | \(0.352670\pi\) | |||||||
\(350\) | −0.609593 | −0.0325841 | ||||||||
\(351\) | −11.4659 | −0.612004 | ||||||||
\(352\) | 21.2183 | 1.13094 | ||||||||
\(353\) | 14.7560 | 0.785381 | 0.392690 | − | 0.919671i | \(-0.371544\pi\) | ||||
0.392690 | + | 0.919671i | \(0.371544\pi\) | |||||||
\(354\) | 8.88619 | 0.472296 | ||||||||
\(355\) | 1.07440 | 0.0570234 | ||||||||
\(356\) | −26.5237 | −1.40576 | ||||||||
\(357\) | −5.26362 | −0.278580 | ||||||||
\(358\) | 7.08428 | 0.374416 | ||||||||
\(359\) | 16.6736 | 0.879998 | 0.439999 | − | 0.897998i | \(-0.354979\pi\) | ||||
0.439999 | + | 0.897998i | \(0.354979\pi\) | |||||||
\(360\) | 4.87522 | 0.256947 | ||||||||
\(361\) | −14.6722 | −0.772221 | ||||||||
\(362\) | 4.68105 | 0.246031 | ||||||||
\(363\) | 7.80859 | 0.409845 | ||||||||
\(364\) | 10.2839 | 0.539023 | ||||||||
\(365\) | −13.5549 | −0.709497 | ||||||||
\(366\) | 0.326122 | 0.0170467 | ||||||||
\(367\) | 7.63042 | 0.398305 | 0.199152 | − | 0.979969i | \(-0.436181\pi\) | ||||
0.199152 | + | 0.979969i | \(0.436181\pi\) | |||||||
\(368\) | 0.503777 | 0.0262612 | ||||||||
\(369\) | −26.0916 | −1.35828 | ||||||||
\(370\) | −1.08958 | −0.0566448 | ||||||||
\(371\) | 10.1754 | 0.528279 | ||||||||
\(372\) | 15.4634 | 0.801740 | ||||||||
\(373\) | 27.0632 | 1.40128 | 0.700640 | − | 0.713515i | \(-0.252898\pi\) | ||||
0.700640 | + | 0.713515i | \(0.252898\pi\) | |||||||
\(374\) | 5.34166 | 0.276211 | ||||||||
\(375\) | −2.28126 | −0.117804 | ||||||||
\(376\) | −7.82551 | −0.403570 | ||||||||
\(377\) | 36.2864 | 1.86885 | ||||||||
\(378\) | 1.10675 | 0.0569250 | ||||||||
\(379\) | 9.09630 | 0.467245 | 0.233623 | − | 0.972327i | \(-0.424942\pi\) | ||||
0.233623 | + | 0.972327i | \(0.424942\pi\) | |||||||
\(380\) | −3.38762 | −0.173781 | ||||||||
\(381\) | 44.2565 | 2.26733 | ||||||||
\(382\) | −7.11111 | −0.363836 | ||||||||
\(383\) | −8.50193 | −0.434429 | −0.217214 | − | 0.976124i | \(-0.569697\pi\) | ||||
−0.217214 | + | 0.976124i | \(0.569697\pi\) | |||||||
\(384\) | −26.0628 | −1.33001 | ||||||||
\(385\) | 3.79775 | 0.193551 | ||||||||
\(386\) | −4.64803 | −0.236578 | ||||||||
\(387\) | 6.74616 | 0.342927 | ||||||||
\(388\) | −1.39982 | −0.0710650 | ||||||||
\(389\) | −34.3231 | −1.74025 | −0.870125 | − | 0.492831i | \(-0.835962\pi\) | ||||
−0.870125 | + | 0.492831i | \(0.835962\pi\) | |||||||
\(390\) | −8.78238 | −0.444713 | ||||||||
\(391\) | 0.609064 | 0.0308017 | ||||||||
\(392\) | −2.21184 | −0.111715 | ||||||||
\(393\) | 44.3754 | 2.23844 | ||||||||
\(394\) | 1.21153 | 0.0610361 | ||||||||
\(395\) | 0.238780 | 0.0120143 | ||||||||
\(396\) | −13.6310 | −0.684982 | ||||||||
\(397\) | −32.9950 | −1.65597 | −0.827986 | − | 0.560748i | \(-0.810514\pi\) | ||||
−0.827986 | + | 0.560748i | \(0.810514\pi\) | |||||||
\(398\) | −12.3223 | −0.617661 | ||||||||
\(399\) | 4.74579 | 0.237587 | ||||||||
\(400\) | 1.90847 | 0.0954235 | ||||||||
\(401\) | 20.4563 | 1.02154 | 0.510769 | − | 0.859718i | \(-0.329361\pi\) | ||||
0.510769 | + | 0.859718i | \(0.329361\pi\) | |||||||
\(402\) | −19.0586 | −0.950559 | ||||||||
\(403\) | −26.2886 | −1.30953 | ||||||||
\(404\) | −1.07769 | −0.0536172 | ||||||||
\(405\) | 10.7542 | 0.534380 | ||||||||
\(406\) | −3.50256 | −0.173829 | ||||||||
\(407\) | 6.78809 | 0.336473 | ||||||||
\(408\) | −11.6423 | −0.576380 | ||||||||
\(409\) | −6.65977 | −0.329304 | −0.164652 | − | 0.986352i | \(-0.552650\pi\) | ||||
−0.164652 | + | 0.986352i | \(0.552650\pi\) | |||||||
\(410\) | 7.21607 | 0.356376 | ||||||||
\(411\) | 3.76553 | 0.185740 | ||||||||
\(412\) | 1.95057 | 0.0960976 | ||||||||
\(413\) | −6.39001 | −0.314432 | ||||||||
\(414\) | 0.354677 | 0.0174314 | ||||||||
\(415\) | −0.663084 | −0.0325495 | ||||||||
\(416\) | 35.2844 | 1.72996 | ||||||||
\(417\) | 43.5383 | 2.13208 | ||||||||
\(418\) | −4.81616 | −0.235566 | ||||||||
\(419\) | 1.90366 | 0.0930001 | 0.0465000 | − | 0.998918i | \(-0.485193\pi\) | ||||
0.0465000 | + | 0.998918i | \(0.485193\pi\) | |||||||
\(420\) | −3.71480 | −0.181263 | ||||||||
\(421\) | −3.01582 | −0.146982 | −0.0734911 | − | 0.997296i | \(-0.523414\pi\) | ||||
−0.0734911 | + | 0.997296i | \(0.523414\pi\) | |||||||
\(422\) | 0.407904 | 0.0198564 | ||||||||
\(423\) | 7.79826 | 0.379165 | ||||||||
\(424\) | 22.5063 | 1.09300 | ||||||||
\(425\) | 2.30733 | 0.111922 | ||||||||
\(426\) | −1.49411 | −0.0723897 | ||||||||
\(427\) | −0.234512 | −0.0113488 | ||||||||
\(428\) | −15.8405 | −0.765681 | ||||||||
\(429\) | 54.7141 | 2.64162 | ||||||||
\(430\) | −1.86576 | −0.0899751 | ||||||||
\(431\) | −4.68990 | −0.225905 | −0.112952 | − | 0.993600i | \(-0.536031\pi\) | ||||
−0.112952 | + | 0.993600i | \(0.536031\pi\) | |||||||
\(432\) | −3.46493 | −0.166707 | ||||||||
\(433\) | 22.3918 | 1.07608 | 0.538040 | − | 0.842919i | \(-0.319165\pi\) | ||||
0.538040 | + | 0.842919i | \(0.319165\pi\) | |||||||
\(434\) | 2.53752 | 0.121805 | ||||||||
\(435\) | −13.1075 | −0.628458 | ||||||||
\(436\) | −28.8819 | −1.38319 | ||||||||
\(437\) | −0.549145 | −0.0262692 | ||||||||
\(438\) | 18.8500 | 0.900687 | ||||||||
\(439\) | −36.5093 | −1.74249 | −0.871247 | − | 0.490844i | \(-0.836688\pi\) | ||||
−0.871247 | + | 0.490844i | \(0.836688\pi\) | |||||||
\(440\) | 8.40004 | 0.400456 | ||||||||
\(441\) | 2.20414 | 0.104959 | ||||||||
\(442\) | 8.88275 | 0.422509 | ||||||||
\(443\) | −32.1161 | −1.52588 | −0.762940 | − | 0.646470i | \(-0.776245\pi\) | ||||
−0.762940 | + | 0.646470i | \(0.776245\pi\) | |||||||
\(444\) | −6.63981 | −0.315111 | ||||||||
\(445\) | −16.2882 | −0.772137 | ||||||||
\(446\) | 5.10617 | 0.241784 | ||||||||
\(447\) | −5.22237 | −0.247010 | ||||||||
\(448\) | 0.411098 | 0.0194226 | ||||||||
\(449\) | 16.3807 | 0.773054 | 0.386527 | − | 0.922278i | \(-0.373675\pi\) | ||||
0.386527 | + | 0.922278i | \(0.373675\pi\) | |||||||
\(450\) | 1.34363 | 0.0633393 | ||||||||
\(451\) | −44.9560 | −2.11690 | ||||||||
\(452\) | −20.0302 | −0.942142 | ||||||||
\(453\) | −7.82476 | −0.367639 | ||||||||
\(454\) | −2.04009 | −0.0957463 | ||||||||
\(455\) | 6.31536 | 0.296069 | ||||||||
\(456\) | 10.4970 | 0.491565 | ||||||||
\(457\) | −21.5899 | −1.00993 | −0.504967 | − | 0.863139i | \(-0.668495\pi\) | ||||
−0.504967 | + | 0.863139i | \(0.668495\pi\) | |||||||
\(458\) | 0.609593 | 0.0284844 | ||||||||
\(459\) | −4.18909 | −0.195530 | ||||||||
\(460\) | 0.429846 | 0.0200417 | ||||||||
\(461\) | −4.31949 | −0.201179 | −0.100589 | − | 0.994928i | \(-0.532073\pi\) | ||||
−0.100589 | + | 0.994928i | \(0.532073\pi\) | |||||||
\(462\) | −5.28130 | −0.245708 | ||||||||
\(463\) | 8.35380 | 0.388234 | 0.194117 | − | 0.980978i | \(-0.437816\pi\) | ||||
0.194117 | + | 0.980978i | \(0.437816\pi\) | |||||||
\(464\) | 10.9656 | 0.509064 | ||||||||
\(465\) | 9.49609 | 0.440371 | ||||||||
\(466\) | −8.56210 | −0.396632 | ||||||||
\(467\) | −22.4340 | −1.03812 | −0.519060 | − | 0.854738i | \(-0.673718\pi\) | ||||
−0.519060 | + | 0.854738i | \(0.673718\pi\) | |||||||
\(468\) | −22.6672 | −1.04779 | ||||||||
\(469\) | 13.7050 | 0.632836 | ||||||||
\(470\) | −2.15674 | −0.0994830 | ||||||||
\(471\) | 10.8297 | 0.499004 | ||||||||
\(472\) | −14.1337 | −0.650556 | ||||||||
\(473\) | 11.6237 | 0.534458 | ||||||||
\(474\) | −0.332057 | −0.0152519 | ||||||||
\(475\) | −2.08034 | −0.0954525 | ||||||||
\(476\) | 3.75725 | 0.172213 | ||||||||
\(477\) | −22.4280 | −1.02691 | ||||||||
\(478\) | 15.3655 | 0.702801 | ||||||||
\(479\) | 12.9007 | 0.589446 | 0.294723 | − | 0.955583i | \(-0.404773\pi\) | ||||
0.294723 | + | 0.955583i | \(0.404773\pi\) | |||||||
\(480\) | −12.7456 | −0.581753 | ||||||||
\(481\) | 11.2880 | 0.514691 | ||||||||
\(482\) | 3.73062 | 0.169925 | ||||||||
\(483\) | −0.602182 | −0.0274002 | ||||||||
\(484\) | −5.57389 | −0.253359 | ||||||||
\(485\) | −0.859629 | −0.0390338 | ||||||||
\(486\) | −11.6349 | −0.527771 | ||||||||
\(487\) | −16.5679 | −0.750762 | −0.375381 | − | 0.926871i | \(-0.622488\pi\) | ||||
−0.375381 | + | 0.926871i | \(0.622488\pi\) | |||||||
\(488\) | −0.518705 | −0.0234807 | ||||||||
\(489\) | −6.90108 | −0.312078 | ||||||||
\(490\) | −0.609593 | −0.0275386 | ||||||||
\(491\) | 23.4466 | 1.05813 | 0.529065 | − | 0.848582i | \(-0.322543\pi\) | ||||
0.529065 | + | 0.848582i | \(0.322543\pi\) | |||||||
\(492\) | 43.9740 | 1.98250 | ||||||||
\(493\) | 13.2573 | 0.597080 | ||||||||
\(494\) | −8.00888 | −0.360336 | ||||||||
\(495\) | −8.37079 | −0.376239 | ||||||||
\(496\) | −7.94430 | −0.356709 | ||||||||
\(497\) | 1.07440 | 0.0481936 | ||||||||
\(498\) | 0.922111 | 0.0413208 | ||||||||
\(499\) | −13.0359 | −0.583566 | −0.291783 | − | 0.956485i | \(-0.594248\pi\) | ||||
−0.291783 | + | 0.956485i | \(0.594248\pi\) | |||||||
\(500\) | 1.62840 | 0.0728241 | ||||||||
\(501\) | 19.7474 | 0.882247 | ||||||||
\(502\) | −12.5863 | −0.561755 | ||||||||
\(503\) | −15.9848 | −0.712727 | −0.356364 | − | 0.934347i | \(-0.615984\pi\) | ||||
−0.356364 | + | 0.934347i | \(0.615984\pi\) | |||||||
\(504\) | 4.87522 | 0.217160 | ||||||||
\(505\) | −0.661812 | −0.0294503 | ||||||||
\(506\) | 0.611110 | 0.0271672 | ||||||||
\(507\) | 61.3288 | 2.72371 | ||||||||
\(508\) | −31.5909 | −1.40162 | ||||||||
\(509\) | −31.3783 | −1.39082 | −0.695409 | − | 0.718614i | \(-0.744777\pi\) | ||||
−0.695409 | + | 0.718614i | \(0.744777\pi\) | |||||||
\(510\) | −3.20866 | −0.142082 | ||||||||
\(511\) | −13.5549 | −0.599634 | ||||||||
\(512\) | 19.1052 | 0.844340 | ||||||||
\(513\) | 3.77697 | 0.166757 | ||||||||
\(514\) | −0.757904 | −0.0334297 | ||||||||
\(515\) | 1.19785 | 0.0527834 | ||||||||
\(516\) | −11.3698 | −0.500526 | ||||||||
\(517\) | 13.4365 | 0.590935 | ||||||||
\(518\) | −1.08958 | −0.0478736 | ||||||||
\(519\) | −29.9983 | −1.31678 | ||||||||
\(520\) | 13.9686 | 0.612563 | ||||||||
\(521\) | 11.2520 | 0.492960 | 0.246480 | − | 0.969148i | \(-0.420726\pi\) | ||||
0.246480 | + | 0.969148i | \(0.420726\pi\) | |||||||
\(522\) | 7.72015 | 0.337902 | ||||||||
\(523\) | −18.4116 | −0.805083 | −0.402541 | − | 0.915402i | \(-0.631873\pi\) | ||||
−0.402541 | + | 0.915402i | \(0.631873\pi\) | |||||||
\(524\) | −31.6758 | −1.38376 | ||||||||
\(525\) | −2.28126 | −0.0995623 | ||||||||
\(526\) | 10.4008 | 0.453498 | ||||||||
\(527\) | −9.60461 | −0.418384 | ||||||||
\(528\) | 16.5343 | 0.719564 | ||||||||
\(529\) | −22.9303 | −0.996970 | ||||||||
\(530\) | 6.20283 | 0.269434 | ||||||||
\(531\) | 14.0845 | 0.611215 | ||||||||
\(532\) | −3.38762 | −0.146872 | ||||||||
\(533\) | −74.7583 | −3.23814 | ||||||||
\(534\) | 22.6511 | 0.980208 | ||||||||
\(535\) | −9.72768 | −0.420564 | ||||||||
\(536\) | 30.3132 | 1.30933 | ||||||||
\(537\) | 26.5113 | 1.14405 | ||||||||
\(538\) | 8.95753 | 0.386187 | ||||||||
\(539\) | 3.79775 | 0.163581 | ||||||||
\(540\) | −2.95644 | −0.127225 | ||||||||
\(541\) | 14.4700 | 0.622114 | 0.311057 | − | 0.950391i | \(-0.399317\pi\) | ||||
0.311057 | + | 0.950391i | \(0.399317\pi\) | |||||||
\(542\) | −17.9277 | −0.770059 | ||||||||
\(543\) | 17.5177 | 0.751758 | ||||||||
\(544\) | 12.8912 | 0.552707 | ||||||||
\(545\) | −17.7364 | −0.759745 | ||||||||
\(546\) | −8.78238 | −0.375851 | ||||||||
\(547\) | 12.6106 | 0.539190 | 0.269595 | − | 0.962974i | \(-0.413110\pi\) | ||||
0.269595 | + | 0.962974i | \(0.413110\pi\) | |||||||
\(548\) | −2.68789 | −0.114821 | ||||||||
\(549\) | 0.516899 | 0.0220607 | ||||||||
\(550\) | 2.31508 | 0.0987155 | ||||||||
\(551\) | −11.9531 | −0.509219 | ||||||||
\(552\) | −1.33193 | −0.0566908 | ||||||||
\(553\) | 0.238780 | 0.0101540 | ||||||||
\(554\) | 3.40753 | 0.144772 | ||||||||
\(555\) | −4.07751 | −0.173081 | ||||||||
\(556\) | −31.0783 | −1.31801 | ||||||||
\(557\) | −10.3207 | −0.437303 | −0.218651 | − | 0.975803i | \(-0.570166\pi\) | ||||
−0.218651 | + | 0.975803i | \(0.570166\pi\) | |||||||
\(558\) | −5.59306 | −0.236773 | ||||||||
\(559\) | 19.3292 | 0.817540 | ||||||||
\(560\) | 1.90847 | 0.0806476 | ||||||||
\(561\) | 19.9899 | 0.843975 | ||||||||
\(562\) | 7.23877 | 0.305349 | ||||||||
\(563\) | −42.2694 | −1.78144 | −0.890720 | − | 0.454552i | \(-0.849800\pi\) | ||||
−0.890720 | + | 0.454552i | \(0.849800\pi\) | |||||||
\(564\) | −13.1430 | −0.553418 | ||||||||
\(565\) | −12.3006 | −0.517489 | ||||||||
\(566\) | 14.0813 | 0.591881 | ||||||||
\(567\) | 10.7542 | 0.451633 | ||||||||
\(568\) | 2.37641 | 0.0997120 | ||||||||
\(569\) | 9.06146 | 0.379876 | 0.189938 | − | 0.981796i | \(-0.439171\pi\) | ||||
0.189938 | + | 0.981796i | \(0.439171\pi\) | |||||||
\(570\) | 2.89300 | 0.121174 | ||||||||
\(571\) | 14.3577 | 0.600852 | 0.300426 | − | 0.953805i | \(-0.402871\pi\) | ||||
0.300426 | + | 0.953805i | \(0.402871\pi\) | |||||||
\(572\) | −39.0557 | −1.63300 | ||||||||
\(573\) | −26.6117 | −1.11172 | ||||||||
\(574\) | 7.21607 | 0.301193 | ||||||||
\(575\) | 0.263969 | 0.0110083 | ||||||||
\(576\) | −0.906120 | −0.0377550 | ||||||||
\(577\) | −31.1895 | −1.29844 | −0.649219 | − | 0.760602i | \(-0.724904\pi\) | ||||
−0.649219 | + | 0.760602i | \(0.724904\pi\) | |||||||
\(578\) | −7.11774 | −0.296059 | ||||||||
\(579\) | −17.3942 | −0.722877 | ||||||||
\(580\) | 9.35635 | 0.388501 | ||||||||
\(581\) | −0.663084 | −0.0275094 | ||||||||
\(582\) | 1.19543 | 0.0495523 | ||||||||
\(583\) | −38.6435 | −1.60045 | ||||||||
\(584\) | −29.9814 | −1.24064 | ||||||||
\(585\) | −13.9200 | −0.575519 | ||||||||
\(586\) | −2.73024 | −0.112785 | ||||||||
\(587\) | 4.50524 | 0.185951 | 0.0929755 | − | 0.995668i | \(-0.470362\pi\) | ||||
0.0929755 | + | 0.995668i | \(0.470362\pi\) | |||||||
\(588\) | −3.71480 | −0.153196 | ||||||||
\(589\) | 8.65973 | 0.356818 | ||||||||
\(590\) | −3.89530 | −0.160367 | ||||||||
\(591\) | 4.53388 | 0.186499 | ||||||||
\(592\) | 3.41119 | 0.140199 | ||||||||
\(593\) | 39.1481 | 1.60762 | 0.803810 | − | 0.594886i | \(-0.202803\pi\) | ||||
0.803810 | + | 0.594886i | \(0.202803\pi\) | |||||||
\(594\) | −4.20316 | −0.172458 | ||||||||
\(595\) | 2.30733 | 0.0945913 | ||||||||
\(596\) | 3.72781 | 0.152697 | ||||||||
\(597\) | −46.1133 | −1.88729 | ||||||||
\(598\) | 1.01623 | 0.0415566 | ||||||||
\(599\) | 0.838810 | 0.0342729 | 0.0171364 | − | 0.999853i | \(-0.494545\pi\) | ||||
0.0171364 | + | 0.999853i | \(0.494545\pi\) | |||||||
\(600\) | −5.04579 | −0.205993 | ||||||||
\(601\) | 26.1208 | 1.06549 | 0.532745 | − | 0.846276i | \(-0.321161\pi\) | ||||
0.532745 | + | 0.846276i | \(0.321161\pi\) | |||||||
\(602\) | −1.86576 | −0.0760429 | ||||||||
\(603\) | −30.2077 | −1.23015 | ||||||||
\(604\) | 5.58543 | 0.227268 | ||||||||
\(605\) | −3.42293 | −0.139162 | ||||||||
\(606\) | 0.920342 | 0.0373863 | ||||||||
\(607\) | 17.3205 | 0.703018 | 0.351509 | − | 0.936184i | \(-0.385669\pi\) | ||||
0.351509 | + | 0.936184i | \(0.385669\pi\) | |||||||
\(608\) | −11.6230 | −0.471375 | ||||||||
\(609\) | −13.1075 | −0.531144 | ||||||||
\(610\) | −0.142957 | −0.00578816 | ||||||||
\(611\) | 22.3437 | 0.903931 | ||||||||
\(612\) | −8.28151 | −0.334760 | ||||||||
\(613\) | 44.9456 | 1.81534 | 0.907668 | − | 0.419689i | \(-0.137861\pi\) | ||||
0.907668 | + | 0.419689i | \(0.137861\pi\) | |||||||
\(614\) | −6.75234 | −0.272502 | ||||||||
\(615\) | 27.0045 | 1.08893 | ||||||||
\(616\) | 8.40004 | 0.338447 | ||||||||
\(617\) | −47.8359 | −1.92580 | −0.962901 | − | 0.269857i | \(-0.913024\pi\) | ||||
−0.962901 | + | 0.269857i | \(0.913024\pi\) | |||||||
\(618\) | −1.66577 | −0.0670071 | ||||||||
\(619\) | −6.13786 | −0.246701 | −0.123351 | − | 0.992363i | \(-0.539364\pi\) | ||||
−0.123351 | + | 0.992363i | \(0.539364\pi\) | |||||||
\(620\) | −6.77845 | −0.272229 | ||||||||
\(621\) | −0.479251 | −0.0192317 | ||||||||
\(622\) | −8.36117 | −0.335252 | ||||||||
\(623\) | −16.2882 | −0.652575 | ||||||||
\(624\) | 27.4953 | 1.10069 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 12.1866 | 0.487074 | ||||||||
\(627\) | −18.0233 | −0.719783 | ||||||||
\(628\) | −7.73037 | −0.308475 | ||||||||
\(629\) | 4.12411 | 0.164439 | ||||||||
\(630\) | 1.34363 | 0.0535315 | ||||||||
\(631\) | −7.33730 | −0.292093 | −0.146047 | − | 0.989278i | \(-0.546655\pi\) | ||||
−0.146047 | + | 0.989278i | \(0.546655\pi\) | |||||||
\(632\) | 0.528144 | 0.0210084 | ||||||||
\(633\) | 1.52648 | 0.0606723 | ||||||||
\(634\) | 12.9882 | 0.515826 | ||||||||
\(635\) | −19.4000 | −0.769866 | ||||||||
\(636\) | 37.7994 | 1.49884 | ||||||||
\(637\) | 6.31536 | 0.250224 | ||||||||
\(638\) | 13.3019 | 0.526626 | ||||||||
\(639\) | −2.36814 | −0.0936821 | ||||||||
\(640\) | 11.4248 | 0.451603 | ||||||||
\(641\) | 25.3709 | 1.00209 | 0.501046 | − | 0.865421i | \(-0.332949\pi\) | ||||
0.501046 | + | 0.865421i | \(0.332949\pi\) | |||||||
\(642\) | 13.5277 | 0.533895 | ||||||||
\(643\) | −5.66988 | −0.223598 | −0.111799 | − | 0.993731i | \(-0.535661\pi\) | ||||
−0.111799 | + | 0.993731i | \(0.535661\pi\) | |||||||
\(644\) | 0.429846 | 0.0169383 | ||||||||
\(645\) | −6.98219 | −0.274923 | ||||||||
\(646\) | −2.92606 | −0.115124 | ||||||||
\(647\) | 9.55879 | 0.375795 | 0.187897 | − | 0.982189i | \(-0.439833\pi\) | ||||
0.187897 | + | 0.982189i | \(0.439833\pi\) | |||||||
\(648\) | 23.7866 | 0.934425 | ||||||||
\(649\) | 24.2677 | 0.952590 | ||||||||
\(650\) | 3.84980 | 0.151001 | ||||||||
\(651\) | 9.49609 | 0.372181 | ||||||||
\(652\) | 4.92609 | 0.192921 | ||||||||
\(653\) | −32.2310 | −1.26130 | −0.630648 | − | 0.776069i | \(-0.717211\pi\) | ||||
−0.630648 | + | 0.776069i | \(0.717211\pi\) | |||||||
\(654\) | 24.6650 | 0.964477 | ||||||||
\(655\) | −19.4521 | −0.760058 | ||||||||
\(656\) | −22.5916 | −0.882053 | ||||||||
\(657\) | 29.8770 | 1.16561 | ||||||||
\(658\) | −2.15674 | −0.0840785 | ||||||||
\(659\) | −6.43221 | −0.250563 | −0.125282 | − | 0.992121i | \(-0.539983\pi\) | ||||
−0.125282 | + | 0.992121i | \(0.539983\pi\) | |||||||
\(660\) | 14.1079 | 0.549148 | ||||||||
\(661\) | 20.2028 | 0.785799 | 0.392900 | − | 0.919581i | \(-0.371472\pi\) | ||||
0.392900 | + | 0.919581i | \(0.371472\pi\) | |||||||
\(662\) | −0.480496 | −0.0186750 | ||||||||
\(663\) | 33.2416 | 1.29100 | ||||||||
\(664\) | −1.46664 | −0.0569166 | ||||||||
\(665\) | −2.08034 | −0.0806721 | ||||||||
\(666\) | 2.40160 | 0.0930600 | ||||||||
\(667\) | 1.51670 | 0.0587268 | ||||||||
\(668\) | −14.0960 | −0.545389 | ||||||||
\(669\) | 19.1087 | 0.738784 | ||||||||
\(670\) | 8.35444 | 0.322760 | ||||||||
\(671\) | 0.890620 | 0.0343820 | ||||||||
\(672\) | −12.7456 | −0.491671 | ||||||||
\(673\) | −40.2837 | −1.55282 | −0.776411 | − | 0.630227i | \(-0.782962\pi\) | ||||
−0.776411 | + | 0.630227i | \(0.782962\pi\) | |||||||
\(674\) | 0.0525197 | 0.00202298 | ||||||||
\(675\) | −1.81556 | −0.0698808 | ||||||||
\(676\) | −43.7774 | −1.68375 | ||||||||
\(677\) | 6.17098 | 0.237170 | 0.118585 | − | 0.992944i | \(-0.462164\pi\) | ||||
0.118585 | + | 0.992944i | \(0.462164\pi\) | |||||||
\(678\) | 17.1057 | 0.656939 | ||||||||
\(679\) | −0.859629 | −0.0329895 | ||||||||
\(680\) | 5.10345 | 0.195709 | ||||||||
\(681\) | −7.63457 | −0.292557 | ||||||||
\(682\) | −9.63689 | −0.369015 | ||||||||
\(683\) | 19.4027 | 0.742424 | 0.371212 | − | 0.928548i | \(-0.378942\pi\) | ||||
0.371212 | + | 0.928548i | \(0.378942\pi\) | |||||||
\(684\) | 7.46679 | 0.285500 | ||||||||
\(685\) | −1.65064 | −0.0630676 | ||||||||
\(686\) | −0.609593 | −0.0232744 | ||||||||
\(687\) | 2.28126 | 0.0870355 | ||||||||
\(688\) | 5.84120 | 0.222694 | ||||||||
\(689\) | −64.2611 | −2.44815 | ||||||||
\(690\) | −0.367086 | −0.0139747 | ||||||||
\(691\) | 23.2145 | 0.883123 | 0.441561 | − | 0.897231i | \(-0.354425\pi\) | ||||
0.441561 | + | 0.897231i | \(0.354425\pi\) | |||||||
\(692\) | 21.4133 | 0.814010 | ||||||||
\(693\) | −8.37079 | −0.317980 | ||||||||
\(694\) | −20.9357 | −0.794708 | ||||||||
\(695\) | −19.0852 | −0.723943 | ||||||||
\(696\) | −28.9918 | −1.09893 | ||||||||
\(697\) | −27.3131 | −1.03456 | ||||||||
\(698\) | 10.1696 | 0.384926 | ||||||||
\(699\) | −32.0417 | −1.21193 | ||||||||
\(700\) | 1.62840 | 0.0615476 | ||||||||
\(701\) | −0.359130 | −0.0135642 | −0.00678208 | − | 0.999977i | \(-0.502159\pi\) | ||||
−0.00678208 | + | 0.999977i | \(0.502159\pi\) | |||||||
\(702\) | −6.98952 | −0.263802 | ||||||||
\(703\) | −3.71839 | −0.140242 | ||||||||
\(704\) | −1.56125 | −0.0588418 | ||||||||
\(705\) | −8.07110 | −0.303975 | ||||||||
\(706\) | 8.99512 | 0.338536 | ||||||||
\(707\) | −0.661812 | −0.0248900 | ||||||||
\(708\) | −23.7376 | −0.892113 | ||||||||
\(709\) | 41.8277 | 1.57087 | 0.785435 | − | 0.618944i | \(-0.212439\pi\) | ||||
0.785435 | + | 0.618944i | \(0.212439\pi\) | |||||||
\(710\) | 0.654948 | 0.0245798 | ||||||||
\(711\) | −0.526305 | −0.0197380 | ||||||||
\(712\) | −36.0271 | −1.35017 | ||||||||
\(713\) | −1.09881 | −0.0411508 | ||||||||
\(714\) | −3.20866 | −0.120081 | ||||||||
\(715\) | −23.9842 | −0.896957 | ||||||||
\(716\) | −18.9241 | −0.707228 | ||||||||
\(717\) | 57.5018 | 2.14744 | ||||||||
\(718\) | 10.1641 | 0.379321 | ||||||||
\(719\) | −11.5715 | −0.431545 | −0.215772 | − | 0.976444i | \(-0.569227\pi\) | ||||
−0.215772 | + | 0.976444i | \(0.569227\pi\) | |||||||
\(720\) | −4.20654 | −0.156769 | ||||||||
\(721\) | 1.19785 | 0.0446101 | ||||||||
\(722\) | −8.94406 | −0.332863 | ||||||||
\(723\) | 13.9610 | 0.519214 | ||||||||
\(724\) | −12.5044 | −0.464723 | ||||||||
\(725\) | 5.74574 | 0.213392 | ||||||||
\(726\) | 4.76006 | 0.176662 | ||||||||
\(727\) | −41.5692 | −1.54172 | −0.770859 | − | 0.637006i | \(-0.780173\pi\) | ||||
−0.770859 | + | 0.637006i | \(0.780173\pi\) | |||||||
\(728\) | 13.9686 | 0.517710 | ||||||||
\(729\) | −11.2785 | −0.417722 | ||||||||
\(730\) | −8.26298 | −0.305826 | ||||||||
\(731\) | 7.06198 | 0.261197 | ||||||||
\(732\) | −0.871165 | −0.0321992 | ||||||||
\(733\) | 31.0415 | 1.14654 | 0.573271 | − | 0.819366i | \(-0.305674\pi\) | ||||
0.573271 | + | 0.819366i | \(0.305674\pi\) | |||||||
\(734\) | 4.65145 | 0.171688 | ||||||||
\(735\) | −2.28126 | −0.0841455 | ||||||||
\(736\) | 1.47482 | 0.0543624 | ||||||||
\(737\) | −52.0481 | −1.91721 | ||||||||
\(738\) | −15.9053 | −0.585481 | ||||||||
\(739\) | −6.34693 | −0.233476 | −0.116738 | − | 0.993163i | \(-0.537244\pi\) | ||||
−0.116738 | + | 0.993163i | \(0.537244\pi\) | |||||||
\(740\) | 2.91059 | 0.106995 | ||||||||
\(741\) | −29.9714 | −1.10103 | ||||||||
\(742\) | 6.20283 | 0.227713 | ||||||||
\(743\) | −3.10557 | −0.113932 | −0.0569662 | − | 0.998376i | \(-0.518143\pi\) | ||||
−0.0569662 | + | 0.998376i | \(0.518143\pi\) | |||||||
\(744\) | 21.0039 | 0.770039 | ||||||||
\(745\) | 2.28925 | 0.0838716 | ||||||||
\(746\) | 16.4975 | 0.604018 | ||||||||
\(747\) | 1.46153 | 0.0534747 | ||||||||
\(748\) | −14.2691 | −0.521730 | ||||||||
\(749\) | −9.72768 | −0.355442 | ||||||||
\(750\) | −1.39064 | −0.0507789 | ||||||||
\(751\) | −26.9835 | −0.984643 | −0.492321 | − | 0.870413i | \(-0.663852\pi\) | ||||
−0.492321 | + | 0.870413i | \(0.663852\pi\) | |||||||
\(752\) | 6.75217 | 0.246226 | ||||||||
\(753\) | −47.1014 | −1.71647 | ||||||||
\(754\) | 22.1199 | 0.805561 | ||||||||
\(755\) | 3.43002 | 0.124831 | ||||||||
\(756\) | −2.95644 | −0.107525 | ||||||||
\(757\) | −28.5549 | −1.03784 | −0.518922 | − | 0.854821i | \(-0.673667\pi\) | ||||
−0.518922 | + | 0.854821i | \(0.673667\pi\) | |||||||
\(758\) | 5.54504 | 0.201405 | ||||||||
\(759\) | 2.28694 | 0.0830106 | ||||||||
\(760\) | −4.60138 | −0.166910 | ||||||||
\(761\) | 32.6720 | 1.18436 | 0.592180 | − | 0.805806i | \(-0.298267\pi\) | ||||
0.592180 | + | 0.805806i | \(0.298267\pi\) | |||||||
\(762\) | 26.9784 | 0.977325 | ||||||||
\(763\) | −17.7364 | −0.642102 | ||||||||
\(764\) | 18.9958 | 0.687245 | ||||||||
\(765\) | −5.08569 | −0.183873 | ||||||||
\(766\) | −5.18272 | −0.187259 | ||||||||
\(767\) | 40.3552 | 1.45714 | ||||||||
\(768\) | −14.0121 | −0.505617 | ||||||||
\(769\) | 36.5131 | 1.31670 | 0.658348 | − | 0.752714i | \(-0.271256\pi\) | ||||
0.658348 | + | 0.752714i | \(0.271256\pi\) | |||||||
\(770\) | 2.31508 | 0.0834298 | ||||||||
\(771\) | −2.83628 | −0.102146 | ||||||||
\(772\) | 12.4162 | 0.446869 | ||||||||
\(773\) | −20.2383 | −0.727919 | −0.363960 | − | 0.931415i | \(-0.618575\pi\) | ||||
−0.363960 | + | 0.931415i | \(0.618575\pi\) | |||||||
\(774\) | 4.11241 | 0.147818 | ||||||||
\(775\) | −4.16265 | −0.149527 | ||||||||
\(776\) | −1.90137 | −0.0682551 | ||||||||
\(777\) | −4.07751 | −0.146280 | ||||||||
\(778\) | −20.9231 | −0.750130 | ||||||||
\(779\) | 24.6261 | 0.882321 | ||||||||
\(780\) | 23.4603 | 0.840012 | ||||||||
\(781\) | −4.08032 | −0.146005 | ||||||||
\(782\) | 0.371281 | 0.0132770 | ||||||||
\(783\) | −10.4317 | −0.372799 | ||||||||
\(784\) | 1.90847 | 0.0681596 | ||||||||
\(785\) | −4.74723 | −0.169436 | ||||||||
\(786\) | 27.0509 | 0.964874 | ||||||||
\(787\) | −0.668350 | −0.0238241 | −0.0119121 | − | 0.999929i | \(-0.503792\pi\) | ||||
−0.0119121 | + | 0.999929i | \(0.503792\pi\) | |||||||
\(788\) | −3.23635 | −0.115290 | ||||||||
\(789\) | 38.9227 | 1.38568 | ||||||||
\(790\) | 0.145558 | 0.00517874 | ||||||||
\(791\) | −12.3006 | −0.437358 | ||||||||
\(792\) | −18.5149 | −0.657898 | ||||||||
\(793\) | 1.48103 | 0.0525929 | ||||||||
\(794\) | −20.1135 | −0.713802 | ||||||||
\(795\) | 23.2126 | 0.823267 | ||||||||
\(796\) | 32.9164 | 1.16669 | ||||||||
\(797\) | −43.8557 | −1.55345 | −0.776724 | − | 0.629841i | \(-0.783120\pi\) | ||||
−0.776724 | + | 0.629841i | \(0.783120\pi\) | |||||||
\(798\) | 2.89300 | 0.102411 | ||||||||
\(799\) | 8.16334 | 0.288798 | ||||||||
\(800\) | 5.58708 | 0.197533 | ||||||||
\(801\) | 35.9016 | 1.26852 | ||||||||
\(802\) | 12.4700 | 0.440331 | ||||||||
\(803\) | 51.4782 | 1.81663 | ||||||||
\(804\) | 50.9111 | 1.79550 | ||||||||
\(805\) | 0.263969 | 0.00930369 | ||||||||
\(806\) | −16.0254 | −0.564469 | ||||||||
\(807\) | 33.5215 | 1.18001 | ||||||||
\(808\) | −1.46383 | −0.0514972 | ||||||||
\(809\) | 41.8880 | 1.47270 | 0.736352 | − | 0.676599i | \(-0.236547\pi\) | ||||
0.736352 | + | 0.676599i | \(0.236547\pi\) | |||||||
\(810\) | 6.55567 | 0.230343 | ||||||||
\(811\) | −20.0408 | −0.703729 | −0.351864 | − | 0.936051i | \(-0.614452\pi\) | ||||
−0.351864 | + | 0.936051i | \(0.614452\pi\) | |||||||
\(812\) | 9.35635 | 0.328344 | ||||||||
\(813\) | −67.0901 | −2.35295 | ||||||||
\(814\) | 4.13797 | 0.145036 | ||||||||
\(815\) | 3.02512 | 0.105965 | ||||||||
\(816\) | 10.0455 | 0.351661 | ||||||||
\(817\) | −6.36724 | −0.222761 | ||||||||
\(818\) | −4.05974 | −0.141946 | ||||||||
\(819\) | −13.9200 | −0.486403 | ||||||||
\(820\) | −19.2762 | −0.673154 | ||||||||
\(821\) | −3.57754 | −0.124857 | −0.0624285 | − | 0.998049i | \(-0.519885\pi\) | ||||
−0.0624285 | + | 0.998049i | \(0.519885\pi\) | |||||||
\(822\) | 2.29544 | 0.0800626 | ||||||||
\(823\) | 27.1110 | 0.945029 | 0.472515 | − | 0.881323i | \(-0.343346\pi\) | ||||
0.472515 | + | 0.881323i | \(0.343346\pi\) | |||||||
\(824\) | 2.64945 | 0.0922978 | ||||||||
\(825\) | 8.66366 | 0.301630 | ||||||||
\(826\) | −3.89530 | −0.135535 | ||||||||
\(827\) | −13.2119 | −0.459424 | −0.229712 | − | 0.973259i | \(-0.573778\pi\) | ||||
−0.229712 | + | 0.973259i | \(0.573778\pi\) | |||||||
\(828\) | −0.947443 | −0.0329259 | ||||||||
\(829\) | −7.55284 | −0.262321 | −0.131161 | − | 0.991361i | \(-0.541870\pi\) | ||||
−0.131161 | + | 0.991361i | \(0.541870\pi\) | |||||||
\(830\) | −0.404211 | −0.0140304 | ||||||||
\(831\) | 12.7519 | 0.442358 | ||||||||
\(832\) | −2.59623 | −0.0900082 | ||||||||
\(833\) | 2.30733 | 0.0799443 | ||||||||
\(834\) | 26.5406 | 0.919027 | ||||||||
\(835\) | −8.65634 | −0.299565 | ||||||||
\(836\) | 12.8653 | 0.444957 | ||||||||
\(837\) | 7.55753 | 0.261226 | ||||||||
\(838\) | 1.16046 | 0.0400874 | ||||||||
\(839\) | −21.4644 | −0.741032 | −0.370516 | − | 0.928826i | \(-0.620819\pi\) | ||||
−0.370516 | + | 0.928826i | \(0.620819\pi\) | |||||||
\(840\) | −5.04579 | −0.174096 | ||||||||
\(841\) | 4.01358 | 0.138399 | ||||||||
\(842\) | −1.83842 | −0.0633562 | ||||||||
\(843\) | 27.0894 | 0.933009 | ||||||||
\(844\) | −1.08963 | −0.0375065 | ||||||||
\(845\) | −26.8837 | −0.924829 | ||||||||
\(846\) | 4.75376 | 0.163438 | ||||||||
\(847\) | −3.42293 | −0.117613 | ||||||||
\(848\) | −19.4194 | −0.666864 | ||||||||
\(849\) | 52.6959 | 1.80852 | ||||||||
\(850\) | 1.40653 | 0.0482436 | ||||||||
\(851\) | 0.471817 | 0.0161737 | ||||||||
\(852\) | 3.99119 | 0.136736 | ||||||||
\(853\) | 52.3177 | 1.79133 | 0.895663 | − | 0.444734i | \(-0.146702\pi\) | ||||
0.895663 | + | 0.444734i | \(0.146702\pi\) | |||||||
\(854\) | −0.142957 | −0.00489189 | ||||||||
\(855\) | 4.58536 | 0.156816 | ||||||||
\(856\) | −21.5161 | −0.735405 | ||||||||
\(857\) | 5.25720 | 0.179583 | 0.0897913 | − | 0.995961i | \(-0.471380\pi\) | ||||
0.0897913 | + | 0.995961i | \(0.471380\pi\) | |||||||
\(858\) | 33.3533 | 1.13866 | ||||||||
\(859\) | −29.6058 | −1.01014 | −0.505068 | − | 0.863079i | \(-0.668533\pi\) | ||||
−0.505068 | + | 0.863079i | \(0.668533\pi\) | |||||||
\(860\) | 4.98399 | 0.169953 | ||||||||
\(861\) | 27.0045 | 0.920310 | ||||||||
\(862\) | −2.85893 | −0.0973755 | ||||||||
\(863\) | −14.3280 | −0.487731 | −0.243866 | − | 0.969809i | \(-0.578416\pi\) | ||||
−0.243866 | + | 0.969809i | \(0.578416\pi\) | |||||||
\(864\) | −10.1436 | −0.345094 | ||||||||
\(865\) | 13.1499 | 0.447110 | ||||||||
\(866\) | 13.6499 | 0.463841 | ||||||||
\(867\) | −26.6365 | −0.904623 | ||||||||
\(868\) | −6.77845 | −0.230076 | ||||||||
\(869\) | −0.906827 | −0.0307620 | ||||||||
\(870\) | −7.99025 | −0.270895 | ||||||||
\(871\) | −86.5517 | −2.93269 | ||||||||
\(872\) | −39.2302 | −1.32850 | ||||||||
\(873\) | 1.89475 | 0.0641274 | ||||||||
\(874\) | −0.334755 | −0.0113233 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | −50.3537 | −1.70129 | ||||||||
\(877\) | 13.9713 | 0.471776 | 0.235888 | − | 0.971780i | \(-0.424200\pi\) | ||||
0.235888 | + | 0.971780i | \(0.424200\pi\) | |||||||
\(878\) | −22.2558 | −0.751097 | ||||||||
\(879\) | −10.2173 | −0.344621 | ||||||||
\(880\) | −7.24790 | −0.244327 | ||||||||
\(881\) | −7.31628 | −0.246492 | −0.123246 | − | 0.992376i | \(-0.539330\pi\) | ||||
−0.123246 | + | 0.992376i | \(0.539330\pi\) | |||||||
\(882\) | 1.34363 | 0.0452424 | ||||||||
\(883\) | −7.48992 | −0.252056 | −0.126028 | − | 0.992027i | \(-0.540223\pi\) | ||||
−0.126028 | + | 0.992027i | \(0.540223\pi\) | |||||||
\(884\) | −23.7284 | −0.798072 | ||||||||
\(885\) | −14.5773 | −0.490009 | ||||||||
\(886\) | −19.5777 | −0.657726 | ||||||||
\(887\) | 7.56087 | 0.253869 | 0.126935 | − | 0.991911i | \(-0.459486\pi\) | ||||
0.126935 | + | 0.991911i | \(0.459486\pi\) | |||||||
\(888\) | −9.01882 | −0.302652 | ||||||||
\(889\) | −19.4000 | −0.650656 | ||||||||
\(890\) | −9.92920 | −0.332827 | ||||||||
\(891\) | −40.8417 | −1.36825 | ||||||||
\(892\) | −13.6400 | −0.456703 | ||||||||
\(893\) | −7.36024 | −0.246301 | ||||||||
\(894\) | −3.18352 | −0.106473 | ||||||||
\(895\) | −11.6213 | −0.388458 | ||||||||
\(896\) | 11.4248 | 0.381674 | ||||||||
\(897\) | 3.80299 | 0.126978 | ||||||||
\(898\) | 9.98557 | 0.333223 | ||||||||
\(899\) | −23.9175 | −0.797695 | ||||||||
\(900\) | −3.58922 | −0.119641 | ||||||||
\(901\) | −23.4779 | −0.782163 | ||||||||
\(902\) | −27.4049 | −0.912482 | ||||||||
\(903\) | −6.98219 | −0.232353 | ||||||||
\(904\) | −27.2070 | −0.904890 | ||||||||
\(905\) | −7.67898 | −0.255258 | ||||||||
\(906\) | −4.76992 | −0.158470 | ||||||||
\(907\) | 19.0567 | 0.632769 | 0.316384 | − | 0.948631i | \(-0.397531\pi\) | ||||
0.316384 | + | 0.948631i | \(0.397531\pi\) | |||||||
\(908\) | 5.44967 | 0.180854 | ||||||||
\(909\) | 1.45873 | 0.0483830 | ||||||||
\(910\) | 3.84980 | 0.127619 | ||||||||
\(911\) | −28.3228 | −0.938376 | −0.469188 | − | 0.883098i | \(-0.655453\pi\) | ||||
−0.469188 | + | 0.883098i | \(0.655453\pi\) | |||||||
\(912\) | −9.05720 | −0.299914 | ||||||||
\(913\) | 2.51823 | 0.0833413 | ||||||||
\(914\) | −13.1611 | −0.435329 | ||||||||
\(915\) | −0.534983 | −0.0176860 | ||||||||
\(916\) | −1.62840 | −0.0538037 | ||||||||
\(917\) | −19.4521 | −0.642366 | ||||||||
\(918\) | −2.55364 | −0.0842825 | ||||||||
\(919\) | −46.8679 | −1.54603 | −0.773014 | − | 0.634389i | \(-0.781252\pi\) | ||||
−0.773014 | + | 0.634389i | \(0.781252\pi\) | |||||||
\(920\) | 0.583859 | 0.0192492 | ||||||||
\(921\) | −25.2691 | −0.832644 | ||||||||
\(922\) | −2.63313 | −0.0867175 | ||||||||
\(923\) | −6.78524 | −0.223339 | ||||||||
\(924\) | 14.1079 | 0.464115 | ||||||||
\(925\) | 1.78740 | 0.0587692 | ||||||||
\(926\) | 5.09241 | 0.167347 | ||||||||
\(927\) | −2.64022 | −0.0867163 | ||||||||
\(928\) | 32.1019 | 1.05380 | ||||||||
\(929\) | −0.543077 | −0.0178178 | −0.00890889 | − | 0.999960i | \(-0.502836\pi\) | ||||
−0.00890889 | + | 0.999960i | \(0.502836\pi\) | |||||||
\(930\) | 5.78875 | 0.189820 | ||||||||
\(931\) | −2.08034 | −0.0681803 | ||||||||
\(932\) | 22.8718 | 0.749192 | ||||||||
\(933\) | −31.2897 | −1.02438 | ||||||||
\(934\) | −13.6756 | −0.447479 | ||||||||
\(935\) | −8.76267 | −0.286570 | ||||||||
\(936\) | −30.7888 | −1.00636 | ||||||||
\(937\) | −40.3388 | −1.31781 | −0.658906 | − | 0.752225i | \(-0.728981\pi\) | ||||
−0.658906 | + | 0.752225i | \(0.728981\pi\) | |||||||
\(938\) | 8.35444 | 0.272782 | ||||||||
\(939\) | 45.6055 | 1.48828 | ||||||||
\(940\) | 5.76127 | 0.187912 | ||||||||
\(941\) | −25.9572 | −0.846179 | −0.423089 | − | 0.906088i | \(-0.639054\pi\) | ||||
−0.423089 | + | 0.906088i | \(0.639054\pi\) | |||||||
\(942\) | 6.60168 | 0.215094 | ||||||||
\(943\) | −3.12474 | −0.101756 | ||||||||
\(944\) | 12.1951 | 0.396918 | ||||||||
\(945\) | −1.81556 | −0.0590600 | ||||||||
\(946\) | 7.08571 | 0.230376 | ||||||||
\(947\) | −21.6527 | −0.703618 | −0.351809 | − | 0.936072i | \(-0.614433\pi\) | ||||
−0.351809 | + | 0.936072i | \(0.614433\pi\) | |||||||
\(948\) | 0.887019 | 0.0288090 | ||||||||
\(949\) | 85.6041 | 2.77883 | ||||||||
\(950\) | −1.26816 | −0.0411445 | ||||||||
\(951\) | 48.6052 | 1.57613 | ||||||||
\(952\) | 5.10345 | 0.165404 | ||||||||
\(953\) | −45.8460 | −1.48510 | −0.742549 | − | 0.669792i | \(-0.766383\pi\) | ||||
−0.742549 | + | 0.669792i | \(0.766383\pi\) | |||||||
\(954\) | −13.6719 | −0.442645 | ||||||||
\(955\) | 11.6654 | 0.377482 | ||||||||
\(956\) | −41.0456 | −1.32751 | ||||||||
\(957\) | 49.7792 | 1.60913 | ||||||||
\(958\) | 7.86415 | 0.254079 | ||||||||
\(959\) | −1.65064 | −0.0533018 | ||||||||
\(960\) | 0.937822 | 0.0302681 | ||||||||
\(961\) | −13.6723 | −0.441043 | ||||||||
\(962\) | 6.88111 | 0.221856 | ||||||||
\(963\) | 21.4412 | 0.690933 | ||||||||
\(964\) | −9.96555 | −0.320969 | ||||||||
\(965\) | 7.62481 | 0.245451 | ||||||||
\(966\) | −0.367086 | −0.0118108 | ||||||||
\(967\) | 46.0290 | 1.48019 | 0.740097 | − | 0.672500i | \(-0.234780\pi\) | ||||
0.740097 | + | 0.672500i | \(0.234780\pi\) | |||||||
\(968\) | −7.57099 | −0.243341 | ||||||||
\(969\) | −10.9501 | −0.351768 | ||||||||
\(970\) | −0.524024 | −0.0168254 | ||||||||
\(971\) | 16.3045 | 0.523237 | 0.261619 | − | 0.965171i | \(-0.415744\pi\) | ||||
0.261619 | + | 0.965171i | \(0.415744\pi\) | |||||||
\(972\) | 31.0802 | 0.996899 | ||||||||
\(973\) | −19.0852 | −0.611844 | ||||||||
\(974\) | −10.0997 | −0.323614 | ||||||||
\(975\) | 14.4070 | 0.461392 | ||||||||
\(976\) | 0.447560 | 0.0143260 | ||||||||
\(977\) | −19.3729 | −0.619796 | −0.309898 | − | 0.950770i | \(-0.600295\pi\) | ||||
−0.309898 | + | 0.950770i | \(0.600295\pi\) | |||||||
\(978\) | −4.20685 | −0.134520 | ||||||||
\(979\) | 61.8588 | 1.97701 | ||||||||
\(980\) | 1.62840 | 0.0520172 | ||||||||
\(981\) | 39.0936 | 1.24816 | ||||||||
\(982\) | 14.2929 | 0.456103 | ||||||||
\(983\) | 30.7155 | 0.979672 | 0.489836 | − | 0.871815i | \(-0.337057\pi\) | ||||
0.489836 | + | 0.871815i | \(0.337057\pi\) | |||||||
\(984\) | 59.7297 | 1.90411 | ||||||||
\(985\) | −1.98744 | −0.0633253 | ||||||||
\(986\) | 8.08157 | 0.257370 | ||||||||
\(987\) | −8.07110 | −0.256906 | ||||||||
\(988\) | 21.3940 | 0.680634 | ||||||||
\(989\) | 0.807923 | 0.0256905 | ||||||||
\(990\) | −5.10277 | −0.162177 | ||||||||
\(991\) | −15.5511 | −0.493997 | −0.246998 | − | 0.969016i | \(-0.579444\pi\) | ||||
−0.246998 | + | 0.969016i | \(0.579444\pi\) | |||||||
\(992\) | −23.2571 | −0.738413 | ||||||||
\(993\) | −1.79814 | −0.0570623 | ||||||||
\(994\) | 0.654948 | 0.0207737 | ||||||||
\(995\) | 20.2140 | 0.640826 | ||||||||
\(996\) | −2.46322 | −0.0780502 | ||||||||
\(997\) | 28.5147 | 0.903071 | 0.451535 | − | 0.892253i | \(-0.350876\pi\) | ||||
0.451535 | + | 0.892253i | \(0.350876\pi\) | |||||||
\(998\) | −7.94657 | −0.251544 | ||||||||
\(999\) | −3.24512 | −0.102671 |
(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 | 8015.2.a.l.1.37 | ✓ | 62 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8015.2.a.l.1.37 | ✓ | 62 | 1.1 | even | 1 | trivial |