Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2541,2,Mod(1,2541)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2541, 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("2541.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2541 = 3 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2541.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: | \(20.2899871536\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 19x^{8} - x^{7} + 124x^{6} + 6x^{5} - 316x^{4} + 17x^{3} + 253x^{2} - 70x - 11 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 231) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(-2.65195\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2541.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.65195 | 1.87521 | 0.937607 | − | 0.347696i | \(-0.113036\pi\) | ||||
0.937607 | + | 0.347696i | \(0.113036\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 5.03286 | 2.51643 | ||||||||
\(5\) | 1.71311 | 0.766125 | 0.383063 | − | 0.923722i | \(-0.374869\pi\) | ||||
0.383063 | + | 0.923722i | \(0.374869\pi\) | |||||||
\(6\) | 2.65195 | 1.08266 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 8.04301 | 2.84363 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 4.54308 | 1.43665 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 5.03286 | 1.45286 | ||||||||
\(13\) | −1.51161 | −0.419246 | −0.209623 | − | 0.977782i | \(-0.567224\pi\) | ||||
−0.209623 | + | 0.977782i | \(0.567224\pi\) | |||||||
\(14\) | 2.65195 | 0.708765 | ||||||||
\(15\) | 1.71311 | 0.442323 | ||||||||
\(16\) | 11.2640 | 2.81599 | ||||||||
\(17\) | 2.39386 | 0.580597 | 0.290298 | − | 0.956936i | \(-0.406245\pi\) | ||||
0.290298 | + | 0.956936i | \(0.406245\pi\) | |||||||
\(18\) | 2.65195 | 0.625072 | ||||||||
\(19\) | −6.33123 | −1.45248 | −0.726242 | − | 0.687439i | \(-0.758735\pi\) | ||||
−0.726242 | + | 0.687439i | \(0.758735\pi\) | |||||||
\(20\) | 8.62183 | 1.92790 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.05885 | −1.05484 | −0.527422 | − | 0.849604i | \(-0.676841\pi\) | ||||
−0.527422 | + | 0.849604i | \(0.676841\pi\) | |||||||
\(24\) | 8.04301 | 1.64177 | ||||||||
\(25\) | −2.06526 | −0.413052 | ||||||||
\(26\) | −4.00873 | −0.786177 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 5.03286 | 0.951121 | ||||||||
\(29\) | −8.34554 | −1.54973 | −0.774864 | − | 0.632128i | \(-0.782182\pi\) | ||||
−0.774864 | + | 0.632128i | \(0.782182\pi\) | |||||||
\(30\) | 4.54308 | 0.829450 | ||||||||
\(31\) | 6.03882 | 1.08460 | 0.542302 | − | 0.840184i | \(-0.317553\pi\) | ||||
0.542302 | + | 0.840184i | \(0.317553\pi\) | |||||||
\(32\) | 13.7855 | 2.43696 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.34841 | 1.08874 | ||||||||
\(35\) | 1.71311 | 0.289568 | ||||||||
\(36\) | 5.03286 | 0.838810 | ||||||||
\(37\) | −7.47381 | −1.22869 | −0.614343 | − | 0.789039i | \(-0.710579\pi\) | ||||
−0.614343 | + | 0.789039i | \(0.710579\pi\) | |||||||
\(38\) | −16.7901 | −2.72372 | ||||||||
\(39\) | −1.51161 | −0.242052 | ||||||||
\(40\) | 13.7785 | 2.17858 | ||||||||
\(41\) | 5.03457 | 0.786269 | 0.393134 | − | 0.919481i | \(-0.371391\pi\) | ||||
0.393134 | + | 0.919481i | \(0.371391\pi\) | |||||||
\(42\) | 2.65195 | 0.409205 | ||||||||
\(43\) | −2.02506 | −0.308818 | −0.154409 | − | 0.988007i | \(-0.549347\pi\) | ||||
−0.154409 | + | 0.988007i | \(0.549347\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.71311 | 0.255375 | ||||||||
\(46\) | −13.4158 | −1.97806 | ||||||||
\(47\) | −5.53026 | −0.806672 | −0.403336 | − | 0.915052i | \(-0.632149\pi\) | ||||
−0.403336 | + | 0.915052i | \(0.632149\pi\) | |||||||
\(48\) | 11.2640 | 1.62581 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −5.47698 | −0.774562 | ||||||||
\(51\) | 2.39386 | 0.335208 | ||||||||
\(52\) | −7.60775 | −1.05500 | ||||||||
\(53\) | 6.23728 | 0.856757 | 0.428378 | − | 0.903599i | \(-0.359085\pi\) | ||||
0.428378 | + | 0.903599i | \(0.359085\pi\) | |||||||
\(54\) | 2.65195 | 0.360885 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 8.04301 | 1.07479 | ||||||||
\(57\) | −6.33123 | −0.838592 | ||||||||
\(58\) | −22.1320 | −2.90607 | ||||||||
\(59\) | 11.1742 | 1.45476 | 0.727381 | − | 0.686234i | \(-0.240737\pi\) | ||||
0.727381 | + | 0.686234i | \(0.240737\pi\) | |||||||
\(60\) | 8.62183 | 1.11307 | ||||||||
\(61\) | −13.8096 | −1.76814 | −0.884072 | − | 0.467351i | \(-0.845209\pi\) | ||||
−0.884072 | + | 0.467351i | \(0.845209\pi\) | |||||||
\(62\) | 16.0147 | 2.03387 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 14.0306 | 1.75382 | ||||||||
\(65\) | −2.58956 | −0.321195 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.6173 | 1.66362 | 0.831811 | − | 0.555059i | \(-0.187304\pi\) | ||||
0.831811 | + | 0.555059i | \(0.187304\pi\) | |||||||
\(68\) | 12.0480 | 1.46103 | ||||||||
\(69\) | −5.05885 | −0.609014 | ||||||||
\(70\) | 4.54308 | 0.543002 | ||||||||
\(71\) | −14.3329 | −1.70100 | −0.850501 | − | 0.525974i | \(-0.823701\pi\) | ||||
−0.850501 | + | 0.525974i | \(0.823701\pi\) | |||||||
\(72\) | 8.04301 | 0.947877 | ||||||||
\(73\) | 1.43030 | 0.167404 | 0.0837022 | − | 0.996491i | \(-0.473326\pi\) | ||||
0.0837022 | + | 0.996491i | \(0.473326\pi\) | |||||||
\(74\) | −19.8202 | −2.30405 | ||||||||
\(75\) | −2.06526 | −0.238476 | ||||||||
\(76\) | −31.8642 | −3.65508 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −4.00873 | −0.453900 | ||||||||
\(79\) | −6.71734 | −0.755760 | −0.377880 | − | 0.925855i | \(-0.623347\pi\) | ||||
−0.377880 | + | 0.925855i | \(0.623347\pi\) | |||||||
\(80\) | 19.2964 | 2.15740 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 13.3515 | 1.47442 | ||||||||
\(83\) | −5.86977 | −0.644291 | −0.322145 | − | 0.946690i | \(-0.604404\pi\) | ||||
−0.322145 | + | 0.946690i | \(0.604404\pi\) | |||||||
\(84\) | 5.03286 | 0.549130 | ||||||||
\(85\) | 4.10094 | 0.444810 | ||||||||
\(86\) | −5.37036 | −0.579101 | ||||||||
\(87\) | −8.34554 | −0.894736 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 16.4241 | 1.74095 | 0.870473 | − | 0.492215i | \(-0.163813\pi\) | ||||
0.870473 | + | 0.492215i | \(0.163813\pi\) | |||||||
\(90\) | 4.54308 | 0.478883 | ||||||||
\(91\) | −1.51161 | −0.158460 | ||||||||
\(92\) | −25.4605 | −2.65444 | ||||||||
\(93\) | 6.03882 | 0.626197 | ||||||||
\(94\) | −14.6660 | −1.51268 | ||||||||
\(95\) | −10.8461 | −1.11279 | ||||||||
\(96\) | 13.7855 | 1.40698 | ||||||||
\(97\) | 12.0516 | 1.22365 | 0.611827 | − | 0.790992i | \(-0.290435\pi\) | ||||
0.611827 | + | 0.790992i | \(0.290435\pi\) | |||||||
\(98\) | 2.65195 | 0.267888 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −10.3942 | −1.03942 | ||||||||
\(101\) | 5.34845 | 0.532190 | 0.266095 | − | 0.963947i | \(-0.414266\pi\) | ||||
0.266095 | + | 0.963947i | \(0.414266\pi\) | |||||||
\(102\) | 6.34841 | 0.628587 | ||||||||
\(103\) | 9.37773 | 0.924015 | 0.462008 | − | 0.886876i | \(-0.347129\pi\) | ||||
0.462008 | + | 0.886876i | \(0.347129\pi\) | |||||||
\(104\) | −12.1579 | −1.19218 | ||||||||
\(105\) | 1.71311 | 0.167182 | ||||||||
\(106\) | 16.5410 | 1.60660 | ||||||||
\(107\) | 12.1711 | 1.17662 | 0.588311 | − | 0.808635i | \(-0.299793\pi\) | ||||
0.588311 | + | 0.808635i | \(0.299793\pi\) | |||||||
\(108\) | 5.03286 | 0.484287 | ||||||||
\(109\) | 6.31429 | 0.604799 | 0.302399 | − | 0.953181i | \(-0.402212\pi\) | ||||
0.302399 | + | 0.953181i | \(0.402212\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.47381 | −0.709383 | ||||||||
\(112\) | 11.2640 | 1.06434 | ||||||||
\(113\) | 3.36767 | 0.316804 | 0.158402 | − | 0.987375i | \(-0.449366\pi\) | ||||
0.158402 | + | 0.987375i | \(0.449366\pi\) | |||||||
\(114\) | −16.7901 | −1.57254 | ||||||||
\(115\) | −8.66636 | −0.808142 | ||||||||
\(116\) | −42.0020 | −3.89978 | ||||||||
\(117\) | −1.51161 | −0.139749 | ||||||||
\(118\) | 29.6336 | 2.72799 | ||||||||
\(119\) | 2.39386 | 0.219445 | ||||||||
\(120\) | 13.7785 | 1.25780 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −36.6225 | −3.31565 | ||||||||
\(123\) | 5.03457 | 0.453952 | ||||||||
\(124\) | 30.3925 | 2.72933 | ||||||||
\(125\) | −12.1036 | −1.08257 | ||||||||
\(126\) | 2.65195 | 0.236255 | ||||||||
\(127\) | 1.11374 | 0.0988282 | 0.0494141 | − | 0.998778i | \(-0.484265\pi\) | ||||
0.0494141 | + | 0.998778i | \(0.484265\pi\) | |||||||
\(128\) | 9.63748 | 0.851841 | ||||||||
\(129\) | −2.02506 | −0.178296 | ||||||||
\(130\) | −6.86739 | −0.602310 | ||||||||
\(131\) | 14.3843 | 1.25676 | 0.628379 | − | 0.777907i | \(-0.283719\pi\) | ||||
0.628379 | + | 0.777907i | \(0.283719\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.33123 | −0.548988 | ||||||||
\(134\) | 36.1125 | 3.11965 | ||||||||
\(135\) | 1.71311 | 0.147441 | ||||||||
\(136\) | 19.2539 | 1.65100 | ||||||||
\(137\) | 2.72791 | 0.233061 | 0.116530 | − | 0.993187i | \(-0.462823\pi\) | ||||
0.116530 | + | 0.993187i | \(0.462823\pi\) | |||||||
\(138\) | −13.4158 | −1.14203 | ||||||||
\(139\) | −0.353144 | −0.0299533 | −0.0149766 | − | 0.999888i | \(-0.504767\pi\) | ||||
−0.0149766 | + | 0.999888i | \(0.504767\pi\) | |||||||
\(140\) | 8.62183 | 0.728678 | ||||||||
\(141\) | −5.53026 | −0.465732 | ||||||||
\(142\) | −38.0102 | −3.18974 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 11.2640 | 0.938664 | ||||||||
\(145\) | −14.2968 | −1.18729 | ||||||||
\(146\) | 3.79310 | 0.313919 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | −37.6146 | −3.09190 | ||||||||
\(149\) | 0.511399 | 0.0418954 | 0.0209477 | − | 0.999781i | \(-0.493332\pi\) | ||||
0.0209477 | + | 0.999781i | \(0.493332\pi\) | |||||||
\(150\) | −5.47698 | −0.447194 | ||||||||
\(151\) | −0.977763 | −0.0795693 | −0.0397846 | − | 0.999208i | \(-0.512667\pi\) | ||||
−0.0397846 | + | 0.999208i | \(0.512667\pi\) | |||||||
\(152\) | −50.9222 | −4.13033 | ||||||||
\(153\) | 2.39386 | 0.193532 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.3452 | 0.830942 | ||||||||
\(156\) | −7.60775 | −0.609107 | ||||||||
\(157\) | −3.28963 | −0.262541 | −0.131270 | − | 0.991347i | \(-0.541906\pi\) | ||||
−0.131270 | + | 0.991347i | \(0.541906\pi\) | |||||||
\(158\) | −17.8141 | −1.41721 | ||||||||
\(159\) | 6.23728 | 0.494649 | ||||||||
\(160\) | 23.6160 | 1.86701 | ||||||||
\(161\) | −5.05885 | −0.398693 | ||||||||
\(162\) | 2.65195 | 0.208357 | ||||||||
\(163\) | 3.48225 | 0.272751 | 0.136375 | − | 0.990657i | \(-0.456455\pi\) | ||||
0.136375 | + | 0.990657i | \(0.456455\pi\) | |||||||
\(164\) | 25.3383 | 1.97859 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −15.5664 | −1.20818 | ||||||||
\(167\) | 4.57477 | 0.354006 | 0.177003 | − | 0.984210i | \(-0.443360\pi\) | ||||
0.177003 | + | 0.984210i | \(0.443360\pi\) | |||||||
\(168\) | 8.04301 | 0.620531 | ||||||||
\(169\) | −10.7150 | −0.824232 | ||||||||
\(170\) | 10.8755 | 0.834114 | ||||||||
\(171\) | −6.33123 | −0.484162 | ||||||||
\(172\) | −10.1918 | −0.777120 | ||||||||
\(173\) | −5.72474 | −0.435244 | −0.217622 | − | 0.976033i | \(-0.569830\pi\) | ||||
−0.217622 | + | 0.976033i | \(0.569830\pi\) | |||||||
\(174\) | −22.1320 | −1.67782 | ||||||||
\(175\) | −2.06526 | −0.156119 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 11.1742 | 0.839907 | ||||||||
\(178\) | 43.5559 | 3.26465 | ||||||||
\(179\) | 2.95701 | 0.221017 | 0.110509 | − | 0.993875i | \(-0.464752\pi\) | ||||
0.110509 | + | 0.993875i | \(0.464752\pi\) | |||||||
\(180\) | 8.62183 | 0.642633 | ||||||||
\(181\) | −9.40004 | −0.698699 | −0.349350 | − | 0.936992i | \(-0.613597\pi\) | ||||
−0.349350 | + | 0.936992i | \(0.613597\pi\) | |||||||
\(182\) | −4.00873 | −0.297147 | ||||||||
\(183\) | −13.8096 | −1.02084 | ||||||||
\(184\) | −40.6884 | −2.99959 | ||||||||
\(185\) | −12.8034 | −0.941328 | ||||||||
\(186\) | 16.0147 | 1.17425 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −27.8330 | −2.02993 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | −28.7633 | −2.08671 | ||||||||
\(191\) | −9.20911 | −0.666348 | −0.333174 | − | 0.942865i | \(-0.608120\pi\) | ||||
−0.333174 | + | 0.942865i | \(0.608120\pi\) | |||||||
\(192\) | 14.0306 | 1.01257 | ||||||||
\(193\) | 1.49221 | 0.107412 | 0.0537059 | − | 0.998557i | \(-0.482897\pi\) | ||||
0.0537059 | + | 0.998557i | \(0.482897\pi\) | |||||||
\(194\) | 31.9603 | 2.29461 | ||||||||
\(195\) | −2.58956 | −0.185442 | ||||||||
\(196\) | 5.03286 | 0.359490 | ||||||||
\(197\) | −3.37718 | −0.240614 | −0.120307 | − | 0.992737i | \(-0.538388\pi\) | ||||
−0.120307 | + | 0.992737i | \(0.538388\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 27.8114 | 1.97150 | 0.985750 | − | 0.168215i | \(-0.0538002\pi\) | ||||
0.985750 | + | 0.168215i | \(0.0538002\pi\) | |||||||
\(200\) | −16.6109 | −1.17457 | ||||||||
\(201\) | 13.6173 | 0.960493 | ||||||||
\(202\) | 14.1838 | 0.997971 | ||||||||
\(203\) | −8.34554 | −0.585742 | ||||||||
\(204\) | 12.0480 | 0.843527 | ||||||||
\(205\) | 8.62477 | 0.602380 | ||||||||
\(206\) | 24.8693 | 1.73273 | ||||||||
\(207\) | −5.05885 | −0.351614 | ||||||||
\(208\) | −17.0268 | −1.18059 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 4.54308 | 0.313503 | ||||||||
\(211\) | 24.0068 | 1.65270 | 0.826350 | − | 0.563157i | \(-0.190413\pi\) | ||||
0.826350 | + | 0.563157i | \(0.190413\pi\) | |||||||
\(212\) | 31.3914 | 2.15597 | ||||||||
\(213\) | −14.3329 | −0.982073 | ||||||||
\(214\) | 32.2771 | 2.20642 | ||||||||
\(215\) | −3.46914 | −0.236593 | ||||||||
\(216\) | 8.04301 | 0.547257 | ||||||||
\(217\) | 6.03882 | 0.409942 | ||||||||
\(218\) | 16.7452 | 1.13413 | ||||||||
\(219\) | 1.43030 | 0.0966510 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.61860 | −0.243413 | ||||||||
\(222\) | −19.8202 | −1.33024 | ||||||||
\(223\) | 22.8178 | 1.52799 | 0.763997 | − | 0.645220i | \(-0.223234\pi\) | ||||
0.763997 | + | 0.645220i | \(0.223234\pi\) | |||||||
\(224\) | 13.7855 | 0.921083 | ||||||||
\(225\) | −2.06526 | −0.137684 | ||||||||
\(226\) | 8.93091 | 0.594075 | ||||||||
\(227\) | −14.4047 | −0.956071 | −0.478035 | − | 0.878341i | \(-0.658651\pi\) | ||||
−0.478035 | + | 0.878341i | \(0.658651\pi\) | |||||||
\(228\) | −31.8642 | −2.11026 | ||||||||
\(229\) | −3.79367 | −0.250693 | −0.125346 | − | 0.992113i | \(-0.540004\pi\) | ||||
−0.125346 | + | 0.992113i | \(0.540004\pi\) | |||||||
\(230\) | −22.9828 | −1.51544 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −67.1233 | −4.40686 | ||||||||
\(233\) | −27.4844 | −1.80056 | −0.900282 | − | 0.435307i | \(-0.856640\pi\) | ||||
−0.900282 | + | 0.435307i | \(0.856640\pi\) | |||||||
\(234\) | −4.00873 | −0.262059 | ||||||||
\(235\) | −9.47394 | −0.618011 | ||||||||
\(236\) | 56.2384 | 3.66081 | ||||||||
\(237\) | −6.71734 | −0.436338 | ||||||||
\(238\) | 6.34841 | 0.411507 | ||||||||
\(239\) | −11.2335 | −0.726636 | −0.363318 | − | 0.931665i | \(-0.618356\pi\) | ||||
−0.363318 | + | 0.931665i | \(0.618356\pi\) | |||||||
\(240\) | 19.2964 | 1.24558 | ||||||||
\(241\) | −14.7496 | −0.950105 | −0.475052 | − | 0.879958i | \(-0.657571\pi\) | ||||
−0.475052 | + | 0.879958i | \(0.657571\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −69.5020 | −4.44941 | ||||||||
\(245\) | 1.71311 | 0.109446 | ||||||||
\(246\) | 13.3515 | 0.851258 | ||||||||
\(247\) | 9.57039 | 0.608949 | ||||||||
\(248\) | 48.5703 | 3.08422 | ||||||||
\(249\) | −5.86977 | −0.371981 | ||||||||
\(250\) | −32.0981 | −2.03006 | ||||||||
\(251\) | 7.61933 | 0.480928 | 0.240464 | − | 0.970658i | \(-0.422700\pi\) | ||||
0.240464 | + | 0.970658i | \(0.422700\pi\) | |||||||
\(252\) | 5.03286 | 0.317040 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 2.95358 | 0.185324 | ||||||||
\(255\) | 4.10094 | 0.256811 | ||||||||
\(256\) | −2.50303 | −0.156440 | ||||||||
\(257\) | −0.289382 | −0.0180512 | −0.00902559 | − | 0.999959i | \(-0.502873\pi\) | ||||
−0.00902559 | + | 0.999959i | \(0.502873\pi\) | |||||||
\(258\) | −5.37036 | −0.334344 | ||||||||
\(259\) | −7.47381 | −0.464400 | ||||||||
\(260\) | −13.0329 | −0.808265 | ||||||||
\(261\) | −8.34554 | −0.516576 | ||||||||
\(262\) | 38.1464 | 2.35669 | ||||||||
\(263\) | −12.3251 | −0.759998 | −0.379999 | − | 0.924987i | \(-0.624076\pi\) | ||||
−0.379999 | + | 0.924987i | \(0.624076\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.6851 | 0.656383 | ||||||||
\(266\) | −16.7901 | −1.02947 | ||||||||
\(267\) | 16.4241 | 1.00514 | ||||||||
\(268\) | 68.5341 | 4.18639 | ||||||||
\(269\) | 12.6511 | 0.771349 | 0.385674 | − | 0.922635i | \(-0.373969\pi\) | ||||
0.385674 | + | 0.922635i | \(0.373969\pi\) | |||||||
\(270\) | 4.54308 | 0.276483 | ||||||||
\(271\) | −10.7502 | −0.653029 | −0.326515 | − | 0.945192i | \(-0.605874\pi\) | ||||
−0.326515 | + | 0.945192i | \(0.605874\pi\) | |||||||
\(272\) | 26.9644 | 1.63496 | ||||||||
\(273\) | −1.51161 | −0.0914871 | ||||||||
\(274\) | 7.23428 | 0.437039 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −25.4605 | −1.53254 | ||||||||
\(277\) | 6.08896 | 0.365850 | 0.182925 | − | 0.983127i | \(-0.441443\pi\) | ||||
0.182925 | + | 0.983127i | \(0.441443\pi\) | |||||||
\(278\) | −0.936521 | −0.0561688 | ||||||||
\(279\) | 6.03882 | 0.361535 | ||||||||
\(280\) | 13.7785 | 0.823425 | ||||||||
\(281\) | 8.61127 | 0.513705 | 0.256853 | − | 0.966451i | \(-0.417314\pi\) | ||||
0.256853 | + | 0.966451i | \(0.417314\pi\) | |||||||
\(282\) | −14.6660 | −0.873348 | ||||||||
\(283\) | −3.19557 | −0.189957 | −0.0949785 | − | 0.995479i | \(-0.530278\pi\) | ||||
−0.0949785 | + | 0.995479i | \(0.530278\pi\) | |||||||
\(284\) | −72.1354 | −4.28045 | ||||||||
\(285\) | −10.8461 | −0.642467 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.03457 | 0.297182 | ||||||||
\(288\) | 13.7855 | 0.812318 | ||||||||
\(289\) | −11.2694 | −0.662907 | ||||||||
\(290\) | −37.9145 | −2.22642 | ||||||||
\(291\) | 12.0516 | 0.706477 | ||||||||
\(292\) | 7.19852 | 0.421262 | ||||||||
\(293\) | 8.55173 | 0.499597 | 0.249799 | − | 0.968298i | \(-0.419636\pi\) | ||||
0.249799 | + | 0.968298i | \(0.419636\pi\) | |||||||
\(294\) | 2.65195 | 0.154665 | ||||||||
\(295\) | 19.1427 | 1.11453 | ||||||||
\(296\) | −60.1119 | −3.49393 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.35621 | 0.0785629 | ||||||||
\(299\) | 7.64703 | 0.442239 | ||||||||
\(300\) | −10.3942 | −0.600108 | ||||||||
\(301\) | −2.02506 | −0.116722 | ||||||||
\(302\) | −2.59298 | −0.149209 | ||||||||
\(303\) | 5.34845 | 0.307260 | ||||||||
\(304\) | −71.3148 | −4.09018 | ||||||||
\(305\) | −23.6574 | −1.35462 | ||||||||
\(306\) | 6.34841 | 0.362915 | ||||||||
\(307\) | 3.49789 | 0.199635 | 0.0998176 | − | 0.995006i | \(-0.468174\pi\) | ||||
0.0998176 | + | 0.995006i | \(0.468174\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.37773 | 0.533480 | ||||||||
\(310\) | 27.4349 | 1.55820 | ||||||||
\(311\) | −3.69038 | −0.209262 | −0.104631 | − | 0.994511i | \(-0.533366\pi\) | ||||
−0.104631 | + | 0.994511i | \(0.533366\pi\) | |||||||
\(312\) | −12.1579 | −0.688307 | ||||||||
\(313\) | −26.2642 | −1.48454 | −0.742270 | − | 0.670101i | \(-0.766251\pi\) | ||||
−0.742270 | + | 0.670101i | \(0.766251\pi\) | |||||||
\(314\) | −8.72394 | −0.492320 | ||||||||
\(315\) | 1.71311 | 0.0965227 | ||||||||
\(316\) | −33.8074 | −1.90182 | ||||||||
\(317\) | 13.0802 | 0.734657 | 0.367328 | − | 0.930091i | \(-0.380273\pi\) | ||||
0.367328 | + | 0.930091i | \(0.380273\pi\) | |||||||
\(318\) | 16.5410 | 0.927572 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 24.0359 | 1.34365 | ||||||||
\(321\) | 12.1711 | 0.679323 | ||||||||
\(322\) | −13.4158 | −0.747636 | ||||||||
\(323\) | −15.1561 | −0.843308 | ||||||||
\(324\) | 5.03286 | 0.279603 | ||||||||
\(325\) | 3.12188 | 0.173171 | ||||||||
\(326\) | 9.23477 | 0.511466 | ||||||||
\(327\) | 6.31429 | 0.349181 | ||||||||
\(328\) | 40.4931 | 2.23586 | ||||||||
\(329\) | −5.53026 | −0.304893 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.93676 | 0.436244 | 0.218122 | − | 0.975922i | \(-0.430007\pi\) | ||||
0.218122 | + | 0.975922i | \(0.430007\pi\) | |||||||
\(332\) | −29.5417 | −1.62131 | ||||||||
\(333\) | −7.47381 | −0.409562 | ||||||||
\(334\) | 12.1321 | 0.663838 | ||||||||
\(335\) | 23.3280 | 1.27454 | ||||||||
\(336\) | 11.2640 | 0.614500 | ||||||||
\(337\) | −10.0006 | −0.544765 | −0.272382 | − | 0.962189i | \(-0.587812\pi\) | ||||
−0.272382 | + | 0.962189i | \(0.587812\pi\) | |||||||
\(338\) | −28.4157 | −1.54561 | ||||||||
\(339\) | 3.36767 | 0.182907 | ||||||||
\(340\) | 20.6395 | 1.11933 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −16.7901 | −0.907907 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −16.2876 | −0.878166 | ||||||||
\(345\) | −8.66636 | −0.466581 | ||||||||
\(346\) | −15.1818 | −0.816176 | ||||||||
\(347\) | 5.40853 | 0.290345 | 0.145173 | − | 0.989406i | \(-0.453626\pi\) | ||||
0.145173 | + | 0.989406i | \(0.453626\pi\) | |||||||
\(348\) | −42.0020 | −2.25154 | ||||||||
\(349\) | 28.5311 | 1.52723 | 0.763617 | − | 0.645670i | \(-0.223422\pi\) | ||||
0.763617 | + | 0.645670i | \(0.223422\pi\) | |||||||
\(350\) | −5.47698 | −0.292757 | ||||||||
\(351\) | −1.51161 | −0.0806840 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −19.2226 | −1.02312 | −0.511559 | − | 0.859248i | \(-0.670932\pi\) | ||||
−0.511559 | + | 0.859248i | \(0.670932\pi\) | |||||||
\(354\) | 29.6336 | 1.57501 | ||||||||
\(355\) | −24.5538 | −1.30318 | ||||||||
\(356\) | 82.6600 | 4.38097 | ||||||||
\(357\) | 2.39386 | 0.126697 | ||||||||
\(358\) | 7.84185 | 0.414455 | ||||||||
\(359\) | −22.3528 | −1.17974 | −0.589868 | − | 0.807500i | \(-0.700820\pi\) | ||||
−0.589868 | + | 0.807500i | \(0.700820\pi\) | |||||||
\(360\) | 13.7785 | 0.726193 | ||||||||
\(361\) | 21.0845 | 1.10971 | ||||||||
\(362\) | −24.9285 | −1.31021 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −7.60775 | −0.398754 | ||||||||
\(365\) | 2.45027 | 0.128253 | ||||||||
\(366\) | −36.6225 | −1.91429 | ||||||||
\(367\) | −23.4448 | −1.22381 | −0.611905 | − | 0.790931i | \(-0.709597\pi\) | ||||
−0.611905 | + | 0.790931i | \(0.709597\pi\) | |||||||
\(368\) | −56.9827 | −2.97043 | ||||||||
\(369\) | 5.03457 | 0.262090 | ||||||||
\(370\) | −33.9541 | −1.76519 | ||||||||
\(371\) | 6.23728 | 0.323824 | ||||||||
\(372\) | 30.3925 | 1.57578 | ||||||||
\(373\) | 33.4536 | 1.73216 | 0.866082 | − | 0.499903i | \(-0.166631\pi\) | ||||
0.866082 | + | 0.499903i | \(0.166631\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −12.1036 | −0.625025 | ||||||||
\(376\) | −44.4799 | −2.29388 | ||||||||
\(377\) | 12.6152 | 0.649718 | ||||||||
\(378\) | 2.65195 | 0.136402 | ||||||||
\(379\) | −18.3796 | −0.944094 | −0.472047 | − | 0.881573i | \(-0.656485\pi\) | ||||
−0.472047 | + | 0.881573i | \(0.656485\pi\) | |||||||
\(380\) | −54.5868 | −2.80025 | ||||||||
\(381\) | 1.11374 | 0.0570585 | ||||||||
\(382\) | −24.4221 | −1.24954 | ||||||||
\(383\) | 21.3403 | 1.09044 | 0.545220 | − | 0.838293i | \(-0.316446\pi\) | ||||
0.545220 | + | 0.838293i | \(0.316446\pi\) | |||||||
\(384\) | 9.63748 | 0.491810 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.95728 | 0.201420 | ||||||||
\(387\) | −2.02506 | −0.102939 | ||||||||
\(388\) | 60.6540 | 3.07924 | ||||||||
\(389\) | 15.5214 | 0.786969 | 0.393484 | − | 0.919331i | \(-0.371270\pi\) | ||||
0.393484 | + | 0.919331i | \(0.371270\pi\) | |||||||
\(390\) | −6.86739 | −0.347744 | ||||||||
\(391\) | −12.1102 | −0.612439 | ||||||||
\(392\) | 8.04301 | 0.406233 | ||||||||
\(393\) | 14.3843 | 0.725590 | ||||||||
\(394\) | −8.95614 | −0.451204 | ||||||||
\(395\) | −11.5075 | −0.579007 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.4777 | 1.07794 | 0.538968 | − | 0.842326i | \(-0.318815\pi\) | ||||
0.538968 | + | 0.842326i | \(0.318815\pi\) | |||||||
\(398\) | 73.7547 | 3.69699 | ||||||||
\(399\) | −6.33123 | −0.316958 | ||||||||
\(400\) | −23.2630 | −1.16315 | ||||||||
\(401\) | 8.88106 | 0.443499 | 0.221749 | − | 0.975104i | \(-0.428823\pi\) | ||||
0.221749 | + | 0.975104i | \(0.428823\pi\) | |||||||
\(402\) | 36.1125 | 1.80113 | ||||||||
\(403\) | −9.12837 | −0.454717 | ||||||||
\(404\) | 26.9180 | 1.33922 | ||||||||
\(405\) | 1.71311 | 0.0851250 | ||||||||
\(406\) | −22.1320 | −1.09839 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 19.2539 | 0.953208 | ||||||||
\(409\) | −5.45776 | −0.269869 | −0.134934 | − | 0.990855i | \(-0.543082\pi\) | ||||
−0.134934 | + | 0.990855i | \(0.543082\pi\) | |||||||
\(410\) | 22.8725 | 1.12959 | ||||||||
\(411\) | 2.72791 | 0.134558 | ||||||||
\(412\) | 47.1968 | 2.32522 | ||||||||
\(413\) | 11.1742 | 0.549848 | ||||||||
\(414\) | −13.4158 | −0.659353 | ||||||||
\(415\) | −10.0555 | −0.493607 | ||||||||
\(416\) | −20.8384 | −1.02169 | ||||||||
\(417\) | −0.353144 | −0.0172935 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 19.9805 | 0.976114 | 0.488057 | − | 0.872812i | \(-0.337706\pi\) | ||||
0.488057 | + | 0.872812i | \(0.337706\pi\) | |||||||
\(420\) | 8.62183 | 0.420702 | ||||||||
\(421\) | −28.3122 | −1.37985 | −0.689926 | − | 0.723880i | \(-0.742357\pi\) | ||||
−0.689926 | + | 0.723880i | \(0.742357\pi\) | |||||||
\(422\) | 63.6651 | 3.09917 | ||||||||
\(423\) | −5.53026 | −0.268891 | ||||||||
\(424\) | 50.1665 | 2.43630 | ||||||||
\(425\) | −4.94395 | −0.239817 | ||||||||
\(426\) | −38.0102 | −1.84160 | ||||||||
\(427\) | −13.8096 | −0.668296 | ||||||||
\(428\) | 61.2553 | 2.96089 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −9.20000 | −0.443664 | ||||||||
\(431\) | −31.7647 | −1.53005 | −0.765026 | − | 0.643999i | \(-0.777274\pi\) | ||||
−0.765026 | + | 0.643999i | \(0.777274\pi\) | |||||||
\(432\) | 11.2640 | 0.541938 | ||||||||
\(433\) | −13.1661 | −0.632725 | −0.316362 | − | 0.948638i | \(-0.602462\pi\) | ||||
−0.316362 | + | 0.948638i | \(0.602462\pi\) | |||||||
\(434\) | 16.0147 | 0.768729 | ||||||||
\(435\) | −14.2968 | −0.685480 | ||||||||
\(436\) | 31.7789 | 1.52193 | ||||||||
\(437\) | 32.0288 | 1.53214 | ||||||||
\(438\) | 3.79310 | 0.181241 | ||||||||
\(439\) | 9.81161 | 0.468283 | 0.234141 | − | 0.972203i | \(-0.424772\pi\) | ||||
0.234141 | + | 0.972203i | \(0.424772\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −9.59636 | −0.456452 | ||||||||
\(443\) | 2.48514 | 0.118072 | 0.0590362 | − | 0.998256i | \(-0.481197\pi\) | ||||
0.0590362 | + | 0.998256i | \(0.481197\pi\) | |||||||
\(444\) | −37.6146 | −1.78511 | ||||||||
\(445\) | 28.1362 | 1.33378 | ||||||||
\(446\) | 60.5118 | 2.86532 | ||||||||
\(447\) | 0.511399 | 0.0241883 | ||||||||
\(448\) | 14.0306 | 0.662883 | ||||||||
\(449\) | −15.6097 | −0.736667 | −0.368334 | − | 0.929694i | \(-0.620072\pi\) | ||||
−0.368334 | + | 0.929694i | \(0.620072\pi\) | |||||||
\(450\) | −5.47698 | −0.258187 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 16.9490 | 0.797215 | ||||||||
\(453\) | −0.977763 | −0.0459393 | ||||||||
\(454\) | −38.2005 | −1.79284 | ||||||||
\(455\) | −2.58956 | −0.121400 | ||||||||
\(456\) | −50.9222 | −2.38465 | ||||||||
\(457\) | −13.6652 | −0.639233 | −0.319616 | − | 0.947547i | \(-0.603554\pi\) | ||||
−0.319616 | + | 0.947547i | \(0.603554\pi\) | |||||||
\(458\) | −10.0606 | −0.470103 | ||||||||
\(459\) | 2.39386 | 0.111736 | ||||||||
\(460\) | −43.6166 | −2.03363 | ||||||||
\(461\) | −18.6545 | −0.868825 | −0.434412 | − | 0.900714i | \(-0.643044\pi\) | ||||
−0.434412 | + | 0.900714i | \(0.643044\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18.5697 | −0.863006 | −0.431503 | − | 0.902111i | \(-0.642017\pi\) | ||||
−0.431503 | + | 0.902111i | \(0.642017\pi\) | |||||||
\(464\) | −94.0039 | −4.36402 | ||||||||
\(465\) | 10.3452 | 0.479745 | ||||||||
\(466\) | −72.8874 | −3.37644 | ||||||||
\(467\) | 34.9579 | 1.61766 | 0.808828 | − | 0.588045i | \(-0.200102\pi\) | ||||
0.808828 | + | 0.588045i | \(0.200102\pi\) | |||||||
\(468\) | −7.60775 | −0.351668 | ||||||||
\(469\) | 13.6173 | 0.628790 | ||||||||
\(470\) | −25.1244 | −1.15890 | ||||||||
\(471\) | −3.28963 | −0.151578 | ||||||||
\(472\) | 89.8745 | 4.13681 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −17.8141 | −0.818228 | ||||||||
\(475\) | 13.0757 | 0.599952 | ||||||||
\(476\) | 12.0480 | 0.552218 | ||||||||
\(477\) | 6.23728 | 0.285586 | ||||||||
\(478\) | −29.7908 | −1.36260 | ||||||||
\(479\) | −40.5443 | −1.85252 | −0.926259 | − | 0.376888i | \(-0.876994\pi\) | ||||
−0.926259 | + | 0.376888i | \(0.876994\pi\) | |||||||
\(480\) | 23.6160 | 1.07792 | ||||||||
\(481\) | 11.2975 | 0.515123 | ||||||||
\(482\) | −39.1152 | −1.78165 | ||||||||
\(483\) | −5.05885 | −0.230186 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 20.6457 | 0.937472 | ||||||||
\(486\) | 2.65195 | 0.120295 | ||||||||
\(487\) | 13.5569 | 0.614320 | 0.307160 | − | 0.951658i | \(-0.400621\pi\) | ||||
0.307160 | + | 0.951658i | \(0.400621\pi\) | |||||||
\(488\) | −111.071 | −5.02795 | ||||||||
\(489\) | 3.48225 | 0.157473 | ||||||||
\(490\) | 4.54308 | 0.205236 | ||||||||
\(491\) | 23.4594 | 1.05871 | 0.529354 | − | 0.848401i | \(-0.322435\pi\) | ||||
0.529354 | + | 0.848401i | \(0.322435\pi\) | |||||||
\(492\) | 25.3383 | 1.14234 | ||||||||
\(493\) | −19.9781 | −0.899768 | ||||||||
\(494\) | 25.3802 | 1.14191 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 68.0211 | 3.05424 | ||||||||
\(497\) | −14.3329 | −0.642918 | ||||||||
\(498\) | −15.5664 | −0.697545 | ||||||||
\(499\) | 17.2876 | 0.773899 | 0.386949 | − | 0.922101i | \(-0.373529\pi\) | ||||
0.386949 | + | 0.922101i | \(0.373529\pi\) | |||||||
\(500\) | −60.9155 | −2.72422 | ||||||||
\(501\) | 4.57477 | 0.204386 | ||||||||
\(502\) | 20.2061 | 0.901843 | ||||||||
\(503\) | −3.24592 | −0.144728 | −0.0723641 | − | 0.997378i | \(-0.523054\pi\) | ||||
−0.0723641 | + | 0.997378i | \(0.523054\pi\) | |||||||
\(504\) | 8.04301 | 0.358264 | ||||||||
\(505\) | 9.16247 | 0.407724 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −10.7150 | −0.475871 | ||||||||
\(508\) | 5.60529 | 0.248694 | ||||||||
\(509\) | −15.6005 | −0.691480 | −0.345740 | − | 0.938330i | \(-0.612372\pi\) | ||||
−0.345740 | + | 0.938330i | \(0.612372\pi\) | |||||||
\(510\) | 10.8755 | 0.481576 | ||||||||
\(511\) | 1.43030 | 0.0632729 | ||||||||
\(512\) | −25.9129 | −1.14520 | ||||||||
\(513\) | −6.33123 | −0.279531 | ||||||||
\(514\) | −0.767429 | −0.0338498 | ||||||||
\(515\) | 16.0651 | 0.707911 | ||||||||
\(516\) | −10.1918 | −0.448670 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −19.8202 | −0.870850 | ||||||||
\(519\) | −5.72474 | −0.251288 | ||||||||
\(520\) | −20.8278 | −0.913361 | ||||||||
\(521\) | −4.34383 | −0.190307 | −0.0951534 | − | 0.995463i | \(-0.530334\pi\) | ||||
−0.0951534 | + | 0.995463i | \(0.530334\pi\) | |||||||
\(522\) | −22.1320 | −0.968691 | ||||||||
\(523\) | −12.4657 | −0.545085 | −0.272543 | − | 0.962144i | \(-0.587865\pi\) | ||||
−0.272543 | + | 0.962144i | \(0.587865\pi\) | |||||||
\(524\) | 72.3940 | 3.16254 | ||||||||
\(525\) | −2.06526 | −0.0901354 | ||||||||
\(526\) | −32.6856 | −1.42516 | ||||||||
\(527\) | 14.4561 | 0.629718 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.59198 | 0.112695 | ||||||||
\(530\) | 28.3365 | 1.23086 | ||||||||
\(531\) | 11.1742 | 0.484921 | ||||||||
\(532\) | −31.8642 | −1.38149 | ||||||||
\(533\) | −7.61034 | −0.329640 | ||||||||
\(534\) | 43.5559 | 1.88485 | ||||||||
\(535\) | 20.8504 | 0.901439 | ||||||||
\(536\) | 109.524 | 4.73073 | ||||||||
\(537\) | 2.95701 | 0.127604 | ||||||||
\(538\) | 33.5500 | 1.44644 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 8.62183 | 0.371025 | ||||||||
\(541\) | 12.5756 | 0.540666 | 0.270333 | − | 0.962767i | \(-0.412866\pi\) | ||||
0.270333 | + | 0.962767i | \(0.412866\pi\) | |||||||
\(542\) | −28.5091 | −1.22457 | ||||||||
\(543\) | −9.40004 | −0.403394 | ||||||||
\(544\) | 33.0006 | 1.41489 | ||||||||
\(545\) | 10.8171 | 0.463352 | ||||||||
\(546\) | −4.00873 | −0.171558 | ||||||||
\(547\) | 0.250803 | 0.0107236 | 0.00536178 | − | 0.999986i | \(-0.498293\pi\) | ||||
0.00536178 | + | 0.999986i | \(0.498293\pi\) | |||||||
\(548\) | 13.7292 | 0.586481 | ||||||||
\(549\) | −13.8096 | −0.589381 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 52.8376 | 2.25096 | ||||||||
\(552\) | −40.6884 | −1.73181 | ||||||||
\(553\) | −6.71734 | −0.285650 | ||||||||
\(554\) | 16.1476 | 0.686047 | ||||||||
\(555\) | −12.8034 | −0.543476 | ||||||||
\(556\) | −1.77732 | −0.0753753 | ||||||||
\(557\) | −28.3165 | −1.19981 | −0.599904 | − | 0.800072i | \(-0.704795\pi\) | ||||
−0.599904 | + | 0.800072i | \(0.704795\pi\) | |||||||
\(558\) | 16.0147 | 0.677955 | ||||||||
\(559\) | 3.06111 | 0.129471 | ||||||||
\(560\) | 19.2964 | 0.815421 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 22.8367 | 0.963308 | ||||||||
\(563\) | −16.2038 | −0.682907 | −0.341454 | − | 0.939899i | \(-0.610919\pi\) | ||||
−0.341454 | + | 0.939899i | \(0.610919\pi\) | |||||||
\(564\) | −27.8330 | −1.17198 | ||||||||
\(565\) | 5.76918 | 0.242711 | ||||||||
\(566\) | −8.47450 | −0.356210 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | −115.280 | −4.83702 | ||||||||
\(569\) | 6.40589 | 0.268549 | 0.134274 | − | 0.990944i | \(-0.457130\pi\) | ||||
0.134274 | + | 0.990944i | \(0.457130\pi\) | |||||||
\(570\) | −28.7633 | −1.20476 | ||||||||
\(571\) | −25.9443 | −1.08574 | −0.542868 | − | 0.839818i | \(-0.682662\pi\) | ||||
−0.542868 | + | 0.839818i | \(0.682662\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9.20911 | −0.384716 | ||||||||
\(574\) | 13.3515 | 0.557279 | ||||||||
\(575\) | 10.4479 | 0.435706 | ||||||||
\(576\) | 14.0306 | 0.584608 | ||||||||
\(577\) | 8.96220 | 0.373101 | 0.186551 | − | 0.982445i | \(-0.440269\pi\) | ||||
0.186551 | + | 0.982445i | \(0.440269\pi\) | |||||||
\(578\) | −29.8860 | −1.24309 | ||||||||
\(579\) | 1.49221 | 0.0620142 | ||||||||
\(580\) | −71.9539 | −2.98772 | ||||||||
\(581\) | −5.86977 | −0.243519 | ||||||||
\(582\) | 31.9603 | 1.32480 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 11.5039 | 0.476037 | ||||||||
\(585\) | −2.58956 | −0.107065 | ||||||||
\(586\) | 22.6788 | 0.936852 | ||||||||
\(587\) | 4.96137 | 0.204778 | 0.102389 | − | 0.994744i | \(-0.467351\pi\) | ||||
0.102389 | + | 0.994744i | \(0.467351\pi\) | |||||||
\(588\) | 5.03286 | 0.207552 | ||||||||
\(589\) | −38.2332 | −1.57537 | ||||||||
\(590\) | 50.7655 | 2.08998 | ||||||||
\(591\) | −3.37718 | −0.138919 | ||||||||
\(592\) | −84.1847 | −3.45997 | ||||||||
\(593\) | −30.7179 | −1.26143 | −0.630716 | − | 0.776013i | \(-0.717239\pi\) | ||||
−0.630716 | + | 0.776013i | \(0.717239\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.10094 | 0.168122 | ||||||||
\(596\) | 2.57380 | 0.105427 | ||||||||
\(597\) | 27.8114 | 1.13825 | ||||||||
\(598\) | 20.2796 | 0.829294 | ||||||||
\(599\) | −32.7175 | −1.33680 | −0.668401 | − | 0.743801i | \(-0.733021\pi\) | ||||
−0.668401 | + | 0.743801i | \(0.733021\pi\) | |||||||
\(600\) | −16.6109 | −0.678138 | ||||||||
\(601\) | 40.7669 | 1.66292 | 0.831458 | − | 0.555587i | \(-0.187507\pi\) | ||||
0.831458 | + | 0.555587i | \(0.187507\pi\) | |||||||
\(602\) | −5.37036 | −0.218880 | ||||||||
\(603\) | 13.6173 | 0.554541 | ||||||||
\(604\) | −4.92095 | −0.200230 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 14.1838 | 0.576179 | ||||||||
\(607\) | 25.5265 | 1.03609 | 0.518043 | − | 0.855354i | \(-0.326661\pi\) | ||||
0.518043 | + | 0.855354i | \(0.326661\pi\) | |||||||
\(608\) | −87.2792 | −3.53964 | ||||||||
\(609\) | −8.34554 | −0.338179 | ||||||||
\(610\) | −62.7384 | −2.54020 | ||||||||
\(611\) | 8.35963 | 0.338194 | ||||||||
\(612\) | 12.0480 | 0.487011 | ||||||||
\(613\) | 37.0000 | 1.49442 | 0.747208 | − | 0.664590i | \(-0.231394\pi\) | ||||
0.747208 | + | 0.664590i | \(0.231394\pi\) | |||||||
\(614\) | 9.27624 | 0.374359 | ||||||||
\(615\) | 8.62477 | 0.347784 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −43.0676 | −1.73384 | −0.866918 | − | 0.498452i | \(-0.833902\pi\) | ||||
−0.866918 | + | 0.498452i | \(0.833902\pi\) | |||||||
\(618\) | 24.8693 | 1.00039 | ||||||||
\(619\) | 14.5508 | 0.584847 | 0.292424 | − | 0.956289i | \(-0.405538\pi\) | ||||
0.292424 | + | 0.956289i | \(0.405538\pi\) | |||||||
\(620\) | 52.0657 | 2.09101 | ||||||||
\(621\) | −5.05885 | −0.203005 | ||||||||
\(622\) | −9.78672 | −0.392412 | ||||||||
\(623\) | 16.4241 | 0.658016 | ||||||||
\(624\) | −17.0268 | −0.681616 | ||||||||
\(625\) | −10.4084 | −0.416335 | ||||||||
\(626\) | −69.6514 | −2.78383 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −16.5562 | −0.660666 | ||||||||
\(629\) | −17.8913 | −0.713372 | ||||||||
\(630\) | 4.54308 | 0.181001 | ||||||||
\(631\) | 6.82874 | 0.271848 | 0.135924 | − | 0.990719i | \(-0.456600\pi\) | ||||
0.135924 | + | 0.990719i | \(0.456600\pi\) | |||||||
\(632\) | −54.0276 | −2.14910 | ||||||||
\(633\) | 24.0068 | 0.954187 | ||||||||
\(634\) | 34.6881 | 1.37764 | ||||||||
\(635\) | 1.90795 | 0.0757148 | ||||||||
\(636\) | 31.3914 | 1.24475 | ||||||||
\(637\) | −1.51161 | −0.0598924 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −14.3329 | −0.567000 | ||||||||
\(640\) | 16.5100 | 0.652616 | ||||||||
\(641\) | −11.4167 | −0.450934 | −0.225467 | − | 0.974251i | \(-0.572391\pi\) | ||||
−0.225467 | + | 0.974251i | \(0.572391\pi\) | |||||||
\(642\) | 32.2771 | 1.27388 | ||||||||
\(643\) | −36.2291 | −1.42874 | −0.714368 | − | 0.699770i | \(-0.753286\pi\) | ||||
−0.714368 | + | 0.699770i | \(0.753286\pi\) | |||||||
\(644\) | −25.4605 | −1.00328 | ||||||||
\(645\) | −3.46914 | −0.136597 | ||||||||
\(646\) | −40.1933 | −1.58138 | ||||||||
\(647\) | −24.1531 | −0.949557 | −0.474778 | − | 0.880105i | \(-0.657472\pi\) | ||||
−0.474778 | + | 0.880105i | \(0.657472\pi\) | |||||||
\(648\) | 8.04301 | 0.315959 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 8.27908 | 0.324732 | ||||||||
\(651\) | 6.03882 | 0.236680 | ||||||||
\(652\) | 17.5257 | 0.686358 | ||||||||
\(653\) | −18.3457 | −0.717922 | −0.358961 | − | 0.933353i | \(-0.616869\pi\) | ||||
−0.358961 | + | 0.933353i | \(0.616869\pi\) | |||||||
\(654\) | 16.7452 | 0.654789 | ||||||||
\(655\) | 24.6418 | 0.962834 | ||||||||
\(656\) | 56.7093 | 2.21413 | ||||||||
\(657\) | 1.43030 | 0.0558015 | ||||||||
\(658\) | −14.6660 | −0.571740 | ||||||||
\(659\) | 9.32284 | 0.363166 | 0.181583 | − | 0.983376i | \(-0.441878\pi\) | ||||
0.181583 | + | 0.983376i | \(0.441878\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.30120 | −0.361775 | −0.180887 | − | 0.983504i | \(-0.557897\pi\) | ||||
−0.180887 | + | 0.983504i | \(0.557897\pi\) | |||||||
\(662\) | 21.0479 | 0.818051 | ||||||||
\(663\) | −3.61860 | −0.140535 | ||||||||
\(664\) | −47.2106 | −1.83213 | ||||||||
\(665\) | −10.8461 | −0.420593 | ||||||||
\(666\) | −19.8202 | −0.768017 | ||||||||
\(667\) | 42.2189 | 1.63472 | ||||||||
\(668\) | 23.0242 | 0.890832 | ||||||||
\(669\) | 22.8178 | 0.882187 | ||||||||
\(670\) | 61.8647 | 2.39004 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 13.7855 | 0.531787 | ||||||||
\(673\) | −35.9318 | −1.38507 | −0.692535 | − | 0.721385i | \(-0.743506\pi\) | ||||
−0.692535 | + | 0.721385i | \(0.743506\pi\) | |||||||
\(674\) | −26.5210 | −1.02155 | ||||||||
\(675\) | −2.06526 | −0.0794920 | ||||||||
\(676\) | −53.9272 | −2.07412 | ||||||||
\(677\) | 47.4738 | 1.82456 | 0.912282 | − | 0.409562i | \(-0.134318\pi\) | ||||
0.912282 | + | 0.409562i | \(0.134318\pi\) | |||||||
\(678\) | 8.93091 | 0.342990 | ||||||||
\(679\) | 12.0516 | 0.462498 | ||||||||
\(680\) | 32.9839 | 1.26488 | ||||||||
\(681\) | −14.4047 | −0.551988 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −30.1415 | −1.15333 | −0.576667 | − | 0.816980i | \(-0.695647\pi\) | ||||
−0.576667 | + | 0.816980i | \(0.695647\pi\) | |||||||
\(684\) | −31.8642 | −1.21836 | ||||||||
\(685\) | 4.67320 | 0.178554 | ||||||||
\(686\) | 2.65195 | 0.101252 | ||||||||
\(687\) | −3.79367 | −0.144738 | ||||||||
\(688\) | −22.8102 | −0.869630 | ||||||||
\(689\) | −9.42837 | −0.359192 | ||||||||
\(690\) | −22.9828 | −0.874940 | ||||||||
\(691\) | 45.7782 | 1.74149 | 0.870743 | − | 0.491739i | \(-0.163638\pi\) | ||||
0.870743 | + | 0.491739i | \(0.163638\pi\) | |||||||
\(692\) | −28.8118 | −1.09526 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 14.3432 | 0.544459 | ||||||||
\(695\) | −0.604973 | −0.0229479 | ||||||||
\(696\) | −67.1233 | −2.54430 | ||||||||
\(697\) | 12.0521 | 0.456505 | ||||||||
\(698\) | 75.6631 | 2.86389 | ||||||||
\(699\) | −27.4844 | −1.03956 | ||||||||
\(700\) | −10.3942 | −0.392863 | ||||||||
\(701\) | −12.4242 | −0.469257 | −0.234629 | − | 0.972085i | \(-0.575387\pi\) | ||||
−0.234629 | + | 0.972085i | \(0.575387\pi\) | |||||||
\(702\) | −4.00873 | −0.151300 | ||||||||
\(703\) | 47.3184 | 1.78465 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −9.47394 | −0.356809 | ||||||||
\(706\) | −50.9776 | −1.91857 | ||||||||
\(707\) | 5.34845 | 0.201149 | ||||||||
\(708\) | 56.2384 | 2.11357 | ||||||||
\(709\) | −4.52276 | −0.169856 | −0.0849279 | − | 0.996387i | \(-0.527066\pi\) | ||||
−0.0849279 | + | 0.996387i | \(0.527066\pi\) | |||||||
\(710\) | −65.1155 | −2.44374 | ||||||||
\(711\) | −6.71734 | −0.251920 | ||||||||
\(712\) | 132.099 | 4.95061 | ||||||||
\(713\) | −30.5495 | −1.14409 | ||||||||
\(714\) | 6.34841 | 0.237583 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 14.8822 | 0.556174 | ||||||||
\(717\) | −11.2335 | −0.419523 | ||||||||
\(718\) | −59.2786 | −2.21226 | ||||||||
\(719\) | −8.32032 | −0.310296 | −0.155148 | − | 0.987891i | \(-0.549585\pi\) | ||||
−0.155148 | + | 0.987891i | \(0.549585\pi\) | |||||||
\(720\) | 19.2964 | 0.719134 | ||||||||
\(721\) | 9.37773 | 0.349245 | ||||||||
\(722\) | 55.9152 | 2.08095 | ||||||||
\(723\) | −14.7496 | −0.548543 | ||||||||
\(724\) | −47.3091 | −1.75823 | ||||||||
\(725\) | 17.2357 | 0.640119 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 39.9612 | 1.48208 | 0.741040 | − | 0.671461i | \(-0.234333\pi\) | ||||
0.741040 | + | 0.671461i | \(0.234333\pi\) | |||||||
\(728\) | −12.1579 | −0.450603 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 6.49799 | 0.240501 | ||||||||
\(731\) | −4.84771 | −0.179299 | ||||||||
\(732\) | −69.5020 | −2.56887 | ||||||||
\(733\) | 13.2877 | 0.490793 | 0.245396 | − | 0.969423i | \(-0.421082\pi\) | ||||
0.245396 | + | 0.969423i | \(0.421082\pi\) | |||||||
\(734\) | −62.1746 | −2.29491 | ||||||||
\(735\) | 1.71311 | 0.0631889 | ||||||||
\(736\) | −69.7388 | −2.57061 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 13.3515 | 0.491474 | ||||||||
\(739\) | 6.54579 | 0.240791 | 0.120395 | − | 0.992726i | \(-0.461584\pi\) | ||||
0.120395 | + | 0.992726i | \(0.461584\pi\) | |||||||
\(740\) | −64.4379 | −2.36879 | ||||||||
\(741\) | 9.57039 | 0.351577 | ||||||||
\(742\) | 16.5410 | 0.607239 | ||||||||
\(743\) | 33.2519 | 1.21989 | 0.609947 | − | 0.792442i | \(-0.291191\pi\) | ||||
0.609947 | + | 0.792442i | \(0.291191\pi\) | |||||||
\(744\) | 48.5703 | 1.78067 | ||||||||
\(745\) | 0.876081 | 0.0320971 | ||||||||
\(746\) | 88.7175 | 3.24818 | ||||||||
\(747\) | −5.86977 | −0.214764 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12.1711 | 0.444721 | ||||||||
\(750\) | −32.0981 | −1.17206 | ||||||||
\(751\) | −0.769312 | −0.0280726 | −0.0140363 | − | 0.999901i | \(-0.504468\pi\) | ||||
−0.0140363 | + | 0.999901i | \(0.504468\pi\) | |||||||
\(752\) | −62.2927 | −2.27158 | ||||||||
\(753\) | 7.61933 | 0.277664 | ||||||||
\(754\) | 33.4551 | 1.21836 | ||||||||
\(755\) | −1.67501 | −0.0609600 | ||||||||
\(756\) | 5.03286 | 0.183043 | ||||||||
\(757\) | −2.29424 | −0.0833854 | −0.0416927 | − | 0.999130i | \(-0.513275\pi\) | ||||
−0.0416927 | + | 0.999130i | \(0.513275\pi\) | |||||||
\(758\) | −48.7417 | −1.77038 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −87.2351 | −3.16435 | ||||||||
\(761\) | 3.99916 | 0.144970 | 0.0724848 | − | 0.997370i | \(-0.476907\pi\) | ||||
0.0724848 | + | 0.997370i | \(0.476907\pi\) | |||||||
\(762\) | 2.95358 | 0.106997 | ||||||||
\(763\) | 6.31429 | 0.228592 | ||||||||
\(764\) | −46.3481 | −1.67682 | ||||||||
\(765\) | 4.10094 | 0.148270 | ||||||||
\(766\) | 56.5936 | 2.04481 | ||||||||
\(767\) | −16.8911 | −0.609904 | ||||||||
\(768\) | −2.50303 | −0.0903205 | ||||||||
\(769\) | −48.3136 | −1.74223 | −0.871116 | − | 0.491077i | \(-0.836604\pi\) | ||||
−0.871116 | + | 0.491077i | \(0.836604\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.289382 | −0.0104218 | ||||||||
\(772\) | 7.51010 | 0.270294 | ||||||||
\(773\) | −13.4380 | −0.483331 | −0.241666 | − | 0.970360i | \(-0.577694\pi\) | ||||
−0.241666 | + | 0.970360i | \(0.577694\pi\) | |||||||
\(774\) | −5.37036 | −0.193034 | ||||||||
\(775\) | −12.4717 | −0.447998 | ||||||||
\(776\) | 96.9310 | 3.47962 | ||||||||
\(777\) | −7.47381 | −0.268121 | ||||||||
\(778\) | 41.1622 | 1.47574 | ||||||||
\(779\) | −31.8751 | −1.14204 | ||||||||
\(780\) | −13.0329 | −0.466652 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −32.1157 | −1.14845 | ||||||||
\(783\) | −8.34554 | −0.298245 | ||||||||
\(784\) | 11.2640 | 0.402284 | ||||||||
\(785\) | −5.63549 | −0.201139 | ||||||||
\(786\) | 38.1464 | 1.36064 | ||||||||
\(787\) | 7.35759 | 0.262270 | 0.131135 | − | 0.991365i | \(-0.458138\pi\) | ||||
0.131135 | + | 0.991365i | \(0.458138\pi\) | |||||||
\(788\) | −16.9969 | −0.605489 | ||||||||
\(789\) | −12.3251 | −0.438785 | ||||||||
\(790\) | −30.5174 | −1.08576 | ||||||||
\(791\) | 3.36767 | 0.119741 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 20.8749 | 0.741288 | ||||||||
\(794\) | 56.9579 | 2.02136 | ||||||||
\(795\) | 10.6851 | 0.378963 | ||||||||
\(796\) | 139.971 | 4.96114 | ||||||||
\(797\) | −4.82640 | −0.170960 | −0.0854799 | − | 0.996340i | \(-0.527242\pi\) | ||||
−0.0854799 | + | 0.996340i | \(0.527242\pi\) | |||||||
\(798\) | −16.7901 | −0.594365 | ||||||||
\(799\) | −13.2387 | −0.468351 | ||||||||
\(800\) | −28.4707 | −1.00659 | ||||||||
\(801\) | 16.4241 | 0.580316 | ||||||||
\(802\) | 23.5522 | 0.831655 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 68.5341 | 2.41701 | ||||||||
\(805\) | −8.66636 | −0.305449 | ||||||||
\(806\) | −24.2080 | −0.852691 | ||||||||
\(807\) | 12.6511 | 0.445339 | ||||||||
\(808\) | 43.0176 | 1.51335 | ||||||||
\(809\) | 52.2852 | 1.83825 | 0.919125 | − | 0.393965i | \(-0.128897\pi\) | ||||
0.919125 | + | 0.393965i | \(0.128897\pi\) | |||||||
\(810\) | 4.54308 | 0.159628 | ||||||||
\(811\) | 35.3236 | 1.24038 | 0.620189 | − | 0.784453i | \(-0.287056\pi\) | ||||
0.620189 | + | 0.784453i | \(0.287056\pi\) | |||||||
\(812\) | −42.0020 | −1.47398 | ||||||||
\(813\) | −10.7502 | −0.377026 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.96547 | 0.208961 | ||||||||
\(816\) | 26.9644 | 0.943942 | ||||||||
\(817\) | 12.8211 | 0.448554 | ||||||||
\(818\) | −14.4737 | −0.506062 | ||||||||
\(819\) | −1.51161 | −0.0528201 | ||||||||
\(820\) | 43.4073 | 1.51585 | ||||||||
\(821\) | −30.4361 | −1.06223 | −0.531113 | − | 0.847301i | \(-0.678226\pi\) | ||||
−0.531113 | + | 0.847301i | \(0.678226\pi\) | |||||||
\(822\) | 7.23428 | 0.252325 | ||||||||
\(823\) | 45.8835 | 1.59940 | 0.799700 | − | 0.600400i | \(-0.204992\pi\) | ||||
0.799700 | + | 0.600400i | \(0.204992\pi\) | |||||||
\(824\) | 75.4251 | 2.62756 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 29.6336 | 1.03108 | ||||||||
\(827\) | −12.2298 | −0.425270 | −0.212635 | − | 0.977132i | \(-0.568205\pi\) | ||||
−0.212635 | + | 0.977132i | \(0.568205\pi\) | |||||||
\(828\) | −25.4605 | −0.884813 | ||||||||
\(829\) | 19.7416 | 0.685655 | 0.342828 | − | 0.939398i | \(-0.388615\pi\) | ||||
0.342828 | + | 0.939398i | \(0.388615\pi\) | |||||||
\(830\) | −26.6668 | −0.925620 | ||||||||
\(831\) | 6.08896 | 0.211224 | ||||||||
\(832\) | −21.2088 | −0.735284 | ||||||||
\(833\) | 2.39386 | 0.0829424 | ||||||||
\(834\) | −0.936521 | −0.0324291 | ||||||||
\(835\) | 7.83707 | 0.271213 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.03882 | 0.208732 | ||||||||
\(838\) | 52.9875 | 1.83042 | ||||||||
\(839\) | 9.97411 | 0.344345 | 0.172172 | − | 0.985067i | \(-0.444921\pi\) | ||||
0.172172 | + | 0.985067i | \(0.444921\pi\) | |||||||
\(840\) | 13.7785 | 0.475405 | ||||||||
\(841\) | 40.6481 | 1.40166 | ||||||||
\(842\) | −75.0827 | −2.58752 | ||||||||
\(843\) | 8.61127 | 0.296588 | ||||||||
\(844\) | 120.823 | 4.15890 | ||||||||
\(845\) | −18.3560 | −0.631465 | ||||||||
\(846\) | −14.6660 | −0.504228 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 70.2565 | 2.41262 | ||||||||
\(849\) | −3.19557 | −0.109672 | ||||||||
\(850\) | −13.1111 | −0.449708 | ||||||||
\(851\) | 37.8089 | 1.29607 | ||||||||
\(852\) | −72.1354 | −2.47132 | ||||||||
\(853\) | 0.698961 | 0.0239320 | 0.0119660 | − | 0.999928i | \(-0.496191\pi\) | ||||
0.0119660 | + | 0.999928i | \(0.496191\pi\) | |||||||
\(854\) | −36.6225 | −1.25320 | ||||||||
\(855\) | −10.8461 | −0.370928 | ||||||||
\(856\) | 97.8920 | 3.34588 | ||||||||
\(857\) | 40.0835 | 1.36922 | 0.684612 | − | 0.728907i | \(-0.259972\pi\) | ||||
0.684612 | + | 0.728907i | \(0.259972\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −28.0045 | −0.955503 | −0.477751 | − | 0.878495i | \(-0.658548\pi\) | ||||
−0.477751 | + | 0.878495i | \(0.658548\pi\) | |||||||
\(860\) | −17.4597 | −0.595371 | ||||||||
\(861\) | 5.03457 | 0.171578 | ||||||||
\(862\) | −84.2386 | −2.86918 | ||||||||
\(863\) | −26.0484 | −0.886698 | −0.443349 | − | 0.896349i | \(-0.646210\pi\) | ||||
−0.443349 | + | 0.896349i | \(0.646210\pi\) | |||||||
\(864\) | 13.7855 | 0.468992 | ||||||||
\(865\) | −9.80710 | −0.333452 | ||||||||
\(866\) | −34.9160 | −1.18649 | ||||||||
\(867\) | −11.2694 | −0.382730 | ||||||||
\(868\) | 30.3925 | 1.03159 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −37.9145 | −1.28542 | ||||||||
\(871\) | −20.5842 | −0.697468 | ||||||||
\(872\) | 50.7858 | 1.71983 | ||||||||
\(873\) | 12.0516 | 0.407885 | ||||||||
\(874\) | 84.9388 | 2.87310 | ||||||||
\(875\) | −12.1036 | −0.409175 | ||||||||
\(876\) | 7.19852 | 0.243216 | ||||||||
\(877\) | 42.6421 | 1.43992 | 0.719961 | − | 0.694015i | \(-0.244160\pi\) | ||||
0.719961 | + | 0.694015i | \(0.244160\pi\) | |||||||
\(878\) | 26.0199 | 0.878130 | ||||||||
\(879\) | 8.55173 | 0.288443 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5.07985 | −0.171144 | −0.0855722 | − | 0.996332i | \(-0.527272\pi\) | ||||
−0.0855722 | + | 0.996332i | \(0.527272\pi\) | |||||||
\(882\) | 2.65195 | 0.0892959 | ||||||||
\(883\) | 49.0484 | 1.65061 | 0.825305 | − | 0.564687i | \(-0.191003\pi\) | ||||
0.825305 | + | 0.564687i | \(0.191003\pi\) | |||||||
\(884\) | −18.2119 | −0.612532 | ||||||||
\(885\) | 19.1427 | 0.643474 | ||||||||
\(886\) | 6.59047 | 0.221411 | ||||||||
\(887\) | −53.9270 | −1.81069 | −0.905346 | − | 0.424675i | \(-0.860388\pi\) | ||||
−0.905346 | + | 0.424675i | \(0.860388\pi\) | |||||||
\(888\) | −60.1119 | −2.01722 | ||||||||
\(889\) | 1.11374 | 0.0373536 | ||||||||
\(890\) | 74.6159 | 2.50113 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 114.839 | 3.84509 | ||||||||
\(893\) | 35.0134 | 1.17168 | ||||||||
\(894\) | 1.35621 | 0.0453583 | ||||||||
\(895\) | 5.06567 | 0.169327 | ||||||||
\(896\) | 9.63748 | 0.321965 | ||||||||
\(897\) | 7.64703 | 0.255327 | ||||||||
\(898\) | −41.3962 | −1.38141 | ||||||||
\(899\) | −50.3972 | −1.68084 | ||||||||
\(900\) | −10.3942 | −0.346472 | ||||||||
\(901\) | 14.9312 | 0.497430 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.02506 | −0.0673897 | ||||||||
\(904\) | 27.0862 | 0.900874 | ||||||||
\(905\) | −16.1033 | −0.535291 | ||||||||
\(906\) | −2.59298 | −0.0861461 | ||||||||
\(907\) | 25.7626 | 0.855435 | 0.427717 | − | 0.903913i | \(-0.359318\pi\) | ||||
0.427717 | + | 0.903913i | \(0.359318\pi\) | |||||||
\(908\) | −72.4966 | −2.40589 | ||||||||
\(909\) | 5.34845 | 0.177397 | ||||||||
\(910\) | −6.86739 | −0.227652 | ||||||||
\(911\) | −29.1872 | −0.967015 | −0.483507 | − | 0.875340i | \(-0.660637\pi\) | ||||
−0.483507 | + | 0.875340i | \(0.660637\pi\) | |||||||
\(912\) | −71.3148 | −2.36147 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −36.2396 | −1.19870 | ||||||||
\(915\) | −23.6574 | −0.782090 | ||||||||
\(916\) | −19.0930 | −0.630851 | ||||||||
\(917\) | 14.3843 | 0.475010 | ||||||||
\(918\) | 6.34841 | 0.209529 | ||||||||
\(919\) | 40.5202 | 1.33664 | 0.668320 | − | 0.743874i | \(-0.267014\pi\) | ||||
0.668320 | + | 0.743874i | \(0.267014\pi\) | |||||||
\(920\) | −69.7036 | −2.29806 | ||||||||
\(921\) | 3.49789 | 0.115259 | ||||||||
\(922\) | −49.4708 | −1.62923 | ||||||||
\(923\) | 21.6658 | 0.713139 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15.4354 | 0.507512 | ||||||||
\(926\) | −49.2459 | −1.61832 | ||||||||
\(927\) | 9.37773 | 0.308005 | ||||||||
\(928\) | −115.048 | −3.77662 | ||||||||
\(929\) | 5.13344 | 0.168423 | 0.0842113 | − | 0.996448i | \(-0.473163\pi\) | ||||
0.0842113 | + | 0.996448i | \(0.473163\pi\) | |||||||
\(930\) | 27.4349 | 0.899625 | ||||||||
\(931\) | −6.33123 | −0.207498 | ||||||||
\(932\) | −138.325 | −4.53099 | ||||||||
\(933\) | −3.69038 | −0.120818 | ||||||||
\(934\) | 92.7066 | 3.03345 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −12.1579 | −0.397394 | ||||||||
\(937\) | 25.3284 | 0.827443 | 0.413722 | − | 0.910403i | \(-0.364229\pi\) | ||||
0.413722 | + | 0.910403i | \(0.364229\pi\) | |||||||
\(938\) | 36.1125 | 1.17912 | ||||||||
\(939\) | −26.2642 | −0.857099 | ||||||||
\(940\) | −47.6810 | −1.55518 | ||||||||
\(941\) | −21.2749 | −0.693541 | −0.346770 | − | 0.937950i | \(-0.612722\pi\) | ||||
−0.346770 | + | 0.937950i | \(0.612722\pi\) | |||||||
\(942\) | −8.72394 | −0.284241 | ||||||||
\(943\) | −25.4692 | −0.829390 | ||||||||
\(944\) | 125.866 | 4.09660 | ||||||||
\(945\) | 1.71311 | 0.0557274 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −30.1418 | −0.979476 | −0.489738 | − | 0.871870i | \(-0.662908\pi\) | ||||
−0.489738 | + | 0.871870i | \(0.662908\pi\) | |||||||
\(948\) | −33.8074 | −1.09801 | ||||||||
\(949\) | −2.16207 | −0.0701837 | ||||||||
\(950\) | 34.6760 | 1.12504 | ||||||||
\(951\) | 13.0802 | 0.424154 | ||||||||
\(952\) | 19.2539 | 0.624021 | ||||||||
\(953\) | −8.93028 | −0.289280 | −0.144640 | − | 0.989484i | \(-0.546202\pi\) | ||||
−0.144640 | + | 0.989484i | \(0.546202\pi\) | |||||||
\(954\) | 16.5410 | 0.535534 | ||||||||
\(955\) | −15.7762 | −0.510506 | ||||||||
\(956\) | −56.5367 | −1.82853 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −107.522 | −3.47387 | ||||||||
\(959\) | 2.72791 | 0.0880887 | ||||||||
\(960\) | 24.0359 | 0.775756 | ||||||||
\(961\) | 5.46735 | 0.176366 | ||||||||
\(962\) | 29.9605 | 0.965965 | ||||||||
\(963\) | 12.1711 | 0.392207 | ||||||||
\(964\) | −74.2326 | −2.39087 | ||||||||
\(965\) | 2.55632 | 0.0822909 | ||||||||
\(966\) | −13.4158 | −0.431648 | ||||||||
\(967\) | 38.3461 | 1.23313 | 0.616564 | − | 0.787305i | \(-0.288524\pi\) | ||||
0.616564 | + | 0.787305i | \(0.288524\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −15.1561 | −0.486884 | ||||||||
\(970\) | 54.7514 | 1.75796 | ||||||||
\(971\) | 31.1508 | 0.999676 | 0.499838 | − | 0.866119i | \(-0.333393\pi\) | ||||
0.499838 | + | 0.866119i | \(0.333393\pi\) | |||||||
\(972\) | 5.03286 | 0.161429 | ||||||||
\(973\) | −0.353144 | −0.0113213 | ||||||||
\(974\) | 35.9522 | 1.15198 | ||||||||
\(975\) | 3.12188 | 0.0999802 | ||||||||
\(976\) | −155.551 | −4.97908 | ||||||||
\(977\) | 29.7663 | 0.952310 | 0.476155 | − | 0.879361i | \(-0.342030\pi\) | ||||
0.476155 | + | 0.879361i | \(0.342030\pi\) | |||||||
\(978\) | 9.23477 | 0.295295 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 8.62183 | 0.275414 | ||||||||
\(981\) | 6.31429 | 0.201600 | ||||||||
\(982\) | 62.2132 | 1.98530 | ||||||||
\(983\) | −39.9068 | −1.27283 | −0.636415 | − | 0.771347i | \(-0.719583\pi\) | ||||
−0.636415 | + | 0.771347i | \(0.719583\pi\) | |||||||
\(984\) | 40.4931 | 1.29087 | ||||||||
\(985\) | −5.78548 | −0.184341 | ||||||||
\(986\) | −52.9810 | −1.68726 | ||||||||
\(987\) | −5.53026 | −0.176030 | ||||||||
\(988\) | 48.1664 | 1.53238 | ||||||||
\(989\) | 10.2445 | 0.325755 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10.7771 | −0.342345 | −0.171173 | − | 0.985241i | \(-0.554756\pi\) | ||||
−0.171173 | + | 0.985241i | \(0.554756\pi\) | |||||||
\(992\) | 83.2482 | 2.64313 | ||||||||
\(993\) | 7.93676 | 0.251865 | ||||||||
\(994\) | −38.0102 | −1.20561 | ||||||||
\(995\) | 47.6440 | 1.51042 | ||||||||
\(996\) | −29.5417 | −0.936065 | ||||||||
\(997\) | −1.13922 | −0.0360796 | −0.0180398 | − | 0.999837i | \(-0.505743\pi\) | ||||
−0.0180398 | + | 0.999837i | \(0.505743\pi\) | |||||||
\(998\) | 45.8459 | 1.45123 | ||||||||
\(999\) | −7.47381 | −0.236461 |
(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 | 2541.2.a.br.1.10 | 10 | ||
3.2 | odd | 2 | 7623.2.a.cy.1.1 | 10 | |||
11.2 | odd | 10 | 231.2.j.g.169.5 | ✓ | 20 | ||
11.6 | odd | 10 | 231.2.j.g.190.5 | yes | 20 | ||
11.10 | odd | 2 | 2541.2.a.bq.1.1 | 10 | |||
33.2 | even | 10 | 693.2.m.j.631.1 | 20 | |||
33.17 | even | 10 | 693.2.m.j.190.1 | 20 | |||
33.32 | even | 2 | 7623.2.a.cx.1.10 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
231.2.j.g.169.5 | ✓ | 20 | 11.2 | odd | 10 | ||
231.2.j.g.190.5 | yes | 20 | 11.6 | odd | 10 | ||
693.2.m.j.190.1 | 20 | 33.17 | even | 10 | |||
693.2.m.j.631.1 | 20 | 33.2 | even | 10 | |||
2541.2.a.bq.1.1 | 10 | 11.10 | odd | 2 | |||
2541.2.a.br.1.10 | 10 | 1.1 | even | 1 | trivial | ||
7623.2.a.cx.1.10 | 10 | 33.32 | even | 2 | |||
7623.2.a.cy.1.1 | 10 | 3.2 | odd | 2 |