Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3381,2,Mod(1,3381)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3381, 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("3381.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3381 = 3 \cdot 7^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3381.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: | \(26.9974209234\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 483) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3381.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.56155 | 1.10418 | 0.552092 | − | 0.833783i | \(-0.313830\pi\) | ||||
0.552092 | + | 0.833783i | \(0.313830\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0.438447 | 0.219224 | ||||||||
\(5\) | −1.56155 | −0.698348 | −0.349174 | − | 0.937058i | \(-0.613538\pi\) | ||||
−0.349174 | + | 0.937058i | \(0.613538\pi\) | |||||||
\(6\) | −1.56155 | −0.637501 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.43845 | −0.862121 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.43845 | −0.771105 | ||||||||
\(11\) | −2.00000 | −0.603023 | −0.301511 | − | 0.953463i | \(-0.597491\pi\) | ||||
−0.301511 | + | 0.953463i | \(0.597491\pi\) | |||||||
\(12\) | −0.438447 | −0.126569 | ||||||||
\(13\) | 6.12311 | 1.69824 | 0.849122 | − | 0.528197i | \(-0.177132\pi\) | ||||
0.849122 | + | 0.528197i | \(0.177132\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.56155 | 0.403191 | ||||||||
\(16\) | −4.68466 | −1.17116 | ||||||||
\(17\) | 7.56155 | 1.83395 | 0.916973 | − | 0.398949i | \(-0.130625\pi\) | ||||
0.916973 | + | 0.398949i | \(0.130625\pi\) | |||||||
\(18\) | 1.56155 | 0.368062 | ||||||||
\(19\) | −1.43845 | −0.330002 | −0.165001 | − | 0.986293i | \(-0.552763\pi\) | ||||
−0.165001 | + | 0.986293i | \(0.552763\pi\) | |||||||
\(20\) | −0.684658 | −0.153094 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.12311 | −0.665848 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 2.43845 | 0.497746 | ||||||||
\(25\) | −2.56155 | −0.512311 | ||||||||
\(26\) | 9.56155 | 1.87517 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9.12311 | −1.69412 | −0.847059 | − | 0.531499i | \(-0.821629\pi\) | ||||
−0.847059 | + | 0.531499i | \(0.821629\pi\) | |||||||
\(30\) | 2.43845 | 0.445198 | ||||||||
\(31\) | −5.68466 | −1.02099 | −0.510497 | − | 0.859879i | \(-0.670539\pi\) | ||||
−0.510497 | + | 0.859879i | \(0.670539\pi\) | |||||||
\(32\) | −2.43845 | −0.431061 | ||||||||
\(33\) | 2.00000 | 0.348155 | ||||||||
\(34\) | 11.8078 | 2.02501 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.438447 | 0.0730745 | ||||||||
\(37\) | 3.43845 | 0.565277 | 0.282639 | − | 0.959226i | \(-0.408790\pi\) | ||||
0.282639 | + | 0.959226i | \(0.408790\pi\) | |||||||
\(38\) | −2.24621 | −0.364384 | ||||||||
\(39\) | −6.12311 | −0.980482 | ||||||||
\(40\) | 3.80776 | 0.602060 | ||||||||
\(41\) | 10.2462 | 1.60019 | 0.800095 | − | 0.599874i | \(-0.204783\pi\) | ||||
0.800095 | + | 0.599874i | \(0.204783\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.315342 | −0.0480891 | −0.0240446 | − | 0.999711i | \(-0.507654\pi\) | ||||
−0.0240446 | + | 0.999711i | \(0.507654\pi\) | |||||||
\(44\) | −0.876894 | −0.132197 | ||||||||
\(45\) | −1.56155 | −0.232783 | ||||||||
\(46\) | 1.56155 | 0.230238 | ||||||||
\(47\) | −6.68466 | −0.975058 | −0.487529 | − | 0.873107i | \(-0.662102\pi\) | ||||
−0.487529 | + | 0.873107i | \(0.662102\pi\) | |||||||
\(48\) | 4.68466 | 0.676172 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −4.00000 | −0.565685 | ||||||||
\(51\) | −7.56155 | −1.05883 | ||||||||
\(52\) | 2.68466 | 0.372295 | ||||||||
\(53\) | −7.80776 | −1.07248 | −0.536239 | − | 0.844066i | \(-0.680156\pi\) | ||||
−0.536239 | + | 0.844066i | \(0.680156\pi\) | |||||||
\(54\) | −1.56155 | −0.212500 | ||||||||
\(55\) | 3.12311 | 0.421119 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.43845 | 0.190527 | ||||||||
\(58\) | −14.2462 | −1.87062 | ||||||||
\(59\) | −9.12311 | −1.18773 | −0.593864 | − | 0.804566i | \(-0.702398\pi\) | ||||
−0.593864 | + | 0.804566i | \(0.702398\pi\) | |||||||
\(60\) | 0.684658 | 0.0883890 | ||||||||
\(61\) | −6.00000 | −0.768221 | −0.384111 | − | 0.923287i | \(-0.625492\pi\) | ||||
−0.384111 | + | 0.923287i | \(0.625492\pi\) | |||||||
\(62\) | −8.87689 | −1.12737 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5.56155 | 0.695194 | ||||||||
\(65\) | −9.56155 | −1.18596 | ||||||||
\(66\) | 3.12311 | 0.384428 | ||||||||
\(67\) | −14.1231 | −1.72541 | −0.862706 | − | 0.505706i | \(-0.831232\pi\) | ||||
−0.862706 | + | 0.505706i | \(0.831232\pi\) | |||||||
\(68\) | 3.31534 | 0.402044 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.8078 | 1.63868 | 0.819340 | − | 0.573308i | \(-0.194340\pi\) | ||||
0.819340 | + | 0.573308i | \(0.194340\pi\) | |||||||
\(72\) | −2.43845 | −0.287374 | ||||||||
\(73\) | −5.87689 | −0.687838 | −0.343919 | − | 0.938999i | \(-0.611755\pi\) | ||||
−0.343919 | + | 0.938999i | \(0.611755\pi\) | |||||||
\(74\) | 5.36932 | 0.624170 | ||||||||
\(75\) | 2.56155 | 0.295783 | ||||||||
\(76\) | −0.630683 | −0.0723443 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −9.56155 | −1.08263 | ||||||||
\(79\) | −5.43845 | −0.611873 | −0.305937 | − | 0.952052i | \(-0.598970\pi\) | ||||
−0.305937 | + | 0.952052i | \(0.598970\pi\) | |||||||
\(80\) | 7.31534 | 0.817880 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 16.0000 | 1.76690 | ||||||||
\(83\) | −4.87689 | −0.535309 | −0.267654 | − | 0.963515i | \(-0.586249\pi\) | ||||
−0.267654 | + | 0.963515i | \(0.586249\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11.8078 | −1.28073 | ||||||||
\(86\) | −0.492423 | −0.0530993 | ||||||||
\(87\) | 9.12311 | 0.978100 | ||||||||
\(88\) | 4.87689 | 0.519879 | ||||||||
\(89\) | 10.0000 | 1.06000 | 0.529999 | − | 0.847998i | \(-0.322192\pi\) | ||||
0.529999 | + | 0.847998i | \(0.322192\pi\) | |||||||
\(90\) | −2.43845 | −0.257035 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.438447 | 0.0457113 | ||||||||
\(93\) | 5.68466 | 0.589472 | ||||||||
\(94\) | −10.4384 | −1.07664 | ||||||||
\(95\) | 2.24621 | 0.230456 | ||||||||
\(96\) | 2.43845 | 0.248873 | ||||||||
\(97\) | −15.3693 | −1.56052 | −0.780259 | − | 0.625457i | \(-0.784913\pi\) | ||||
−0.780259 | + | 0.625457i | \(0.784913\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.00000 | −0.201008 | ||||||||
\(100\) | −1.12311 | −0.112311 | ||||||||
\(101\) | 0.876894 | 0.0872543 | 0.0436271 | − | 0.999048i | \(-0.486109\pi\) | ||||
0.0436271 | + | 0.999048i | \(0.486109\pi\) | |||||||
\(102\) | −11.8078 | −1.16914 | ||||||||
\(103\) | −14.1231 | −1.39159 | −0.695795 | − | 0.718240i | \(-0.744948\pi\) | ||||
−0.695795 | + | 0.718240i | \(0.744948\pi\) | |||||||
\(104\) | −14.9309 | −1.46409 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −12.1922 | −1.18421 | ||||||||
\(107\) | −6.24621 | −0.603844 | −0.301922 | − | 0.953333i | \(-0.597628\pi\) | ||||
−0.301922 | + | 0.953333i | \(0.597628\pi\) | |||||||
\(108\) | −0.438447 | −0.0421896 | ||||||||
\(109\) | −10.5616 | −1.01161 | −0.505807 | − | 0.862647i | \(-0.668805\pi\) | ||||
−0.505807 | + | 0.862647i | \(0.668805\pi\) | |||||||
\(110\) | 4.87689 | 0.464994 | ||||||||
\(111\) | −3.43845 | −0.326363 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.80776 | 0.922637 | 0.461318 | − | 0.887235i | \(-0.347377\pi\) | ||||
0.461318 | + | 0.887235i | \(0.347377\pi\) | |||||||
\(114\) | 2.24621 | 0.210377 | ||||||||
\(115\) | −1.56155 | −0.145616 | ||||||||
\(116\) | −4.00000 | −0.371391 | ||||||||
\(117\) | 6.12311 | 0.566081 | ||||||||
\(118\) | −14.2462 | −1.31147 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −3.80776 | −0.347600 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | −9.36932 | −0.848258 | ||||||||
\(123\) | −10.2462 | −0.923870 | ||||||||
\(124\) | −2.49242 | −0.223826 | ||||||||
\(125\) | 11.8078 | 1.05612 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.68466 | 0.149489 | 0.0747446 | − | 0.997203i | \(-0.476186\pi\) | ||||
0.0747446 | + | 0.997203i | \(0.476186\pi\) | |||||||
\(128\) | 13.5616 | 1.19868 | ||||||||
\(129\) | 0.315342 | 0.0277643 | ||||||||
\(130\) | −14.9309 | −1.30952 | ||||||||
\(131\) | −12.6847 | −1.10826 | −0.554132 | − | 0.832429i | \(-0.686950\pi\) | ||||
−0.554132 | + | 0.832429i | \(0.686950\pi\) | |||||||
\(132\) | 0.876894 | 0.0763239 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −22.0540 | −1.90517 | ||||||||
\(135\) | 1.56155 | 0.134397 | ||||||||
\(136\) | −18.4384 | −1.58108 | ||||||||
\(137\) | −7.80776 | −0.667062 | −0.333531 | − | 0.942739i | \(-0.608240\pi\) | ||||
−0.333531 | + | 0.942739i | \(0.608240\pi\) | |||||||
\(138\) | −1.56155 | −0.132928 | ||||||||
\(139\) | −11.9309 | −1.01196 | −0.505982 | − | 0.862544i | \(-0.668870\pi\) | ||||
−0.505982 | + | 0.862544i | \(0.668870\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.68466 | 0.562950 | ||||||||
\(142\) | 21.5616 | 1.80941 | ||||||||
\(143\) | −12.2462 | −1.02408 | ||||||||
\(144\) | −4.68466 | −0.390388 | ||||||||
\(145\) | 14.2462 | 1.18308 | ||||||||
\(146\) | −9.17708 | −0.759501 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.50758 | 0.123922 | ||||||||
\(149\) | −1.31534 | −0.107757 | −0.0538785 | − | 0.998547i | \(-0.517158\pi\) | ||||
−0.0538785 | + | 0.998547i | \(0.517158\pi\) | |||||||
\(150\) | 4.00000 | 0.326599 | ||||||||
\(151\) | −18.2462 | −1.48486 | −0.742428 | − | 0.669926i | \(-0.766326\pi\) | ||||
−0.742428 | + | 0.669926i | \(0.766326\pi\) | |||||||
\(152\) | 3.50758 | 0.284502 | ||||||||
\(153\) | 7.56155 | 0.611315 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.87689 | 0.713009 | ||||||||
\(156\) | −2.68466 | −0.214945 | ||||||||
\(157\) | −4.24621 | −0.338885 | −0.169442 | − | 0.985540i | \(-0.554197\pi\) | ||||
−0.169442 | + | 0.985540i | \(0.554197\pi\) | |||||||
\(158\) | −8.49242 | −0.675621 | ||||||||
\(159\) | 7.80776 | 0.619196 | ||||||||
\(160\) | 3.80776 | 0.301030 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.56155 | 0.122687 | ||||||||
\(163\) | 4.00000 | 0.313304 | 0.156652 | − | 0.987654i | \(-0.449930\pi\) | ||||
0.156652 | + | 0.987654i | \(0.449930\pi\) | |||||||
\(164\) | 4.49242 | 0.350799 | ||||||||
\(165\) | −3.12311 | −0.243133 | ||||||||
\(166\) | −7.61553 | −0.591080 | ||||||||
\(167\) | 3.31534 | 0.256549 | 0.128274 | − | 0.991739i | \(-0.459056\pi\) | ||||
0.128274 | + | 0.991739i | \(0.459056\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 24.4924 | 1.88403 | ||||||||
\(170\) | −18.4384 | −1.41416 | ||||||||
\(171\) | −1.43845 | −0.110001 | ||||||||
\(172\) | −0.138261 | −0.0105423 | ||||||||
\(173\) | 23.3693 | 1.77674 | 0.888368 | − | 0.459132i | \(-0.151839\pi\) | ||||
0.888368 | + | 0.459132i | \(0.151839\pi\) | |||||||
\(174\) | 14.2462 | 1.08000 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 9.36932 | 0.706239 | ||||||||
\(177\) | 9.12311 | 0.685735 | ||||||||
\(178\) | 15.6155 | 1.17043 | ||||||||
\(179\) | 6.93087 | 0.518038 | 0.259019 | − | 0.965872i | \(-0.416601\pi\) | ||||
0.259019 | + | 0.965872i | \(0.416601\pi\) | |||||||
\(180\) | −0.684658 | −0.0510314 | ||||||||
\(181\) | 7.93087 | 0.589497 | 0.294748 | − | 0.955575i | \(-0.404764\pi\) | ||||
0.294748 | + | 0.955575i | \(0.404764\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.00000 | 0.443533 | ||||||||
\(184\) | −2.43845 | −0.179765 | ||||||||
\(185\) | −5.36932 | −0.394760 | ||||||||
\(186\) | 8.87689 | 0.650885 | ||||||||
\(187\) | −15.1231 | −1.10591 | ||||||||
\(188\) | −2.93087 | −0.213756 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.50758 | 0.254466 | ||||||||
\(191\) | −1.12311 | −0.0812651 | −0.0406325 | − | 0.999174i | \(-0.512937\pi\) | ||||
−0.0406325 | + | 0.999174i | \(0.512937\pi\) | |||||||
\(192\) | −5.56155 | −0.401371 | ||||||||
\(193\) | 7.87689 | 0.566991 | 0.283496 | − | 0.958974i | \(-0.408506\pi\) | ||||
0.283496 | + | 0.958974i | \(0.408506\pi\) | |||||||
\(194\) | −24.0000 | −1.72310 | ||||||||
\(195\) | 9.56155 | 0.684717 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −21.3693 | −1.52250 | −0.761250 | − | 0.648458i | \(-0.775414\pi\) | ||||
−0.761250 | + | 0.648458i | \(0.775414\pi\) | |||||||
\(198\) | −3.12311 | −0.221949 | ||||||||
\(199\) | 8.00000 | 0.567105 | 0.283552 | − | 0.958957i | \(-0.408487\pi\) | ||||
0.283552 | + | 0.958957i | \(0.408487\pi\) | |||||||
\(200\) | 6.24621 | 0.441674 | ||||||||
\(201\) | 14.1231 | 0.996167 | ||||||||
\(202\) | 1.36932 | 0.0963448 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −3.31534 | −0.232120 | ||||||||
\(205\) | −16.0000 | −1.11749 | ||||||||
\(206\) | −22.0540 | −1.53657 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | −28.6847 | −1.98892 | ||||||||
\(209\) | 2.87689 | 0.198999 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.12311 | −0.490375 | −0.245187 | − | 0.969476i | \(-0.578849\pi\) | ||||
−0.245187 | + | 0.969476i | \(0.578849\pi\) | |||||||
\(212\) | −3.42329 | −0.235113 | ||||||||
\(213\) | −13.8078 | −0.946092 | ||||||||
\(214\) | −9.75379 | −0.666755 | ||||||||
\(215\) | 0.492423 | 0.0335829 | ||||||||
\(216\) | 2.43845 | 0.165915 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −16.4924 | −1.11701 | ||||||||
\(219\) | 5.87689 | 0.397124 | ||||||||
\(220\) | 1.36932 | 0.0923193 | ||||||||
\(221\) | 46.3002 | 3.11449 | ||||||||
\(222\) | −5.36932 | −0.360365 | ||||||||
\(223\) | 20.4924 | 1.37227 | 0.686137 | − | 0.727472i | \(-0.259305\pi\) | ||||
0.686137 | + | 0.727472i | \(0.259305\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.56155 | −0.170770 | ||||||||
\(226\) | 15.3153 | 1.01876 | ||||||||
\(227\) | −2.00000 | −0.132745 | −0.0663723 | − | 0.997795i | \(-0.521143\pi\) | ||||
−0.0663723 | + | 0.997795i | \(0.521143\pi\) | |||||||
\(228\) | 0.630683 | 0.0417680 | ||||||||
\(229\) | 29.3002 | 1.93621 | 0.968105 | − | 0.250543i | \(-0.0806092\pi\) | ||||
0.968105 | + | 0.250543i | \(0.0806092\pi\) | |||||||
\(230\) | −2.43845 | −0.160786 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 22.2462 | 1.46054 | ||||||||
\(233\) | −10.8769 | −0.712569 | −0.356285 | − | 0.934378i | \(-0.615957\pi\) | ||||
−0.356285 | + | 0.934378i | \(0.615957\pi\) | |||||||
\(234\) | 9.56155 | 0.625058 | ||||||||
\(235\) | 10.4384 | 0.680929 | ||||||||
\(236\) | −4.00000 | −0.260378 | ||||||||
\(237\) | 5.43845 | 0.353265 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −18.2462 | −1.18025 | −0.590125 | − | 0.807312i | \(-0.700921\pi\) | ||||
−0.590125 | + | 0.807312i | \(0.700921\pi\) | |||||||
\(240\) | −7.31534 | −0.472203 | ||||||||
\(241\) | −2.00000 | −0.128831 | −0.0644157 | − | 0.997923i | \(-0.520518\pi\) | ||||
−0.0644157 | + | 0.997923i | \(0.520518\pi\) | |||||||
\(242\) | −10.9309 | −0.702663 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −2.63068 | −0.168412 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −16.0000 | −1.02012 | ||||||||
\(247\) | −8.80776 | −0.560425 | ||||||||
\(248\) | 13.8617 | 0.880221 | ||||||||
\(249\) | 4.87689 | 0.309061 | ||||||||
\(250\) | 18.4384 | 1.16615 | ||||||||
\(251\) | −2.00000 | −0.126239 | −0.0631194 | − | 0.998006i | \(-0.520105\pi\) | ||||
−0.0631194 | + | 0.998006i | \(0.520105\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.00000 | −0.125739 | ||||||||
\(254\) | 2.63068 | 0.165064 | ||||||||
\(255\) | 11.8078 | 0.739431 | ||||||||
\(256\) | 10.0540 | 0.628373 | ||||||||
\(257\) | 6.63068 | 0.413611 | 0.206805 | − | 0.978382i | \(-0.433693\pi\) | ||||
0.206805 | + | 0.978382i | \(0.433693\pi\) | |||||||
\(258\) | 0.492423 | 0.0306569 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −4.19224 | −0.259991 | ||||||||
\(261\) | −9.12311 | −0.564706 | ||||||||
\(262\) | −19.8078 | −1.22373 | ||||||||
\(263\) | 4.49242 | 0.277015 | 0.138507 | − | 0.990361i | \(-0.455770\pi\) | ||||
0.138507 | + | 0.990361i | \(0.455770\pi\) | |||||||
\(264\) | −4.87689 | −0.300152 | ||||||||
\(265\) | 12.1922 | 0.748963 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10.0000 | −0.611990 | ||||||||
\(268\) | −6.19224 | −0.378251 | ||||||||
\(269\) | 8.49242 | 0.517792 | 0.258896 | − | 0.965905i | \(-0.416641\pi\) | ||||
0.258896 | + | 0.965905i | \(0.416641\pi\) | |||||||
\(270\) | 2.43845 | 0.148399 | ||||||||
\(271\) | 19.6155 | 1.19156 | 0.595779 | − | 0.803148i | \(-0.296843\pi\) | ||||
0.595779 | + | 0.803148i | \(0.296843\pi\) | |||||||
\(272\) | −35.4233 | −2.14785 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −12.1922 | −0.736560 | ||||||||
\(275\) | 5.12311 | 0.308935 | ||||||||
\(276\) | −0.438447 | −0.0263914 | ||||||||
\(277\) | −29.2462 | −1.75723 | −0.878617 | − | 0.477527i | \(-0.841533\pi\) | ||||
−0.878617 | + | 0.477527i | \(0.841533\pi\) | |||||||
\(278\) | −18.6307 | −1.11739 | ||||||||
\(279\) | −5.68466 | −0.340332 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 19.5616 | 1.16694 | 0.583472 | − | 0.812133i | \(-0.301694\pi\) | ||||
0.583472 | + | 0.812133i | \(0.301694\pi\) | |||||||
\(282\) | 10.4384 | 0.621600 | ||||||||
\(283\) | 24.1231 | 1.43397 | 0.716985 | − | 0.697089i | \(-0.245522\pi\) | ||||
0.716985 | + | 0.697089i | \(0.245522\pi\) | |||||||
\(284\) | 6.05398 | 0.359237 | ||||||||
\(285\) | −2.24621 | −0.133054 | ||||||||
\(286\) | −19.1231 | −1.13077 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −2.43845 | −0.143687 | ||||||||
\(289\) | 40.1771 | 2.36336 | ||||||||
\(290\) | 22.2462 | 1.30634 | ||||||||
\(291\) | 15.3693 | 0.900965 | ||||||||
\(292\) | −2.57671 | −0.150790 | ||||||||
\(293\) | −24.0540 | −1.40525 | −0.702624 | − | 0.711561i | \(-0.747988\pi\) | ||||
−0.702624 | + | 0.711561i | \(0.747988\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.2462 | 0.829446 | ||||||||
\(296\) | −8.38447 | −0.487338 | ||||||||
\(297\) | 2.00000 | 0.116052 | ||||||||
\(298\) | −2.05398 | −0.118984 | ||||||||
\(299\) | 6.12311 | 0.354108 | ||||||||
\(300\) | 1.12311 | 0.0648425 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −28.4924 | −1.63955 | ||||||||
\(303\) | −0.876894 | −0.0503763 | ||||||||
\(304\) | 6.73863 | 0.386487 | ||||||||
\(305\) | 9.36932 | 0.536486 | ||||||||
\(306\) | 11.8078 | 0.675005 | ||||||||
\(307\) | −11.6847 | −0.666879 | −0.333439 | − | 0.942772i | \(-0.608209\pi\) | ||||
−0.333439 | + | 0.942772i | \(0.608209\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.1231 | 0.803435 | ||||||||
\(310\) | 13.8617 | 0.787294 | ||||||||
\(311\) | −7.56155 | −0.428776 | −0.214388 | − | 0.976749i | \(-0.568776\pi\) | ||||
−0.214388 | + | 0.976749i | \(0.568776\pi\) | |||||||
\(312\) | 14.9309 | 0.845294 | ||||||||
\(313\) | −29.3002 | −1.65614 | −0.828072 | − | 0.560621i | \(-0.810562\pi\) | ||||
−0.828072 | + | 0.560621i | \(0.810562\pi\) | |||||||
\(314\) | −6.63068 | −0.374191 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.38447 | −0.134137 | ||||||||
\(317\) | −11.7538 | −0.660159 | −0.330079 | − | 0.943953i | \(-0.607075\pi\) | ||||
−0.330079 | + | 0.943953i | \(0.607075\pi\) | |||||||
\(318\) | 12.1922 | 0.683707 | ||||||||
\(319\) | 18.2462 | 1.02159 | ||||||||
\(320\) | −8.68466 | −0.485487 | ||||||||
\(321\) | 6.24621 | 0.348630 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10.8769 | −0.605207 | ||||||||
\(324\) | 0.438447 | 0.0243582 | ||||||||
\(325\) | −15.6847 | −0.870028 | ||||||||
\(326\) | 6.24621 | 0.345946 | ||||||||
\(327\) | 10.5616 | 0.584055 | ||||||||
\(328\) | −24.9848 | −1.37956 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −4.87689 | −0.268464 | ||||||||
\(331\) | −15.4384 | −0.848574 | −0.424287 | − | 0.905528i | \(-0.639475\pi\) | ||||
−0.424287 | + | 0.905528i | \(0.639475\pi\) | |||||||
\(332\) | −2.13826 | −0.117352 | ||||||||
\(333\) | 3.43845 | 0.188426 | ||||||||
\(334\) | 5.17708 | 0.283277 | ||||||||
\(335\) | 22.0540 | 1.20494 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.8078 | −1.13347 | −0.566736 | − | 0.823900i | \(-0.691794\pi\) | ||||
−0.566736 | + | 0.823900i | \(0.691794\pi\) | |||||||
\(338\) | 38.2462 | 2.08032 | ||||||||
\(339\) | −9.80776 | −0.532685 | ||||||||
\(340\) | −5.17708 | −0.280767 | ||||||||
\(341\) | 11.3693 | 0.615683 | ||||||||
\(342\) | −2.24621 | −0.121461 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0.768944 | 0.0414587 | ||||||||
\(345\) | 1.56155 | 0.0840712 | ||||||||
\(346\) | 36.4924 | 1.96184 | ||||||||
\(347\) | −12.6847 | −0.680948 | −0.340474 | − | 0.940254i | \(-0.610588\pi\) | ||||
−0.340474 | + | 0.940254i | \(0.610588\pi\) | |||||||
\(348\) | 4.00000 | 0.214423 | ||||||||
\(349\) | −0.930870 | −0.0498283 | −0.0249142 | − | 0.999690i | \(-0.507931\pi\) | ||||
−0.0249142 | + | 0.999690i | \(0.507931\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.12311 | −0.326827 | ||||||||
\(352\) | 4.87689 | 0.259939 | ||||||||
\(353\) | 7.36932 | 0.392229 | 0.196115 | − | 0.980581i | \(-0.437168\pi\) | ||||
0.196115 | + | 0.980581i | \(0.437168\pi\) | |||||||
\(354\) | 14.2462 | 0.757178 | ||||||||
\(355\) | −21.5616 | −1.14437 | ||||||||
\(356\) | 4.38447 | 0.232377 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 10.8229 | 0.572009 | ||||||||
\(359\) | 12.7386 | 0.672319 | 0.336160 | − | 0.941805i | \(-0.390872\pi\) | ||||
0.336160 | + | 0.941805i | \(0.390872\pi\) | |||||||
\(360\) | 3.80776 | 0.200687 | ||||||||
\(361\) | −16.9309 | −0.891098 | ||||||||
\(362\) | 12.3845 | 0.650913 | ||||||||
\(363\) | 7.00000 | 0.367405 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.17708 | 0.480350 | ||||||||
\(366\) | 9.36932 | 0.489742 | ||||||||
\(367\) | 8.36932 | 0.436875 | 0.218437 | − | 0.975851i | \(-0.429904\pi\) | ||||
0.218437 | + | 0.975851i | \(0.429904\pi\) | |||||||
\(368\) | −4.68466 | −0.244205 | ||||||||
\(369\) | 10.2462 | 0.533396 | ||||||||
\(370\) | −8.38447 | −0.435888 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 2.49242 | 0.129226 | ||||||||
\(373\) | 9.68466 | 0.501453 | 0.250726 | − | 0.968058i | \(-0.419331\pi\) | ||||
0.250726 | + | 0.968058i | \(0.419331\pi\) | |||||||
\(374\) | −23.6155 | −1.22113 | ||||||||
\(375\) | −11.8078 | −0.609750 | ||||||||
\(376\) | 16.3002 | 0.840618 | ||||||||
\(377\) | −55.8617 | −2.87703 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.61553 | 0.442550 | 0.221275 | − | 0.975211i | \(-0.428978\pi\) | ||||
0.221275 | + | 0.975211i | \(0.428978\pi\) | |||||||
\(380\) | 0.984845 | 0.0505215 | ||||||||
\(381\) | −1.68466 | −0.0863077 | ||||||||
\(382\) | −1.75379 | −0.0897316 | ||||||||
\(383\) | −4.24621 | −0.216971 | −0.108486 | − | 0.994098i | \(-0.534600\pi\) | ||||
−0.108486 | + | 0.994098i | \(0.534600\pi\) | |||||||
\(384\) | −13.5616 | −0.692060 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 12.3002 | 0.626063 | ||||||||
\(387\) | −0.315342 | −0.0160297 | ||||||||
\(388\) | −6.73863 | −0.342102 | ||||||||
\(389\) | 15.6155 | 0.791739 | 0.395869 | − | 0.918307i | \(-0.370443\pi\) | ||||
0.395869 | + | 0.918307i | \(0.370443\pi\) | |||||||
\(390\) | 14.9309 | 0.756054 | ||||||||
\(391\) | 7.56155 | 0.382404 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12.6847 | 0.639856 | ||||||||
\(394\) | −33.3693 | −1.68112 | ||||||||
\(395\) | 8.49242 | 0.427300 | ||||||||
\(396\) | −0.876894 | −0.0440656 | ||||||||
\(397\) | −22.6155 | −1.13504 | −0.567520 | − | 0.823359i | \(-0.692097\pi\) | ||||
−0.567520 | + | 0.823359i | \(0.692097\pi\) | |||||||
\(398\) | 12.4924 | 0.626189 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 12.0000 | 0.600000 | ||||||||
\(401\) | −0.684658 | −0.0341902 | −0.0170951 | − | 0.999854i | \(-0.505442\pi\) | ||||
−0.0170951 | + | 0.999854i | \(0.505442\pi\) | |||||||
\(402\) | 22.0540 | 1.09995 | ||||||||
\(403\) | −34.8078 | −1.73390 | ||||||||
\(404\) | 0.384472 | 0.0191282 | ||||||||
\(405\) | −1.56155 | −0.0775942 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.87689 | −0.340875 | ||||||||
\(408\) | 18.4384 | 0.912839 | ||||||||
\(409\) | −18.8617 | −0.932653 | −0.466326 | − | 0.884613i | \(-0.654423\pi\) | ||||
−0.466326 | + | 0.884613i | \(0.654423\pi\) | |||||||
\(410\) | −24.9848 | −1.23391 | ||||||||
\(411\) | 7.80776 | 0.385129 | ||||||||
\(412\) | −6.19224 | −0.305070 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1.56155 | 0.0767461 | ||||||||
\(415\) | 7.61553 | 0.373832 | ||||||||
\(416\) | −14.9309 | −0.732046 | ||||||||
\(417\) | 11.9309 | 0.584257 | ||||||||
\(418\) | 4.49242 | 0.219732 | ||||||||
\(419\) | 28.4924 | 1.39195 | 0.695973 | − | 0.718068i | \(-0.254973\pi\) | ||||
0.695973 | + | 0.718068i | \(0.254973\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.31534 | −0.210317 | −0.105158 | − | 0.994455i | \(-0.533535\pi\) | ||||
−0.105158 | + | 0.994455i | \(0.533535\pi\) | |||||||
\(422\) | −11.1231 | −0.541464 | ||||||||
\(423\) | −6.68466 | −0.325019 | ||||||||
\(424\) | 19.0388 | 0.924607 | ||||||||
\(425\) | −19.3693 | −0.939550 | ||||||||
\(426\) | −21.5616 | −1.04466 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −2.73863 | −0.132377 | ||||||||
\(429\) | 12.2462 | 0.591253 | ||||||||
\(430\) | 0.768944 | 0.0370818 | ||||||||
\(431\) | 8.00000 | 0.385346 | 0.192673 | − | 0.981263i | \(-0.438284\pi\) | ||||
0.192673 | + | 0.981263i | \(0.438284\pi\) | |||||||
\(432\) | 4.68466 | 0.225391 | ||||||||
\(433\) | 6.80776 | 0.327160 | 0.163580 | − | 0.986530i | \(-0.447696\pi\) | ||||
0.163580 | + | 0.986530i | \(0.447696\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −14.2462 | −0.683054 | ||||||||
\(436\) | −4.63068 | −0.221770 | ||||||||
\(437\) | −1.43845 | −0.0688103 | ||||||||
\(438\) | 9.17708 | 0.438498 | ||||||||
\(439\) | −15.6155 | −0.745288 | −0.372644 | − | 0.927974i | \(-0.621549\pi\) | ||||
−0.372644 | + | 0.927974i | \(0.621549\pi\) | |||||||
\(440\) | −7.61553 | −0.363056 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 72.3002 | 3.43897 | ||||||||
\(443\) | 13.3153 | 0.632631 | 0.316315 | − | 0.948654i | \(-0.397554\pi\) | ||||
0.316315 | + | 0.948654i | \(0.397554\pi\) | |||||||
\(444\) | −1.50758 | −0.0715465 | ||||||||
\(445\) | −15.6155 | −0.740247 | ||||||||
\(446\) | 32.0000 | 1.51524 | ||||||||
\(447\) | 1.31534 | 0.0622135 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −14.0000 | −0.660701 | −0.330350 | − | 0.943858i | \(-0.607167\pi\) | ||||
−0.330350 | + | 0.943858i | \(0.607167\pi\) | |||||||
\(450\) | −4.00000 | −0.188562 | ||||||||
\(451\) | −20.4924 | −0.964950 | ||||||||
\(452\) | 4.30019 | 0.202264 | ||||||||
\(453\) | 18.2462 | 0.857282 | ||||||||
\(454\) | −3.12311 | −0.146575 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.50758 | −0.164257 | ||||||||
\(457\) | 1.43845 | 0.0672877 | 0.0336439 | − | 0.999434i | \(-0.489289\pi\) | ||||
0.0336439 | + | 0.999434i | \(0.489289\pi\) | |||||||
\(458\) | 45.7538 | 2.13793 | ||||||||
\(459\) | −7.56155 | −0.352943 | ||||||||
\(460\) | −0.684658 | −0.0319224 | ||||||||
\(461\) | 4.24621 | 0.197766 | 0.0988829 | − | 0.995099i | \(-0.468473\pi\) | ||||
0.0988829 | + | 0.995099i | \(0.468473\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.6847 | 0.914824 | 0.457412 | − | 0.889255i | \(-0.348777\pi\) | ||||
0.457412 | + | 0.889255i | \(0.348777\pi\) | |||||||
\(464\) | 42.7386 | 1.98409 | ||||||||
\(465\) | −8.87689 | −0.411656 | ||||||||
\(466\) | −16.9848 | −0.786808 | ||||||||
\(467\) | −1.12311 | −0.0519711 | −0.0259856 | − | 0.999662i | \(-0.508272\pi\) | ||||
−0.0259856 | + | 0.999662i | \(0.508272\pi\) | |||||||
\(468\) | 2.68466 | 0.124098 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 16.3002 | 0.751872 | ||||||||
\(471\) | 4.24621 | 0.195655 | ||||||||
\(472\) | 22.2462 | 1.02396 | ||||||||
\(473\) | 0.630683 | 0.0289988 | ||||||||
\(474\) | 8.49242 | 0.390070 | ||||||||
\(475\) | 3.68466 | 0.169064 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.80776 | −0.357493 | ||||||||
\(478\) | −28.4924 | −1.30321 | ||||||||
\(479\) | 19.3693 | 0.885007 | 0.442503 | − | 0.896767i | \(-0.354090\pi\) | ||||
0.442503 | + | 0.896767i | \(0.354090\pi\) | |||||||
\(480\) | −3.80776 | −0.173800 | ||||||||
\(481\) | 21.0540 | 0.959979 | ||||||||
\(482\) | −3.12311 | −0.142254 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.06913 | −0.139506 | ||||||||
\(485\) | 24.0000 | 1.08978 | ||||||||
\(486\) | −1.56155 | −0.0708335 | ||||||||
\(487\) | 22.4233 | 1.01610 | 0.508048 | − | 0.861329i | \(-0.330367\pi\) | ||||
0.508048 | + | 0.861329i | \(0.330367\pi\) | |||||||
\(488\) | 14.6307 | 0.662300 | ||||||||
\(489\) | −4.00000 | −0.180886 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −30.6847 | −1.38478 | −0.692390 | − | 0.721524i | \(-0.743442\pi\) | ||||
−0.692390 | + | 0.721524i | \(0.743442\pi\) | |||||||
\(492\) | −4.49242 | −0.202534 | ||||||||
\(493\) | −68.9848 | −3.10692 | ||||||||
\(494\) | −13.7538 | −0.618812 | ||||||||
\(495\) | 3.12311 | 0.140373 | ||||||||
\(496\) | 26.6307 | 1.19575 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 7.61553 | 0.341260 | ||||||||
\(499\) | −35.6847 | −1.59746 | −0.798732 | − | 0.601686i | \(-0.794496\pi\) | ||||
−0.798732 | + | 0.601686i | \(0.794496\pi\) | |||||||
\(500\) | 5.17708 | 0.231526 | ||||||||
\(501\) | −3.31534 | −0.148119 | ||||||||
\(502\) | −3.12311 | −0.139391 | ||||||||
\(503\) | −9.36932 | −0.417757 | −0.208879 | − | 0.977942i | \(-0.566981\pi\) | ||||
−0.208879 | + | 0.977942i | \(0.566981\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.36932 | −0.0609338 | ||||||||
\(506\) | −3.12311 | −0.138839 | ||||||||
\(507\) | −24.4924 | −1.08775 | ||||||||
\(508\) | 0.738634 | 0.0327716 | ||||||||
\(509\) | −4.87689 | −0.216165 | −0.108082 | − | 0.994142i | \(-0.534471\pi\) | ||||
−0.108082 | + | 0.994142i | \(0.534471\pi\) | |||||||
\(510\) | 18.4384 | 0.816468 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −11.4233 | −0.504843 | ||||||||
\(513\) | 1.43845 | 0.0635090 | ||||||||
\(514\) | 10.3542 | 0.456703 | ||||||||
\(515\) | 22.0540 | 0.971814 | ||||||||
\(516\) | 0.138261 | 0.00608658 | ||||||||
\(517\) | 13.3693 | 0.587982 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −23.3693 | −1.02580 | ||||||||
\(520\) | 23.3153 | 1.02245 | ||||||||
\(521\) | 30.6847 | 1.34432 | 0.672160 | − | 0.740406i | \(-0.265367\pi\) | ||||
0.672160 | + | 0.740406i | \(0.265367\pi\) | |||||||
\(522\) | −14.2462 | −0.623540 | ||||||||
\(523\) | −18.3693 | −0.803234 | −0.401617 | − | 0.915808i | \(-0.631552\pi\) | ||||
−0.401617 | + | 0.915808i | \(0.631552\pi\) | |||||||
\(524\) | −5.56155 | −0.242958 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7.01515 | 0.305875 | ||||||||
\(527\) | −42.9848 | −1.87245 | ||||||||
\(528\) | −9.36932 | −0.407747 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 19.0388 | 0.826994 | ||||||||
\(531\) | −9.12311 | −0.395909 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 62.7386 | 2.71751 | ||||||||
\(534\) | −15.6155 | −0.675750 | ||||||||
\(535\) | 9.75379 | 0.421693 | ||||||||
\(536\) | 34.4384 | 1.48751 | ||||||||
\(537\) | −6.93087 | −0.299089 | ||||||||
\(538\) | 13.2614 | 0.571738 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.684658 | 0.0294630 | ||||||||
\(541\) | 3.73863 | 0.160736 | 0.0803682 | − | 0.996765i | \(-0.474390\pi\) | ||||
0.0803682 | + | 0.996765i | \(0.474390\pi\) | |||||||
\(542\) | 30.6307 | 1.31570 | ||||||||
\(543\) | −7.93087 | −0.340346 | ||||||||
\(544\) | −18.4384 | −0.790542 | ||||||||
\(545\) | 16.4924 | 0.706458 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 29.3693 | 1.25574 | 0.627871 | − | 0.778318i | \(-0.283927\pi\) | ||||
0.627871 | + | 0.778318i | \(0.283927\pi\) | |||||||
\(548\) | −3.42329 | −0.146236 | ||||||||
\(549\) | −6.00000 | −0.256074 | ||||||||
\(550\) | 8.00000 | 0.341121 | ||||||||
\(551\) | 13.1231 | 0.559063 | ||||||||
\(552\) | 2.43845 | 0.103787 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −45.6695 | −1.94031 | ||||||||
\(555\) | 5.36932 | 0.227915 | ||||||||
\(556\) | −5.23106 | −0.221846 | ||||||||
\(557\) | 32.2462 | 1.36632 | 0.683158 | − | 0.730271i | \(-0.260606\pi\) | ||||
0.683158 | + | 0.730271i | \(0.260606\pi\) | |||||||
\(558\) | −8.87689 | −0.375789 | ||||||||
\(559\) | −1.93087 | −0.0816671 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 15.1231 | 0.638498 | ||||||||
\(562\) | 30.5464 | 1.28852 | ||||||||
\(563\) | 14.2462 | 0.600406 | 0.300203 | − | 0.953875i | \(-0.402946\pi\) | ||||
0.300203 | + | 0.953875i | \(0.402946\pi\) | |||||||
\(564\) | 2.93087 | 0.123412 | ||||||||
\(565\) | −15.3153 | −0.644321 | ||||||||
\(566\) | 37.6695 | 1.58337 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −33.6695 | −1.41274 | ||||||||
\(569\) | −25.1771 | −1.05548 | −0.527739 | − | 0.849407i | \(-0.676960\pi\) | ||||
−0.527739 | + | 0.849407i | \(0.676960\pi\) | |||||||
\(570\) | −3.50758 | −0.146916 | ||||||||
\(571\) | 40.8617 | 1.71001 | 0.855005 | − | 0.518619i | \(-0.173554\pi\) | ||||
0.855005 | + | 0.518619i | \(0.173554\pi\) | |||||||
\(572\) | −5.36932 | −0.224502 | ||||||||
\(573\) | 1.12311 | 0.0469184 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.56155 | −0.106824 | ||||||||
\(576\) | 5.56155 | 0.231731 | ||||||||
\(577\) | −10.3153 | −0.429433 | −0.214717 | − | 0.976676i | \(-0.568883\pi\) | ||||
−0.214717 | + | 0.976676i | \(0.568883\pi\) | |||||||
\(578\) | 62.7386 | 2.60958 | ||||||||
\(579\) | −7.87689 | −0.327353 | ||||||||
\(580\) | 6.24621 | 0.259360 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 24.0000 | 0.994832 | ||||||||
\(583\) | 15.6155 | 0.646729 | ||||||||
\(584\) | 14.3305 | 0.593000 | ||||||||
\(585\) | −9.56155 | −0.395322 | ||||||||
\(586\) | −37.5616 | −1.55165 | ||||||||
\(587\) | −0.438447 | −0.0180967 | −0.00904833 | − | 0.999959i | \(-0.502880\pi\) | ||||
−0.00904833 | + | 0.999959i | \(0.502880\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.17708 | 0.336931 | ||||||||
\(590\) | 22.2462 | 0.915862 | ||||||||
\(591\) | 21.3693 | 0.879016 | ||||||||
\(592\) | −16.1080 | −0.662033 | ||||||||
\(593\) | 10.0000 | 0.410651 | 0.205325 | − | 0.978694i | \(-0.434175\pi\) | ||||
0.205325 | + | 0.978694i | \(0.434175\pi\) | |||||||
\(594\) | 3.12311 | 0.128143 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.576708 | −0.0236229 | ||||||||
\(597\) | −8.00000 | −0.327418 | ||||||||
\(598\) | 9.56155 | 0.391001 | ||||||||
\(599\) | −37.1771 | −1.51901 | −0.759507 | − | 0.650499i | \(-0.774560\pi\) | ||||
−0.759507 | + | 0.650499i | \(0.774560\pi\) | |||||||
\(600\) | −6.24621 | −0.255001 | ||||||||
\(601\) | −5.05398 | −0.206156 | −0.103078 | − | 0.994673i | \(-0.532869\pi\) | ||||
−0.103078 | + | 0.994673i | \(0.532869\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −14.1231 | −0.575137 | ||||||||
\(604\) | −8.00000 | −0.325515 | ||||||||
\(605\) | 10.9309 | 0.444403 | ||||||||
\(606\) | −1.36932 | −0.0556247 | ||||||||
\(607\) | −42.8078 | −1.73751 | −0.868757 | − | 0.495239i | \(-0.835080\pi\) | ||||
−0.868757 | + | 0.495239i | \(0.835080\pi\) | |||||||
\(608\) | 3.50758 | 0.142251 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 14.6307 | 0.592379 | ||||||||
\(611\) | −40.9309 | −1.65589 | ||||||||
\(612\) | 3.31534 | 0.134015 | ||||||||
\(613\) | 26.0000 | 1.05013 | 0.525065 | − | 0.851062i | \(-0.324041\pi\) | ||||
0.525065 | + | 0.851062i | \(0.324041\pi\) | |||||||
\(614\) | −18.2462 | −0.736357 | ||||||||
\(615\) | 16.0000 | 0.645182 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.930870 | −0.0374754 | −0.0187377 | − | 0.999824i | \(-0.505965\pi\) | ||||
−0.0187377 | + | 0.999824i | \(0.505965\pi\) | |||||||
\(618\) | 22.0540 | 0.887141 | ||||||||
\(619\) | 22.1231 | 0.889203 | 0.444601 | − | 0.895729i | \(-0.353345\pi\) | ||||
0.444601 | + | 0.895729i | \(0.353345\pi\) | |||||||
\(620\) | 3.89205 | 0.156308 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | −11.8078 | −0.473448 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 28.6847 | 1.14831 | ||||||||
\(625\) | −5.63068 | −0.225227 | ||||||||
\(626\) | −45.7538 | −1.82869 | ||||||||
\(627\) | −2.87689 | −0.114892 | ||||||||
\(628\) | −1.86174 | −0.0742915 | ||||||||
\(629\) | 26.0000 | 1.03669 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.94602 | 0.236708 | 0.118354 | − | 0.992971i | \(-0.462238\pi\) | ||||
0.118354 | + | 0.992971i | \(0.462238\pi\) | |||||||
\(632\) | 13.2614 | 0.527509 | ||||||||
\(633\) | 7.12311 | 0.283118 | ||||||||
\(634\) | −18.3542 | −0.728937 | ||||||||
\(635\) | −2.63068 | −0.104395 | ||||||||
\(636\) | 3.42329 | 0.135742 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 28.4924 | 1.12803 | ||||||||
\(639\) | 13.8078 | 0.546227 | ||||||||
\(640\) | −21.1771 | −0.837098 | ||||||||
\(641\) | −34.4384 | −1.36024 | −0.680118 | − | 0.733102i | \(-0.738072\pi\) | ||||
−0.680118 | + | 0.733102i | \(0.738072\pi\) | |||||||
\(642\) | 9.75379 | 0.384951 | ||||||||
\(643\) | −37.4384 | −1.47643 | −0.738214 | − | 0.674566i | \(-0.764331\pi\) | ||||
−0.738214 | + | 0.674566i | \(0.764331\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.492423 | −0.0193891 | ||||||||
\(646\) | −16.9848 | −0.668260 | ||||||||
\(647\) | −0.630683 | −0.0247947 | −0.0123974 | − | 0.999923i | \(-0.503946\pi\) | ||||
−0.0123974 | + | 0.999923i | \(0.503946\pi\) | |||||||
\(648\) | −2.43845 | −0.0957913 | ||||||||
\(649\) | 18.2462 | 0.716226 | ||||||||
\(650\) | −24.4924 | −0.960672 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.75379 | 0.0686837 | ||||||||
\(653\) | 10.4924 | 0.410600 | 0.205300 | − | 0.978699i | \(-0.434183\pi\) | ||||
0.205300 | + | 0.978699i | \(0.434183\pi\) | |||||||
\(654\) | 16.4924 | 0.644905 | ||||||||
\(655\) | 19.8078 | 0.773953 | ||||||||
\(656\) | −48.0000 | −1.87409 | ||||||||
\(657\) | −5.87689 | −0.229279 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −0.384472 | −0.0149769 | −0.00748845 | − | 0.999972i | \(-0.502384\pi\) | ||||
−0.00748845 | + | 0.999972i | \(0.502384\pi\) | |||||||
\(660\) | −1.36932 | −0.0533006 | ||||||||
\(661\) | −28.8078 | −1.12049 | −0.560246 | − | 0.828326i | \(-0.689293\pi\) | ||||
−0.560246 | + | 0.828326i | \(0.689293\pi\) | |||||||
\(662\) | −24.1080 | −0.936982 | ||||||||
\(663\) | −46.3002 | −1.79815 | ||||||||
\(664\) | 11.8920 | 0.461501 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 5.36932 | 0.208057 | ||||||||
\(667\) | −9.12311 | −0.353248 | ||||||||
\(668\) | 1.45360 | 0.0562416 | ||||||||
\(669\) | −20.4924 | −0.792283 | ||||||||
\(670\) | 34.4384 | 1.33047 | ||||||||
\(671\) | 12.0000 | 0.463255 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.68466 | −0.0649388 | −0.0324694 | − | 0.999473i | \(-0.510337\pi\) | ||||
−0.0324694 | + | 0.999473i | \(0.510337\pi\) | |||||||
\(674\) | −32.4924 | −1.25156 | ||||||||
\(675\) | 2.56155 | 0.0985942 | ||||||||
\(676\) | 10.7386 | 0.413024 | ||||||||
\(677\) | −40.9309 | −1.57310 | −0.786551 | − | 0.617526i | \(-0.788135\pi\) | ||||
−0.786551 | + | 0.617526i | \(0.788135\pi\) | |||||||
\(678\) | −15.3153 | −0.588182 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 28.7926 | 1.10415 | ||||||||
\(681\) | 2.00000 | 0.0766402 | ||||||||
\(682\) | 17.7538 | 0.679828 | ||||||||
\(683\) | −14.0540 | −0.537760 | −0.268880 | − | 0.963174i | \(-0.586654\pi\) | ||||
−0.268880 | + | 0.963174i | \(0.586654\pi\) | |||||||
\(684\) | −0.630683 | −0.0241148 | ||||||||
\(685\) | 12.1922 | 0.465841 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −29.3002 | −1.11787 | ||||||||
\(688\) | 1.47727 | 0.0563203 | ||||||||
\(689\) | −47.8078 | −1.82133 | ||||||||
\(690\) | 2.43845 | 0.0928301 | ||||||||
\(691\) | −14.8078 | −0.563314 | −0.281657 | − | 0.959515i | \(-0.590884\pi\) | ||||
−0.281657 | + | 0.959515i | \(0.590884\pi\) | |||||||
\(692\) | 10.2462 | 0.389503 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −19.8078 | −0.751892 | ||||||||
\(695\) | 18.6307 | 0.706702 | ||||||||
\(696\) | −22.2462 | −0.843240 | ||||||||
\(697\) | 77.4773 | 2.93466 | ||||||||
\(698\) | −1.45360 | −0.0550197 | ||||||||
\(699\) | 10.8769 | 0.411402 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.17708 | 0.271075 | 0.135537 | − | 0.990772i | \(-0.456724\pi\) | ||||
0.135537 | + | 0.990772i | \(0.456724\pi\) | |||||||
\(702\) | −9.56155 | −0.360878 | ||||||||
\(703\) | −4.94602 | −0.186543 | ||||||||
\(704\) | −11.1231 | −0.419218 | ||||||||
\(705\) | −10.4384 | −0.393135 | ||||||||
\(706\) | 11.5076 | 0.433093 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 4.00000 | 0.150329 | ||||||||
\(709\) | 20.6307 | 0.774802 | 0.387401 | − | 0.921911i | \(-0.373373\pi\) | ||||
0.387401 | + | 0.921911i | \(0.373373\pi\) | |||||||
\(710\) | −33.6695 | −1.26359 | ||||||||
\(711\) | −5.43845 | −0.203958 | ||||||||
\(712\) | −24.3845 | −0.913847 | ||||||||
\(713\) | −5.68466 | −0.212892 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 19.1231 | 0.715164 | ||||||||
\(716\) | 3.03882 | 0.113566 | ||||||||
\(717\) | 18.2462 | 0.681417 | ||||||||
\(718\) | 19.8920 | 0.742365 | ||||||||
\(719\) | 36.5464 | 1.36295 | 0.681475 | − | 0.731841i | \(-0.261339\pi\) | ||||
0.681475 | + | 0.731841i | \(0.261339\pi\) | |||||||
\(720\) | 7.31534 | 0.272627 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −26.4384 | −0.983937 | ||||||||
\(723\) | 2.00000 | 0.0743808 | ||||||||
\(724\) | 3.47727 | 0.129232 | ||||||||
\(725\) | 23.3693 | 0.867915 | ||||||||
\(726\) | 10.9309 | 0.405683 | ||||||||
\(727\) | −28.3153 | −1.05016 | −0.525079 | − | 0.851054i | \(-0.675964\pi\) | ||||
−0.525079 | + | 0.851054i | \(0.675964\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 14.3305 | 0.530395 | ||||||||
\(731\) | −2.38447 | −0.0881929 | ||||||||
\(732\) | 2.63068 | 0.0972328 | ||||||||
\(733\) | 1.30019 | 0.0480235 | 0.0240117 | − | 0.999712i | \(-0.492356\pi\) | ||||
0.0240117 | + | 0.999712i | \(0.492356\pi\) | |||||||
\(734\) | 13.0691 | 0.482390 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.43845 | −0.0898824 | ||||||||
\(737\) | 28.2462 | 1.04046 | ||||||||
\(738\) | 16.0000 | 0.588968 | ||||||||
\(739\) | −28.6695 | −1.05462 | −0.527312 | − | 0.849672i | \(-0.676800\pi\) | ||||
−0.527312 | + | 0.849672i | \(0.676800\pi\) | |||||||
\(740\) | −2.35416 | −0.0865407 | ||||||||
\(741\) | 8.80776 | 0.323561 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 27.6155 | 1.01312 | 0.506558 | − | 0.862206i | \(-0.330918\pi\) | ||||
0.506558 | + | 0.862206i | \(0.330918\pi\) | |||||||
\(744\) | −13.8617 | −0.508196 | ||||||||
\(745\) | 2.05398 | 0.0752518 | ||||||||
\(746\) | 15.1231 | 0.553696 | ||||||||
\(747\) | −4.87689 | −0.178436 | ||||||||
\(748\) | −6.63068 | −0.242442 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −18.4384 | −0.673277 | ||||||||
\(751\) | 29.9309 | 1.09219 | 0.546096 | − | 0.837722i | \(-0.316113\pi\) | ||||
0.546096 | + | 0.837722i | \(0.316113\pi\) | |||||||
\(752\) | 31.3153 | 1.14195 | ||||||||
\(753\) | 2.00000 | 0.0728841 | ||||||||
\(754\) | −87.2311 | −3.17677 | ||||||||
\(755\) | 28.4924 | 1.03695 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −21.6155 | −0.785630 | −0.392815 | − | 0.919618i | \(-0.628499\pi\) | ||||
−0.392815 | + | 0.919618i | \(0.628499\pi\) | |||||||
\(758\) | 13.4536 | 0.488657 | ||||||||
\(759\) | 2.00000 | 0.0725954 | ||||||||
\(760\) | −5.47727 | −0.198681 | ||||||||
\(761\) | 6.38447 | 0.231437 | 0.115718 | − | 0.993282i | \(-0.463083\pi\) | ||||
0.115718 | + | 0.993282i | \(0.463083\pi\) | |||||||
\(762\) | −2.63068 | −0.0952996 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −0.492423 | −0.0178152 | ||||||||
\(765\) | −11.8078 | −0.426911 | ||||||||
\(766\) | −6.63068 | −0.239576 | ||||||||
\(767\) | −55.8617 | −2.01705 | ||||||||
\(768\) | −10.0540 | −0.362792 | ||||||||
\(769\) | 18.8078 | 0.678225 | 0.339113 | − | 0.940746i | \(-0.389873\pi\) | ||||
0.339113 | + | 0.940746i | \(0.389873\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.63068 | −0.238798 | ||||||||
\(772\) | 3.45360 | 0.124298 | ||||||||
\(773\) | 30.3002 | 1.08982 | 0.544911 | − | 0.838494i | \(-0.316563\pi\) | ||||
0.544911 | + | 0.838494i | \(0.316563\pi\) | |||||||
\(774\) | −0.492423 | −0.0176998 | ||||||||
\(775\) | 14.5616 | 0.523066 | ||||||||
\(776\) | 37.4773 | 1.34536 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 24.3845 | 0.874226 | ||||||||
\(779\) | −14.7386 | −0.528066 | ||||||||
\(780\) | 4.19224 | 0.150106 | ||||||||
\(781\) | −27.6155 | −0.988161 | ||||||||
\(782\) | 11.8078 | 0.422245 | ||||||||
\(783\) | 9.12311 | 0.326033 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.63068 | 0.236659 | ||||||||
\(786\) | 19.8078 | 0.706520 | ||||||||
\(787\) | 45.5616 | 1.62409 | 0.812047 | − | 0.583592i | \(-0.198353\pi\) | ||||
0.812047 | + | 0.583592i | \(0.198353\pi\) | |||||||
\(788\) | −9.36932 | −0.333768 | ||||||||
\(789\) | −4.49242 | −0.159934 | ||||||||
\(790\) | 13.2614 | 0.471818 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 4.87689 | 0.173293 | ||||||||
\(793\) | −36.7386 | −1.30463 | ||||||||
\(794\) | −35.3153 | −1.25329 | ||||||||
\(795\) | −12.1922 | −0.432414 | ||||||||
\(796\) | 3.50758 | 0.124323 | ||||||||
\(797\) | 30.0540 | 1.06457 | 0.532283 | − | 0.846566i | \(-0.321334\pi\) | ||||
0.532283 | + | 0.846566i | \(0.321334\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −50.5464 | −1.78820 | ||||||||
\(800\) | 6.24621 | 0.220837 | ||||||||
\(801\) | 10.0000 | 0.353333 | ||||||||
\(802\) | −1.06913 | −0.0377523 | ||||||||
\(803\) | 11.7538 | 0.414782 | ||||||||
\(804\) | 6.19224 | 0.218383 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −54.3542 | −1.91454 | ||||||||
\(807\) | −8.49242 | −0.298947 | ||||||||
\(808\) | −2.13826 | −0.0752237 | ||||||||
\(809\) | −18.6307 | −0.655020 | −0.327510 | − | 0.944848i | \(-0.606210\pi\) | ||||
−0.327510 | + | 0.944848i | \(0.606210\pi\) | |||||||
\(810\) | −2.43845 | −0.0856783 | ||||||||
\(811\) | 19.6155 | 0.688794 | 0.344397 | − | 0.938824i | \(-0.388083\pi\) | ||||
0.344397 | + | 0.938824i | \(0.388083\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −19.6155 | −0.687947 | ||||||||
\(814\) | −10.7386 | −0.376389 | ||||||||
\(815\) | −6.24621 | −0.218795 | ||||||||
\(816\) | 35.4233 | 1.24006 | ||||||||
\(817\) | 0.453602 | 0.0158695 | ||||||||
\(818\) | −29.4536 | −1.02982 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −7.01515 | −0.244980 | ||||||||
\(821\) | −12.7386 | −0.444581 | −0.222291 | − | 0.974980i | \(-0.571353\pi\) | ||||
−0.222291 | + | 0.974980i | \(0.571353\pi\) | |||||||
\(822\) | 12.1922 | 0.425253 | ||||||||
\(823\) | 29.8617 | 1.04091 | 0.520457 | − | 0.853888i | \(-0.325761\pi\) | ||||
0.520457 | + | 0.853888i | \(0.325761\pi\) | |||||||
\(824\) | 34.4384 | 1.19972 | ||||||||
\(825\) | −5.12311 | −0.178364 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 22.7386 | 0.790700 | 0.395350 | − | 0.918531i | \(-0.370623\pi\) | ||||
0.395350 | + | 0.918531i | \(0.370623\pi\) | |||||||
\(828\) | 0.438447 | 0.0152371 | ||||||||
\(829\) | −1.49242 | −0.0518340 | −0.0259170 | − | 0.999664i | \(-0.508251\pi\) | ||||
−0.0259170 | + | 0.999664i | \(0.508251\pi\) | |||||||
\(830\) | 11.8920 | 0.412779 | ||||||||
\(831\) | 29.2462 | 1.01454 | ||||||||
\(832\) | 34.0540 | 1.18061 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 18.6307 | 0.645128 | ||||||||
\(835\) | −5.17708 | −0.179160 | ||||||||
\(836\) | 1.26137 | 0.0436253 | ||||||||
\(837\) | 5.68466 | 0.196491 | ||||||||
\(838\) | 44.4924 | 1.53697 | ||||||||
\(839\) | 20.6307 | 0.712250 | 0.356125 | − | 0.934438i | \(-0.384098\pi\) | ||||
0.356125 | + | 0.934438i | \(0.384098\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 54.2311 | 1.87004 | ||||||||
\(842\) | −6.73863 | −0.232229 | ||||||||
\(843\) | −19.5616 | −0.673736 | ||||||||
\(844\) | −3.12311 | −0.107502 | ||||||||
\(845\) | −38.2462 | −1.31571 | ||||||||
\(846\) | −10.4384 | −0.358881 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 36.5767 | 1.25605 | ||||||||
\(849\) | −24.1231 | −0.827903 | ||||||||
\(850\) | −30.2462 | −1.03744 | ||||||||
\(851\) | 3.43845 | 0.117868 | ||||||||
\(852\) | −6.05398 | −0.207406 | ||||||||
\(853\) | 31.9309 | 1.09329 | 0.546646 | − | 0.837364i | \(-0.315904\pi\) | ||||
0.546646 | + | 0.837364i | \(0.315904\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.24621 | 0.0768188 | ||||||||
\(856\) | 15.2311 | 0.520587 | ||||||||
\(857\) | −17.3693 | −0.593325 | −0.296662 | − | 0.954982i | \(-0.595874\pi\) | ||||
−0.296662 | + | 0.954982i | \(0.595874\pi\) | |||||||
\(858\) | 19.1231 | 0.652852 | ||||||||
\(859\) | 26.2462 | 0.895509 | 0.447755 | − | 0.894156i | \(-0.352224\pi\) | ||||
0.447755 | + | 0.894156i | \(0.352224\pi\) | |||||||
\(860\) | 0.215901 | 0.00736217 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 12.4924 | 0.425494 | ||||||||
\(863\) | −6.30019 | −0.214461 | −0.107230 | − | 0.994234i | \(-0.534198\pi\) | ||||
−0.107230 | + | 0.994234i | \(0.534198\pi\) | |||||||
\(864\) | 2.43845 | 0.0829577 | ||||||||
\(865\) | −36.4924 | −1.24078 | ||||||||
\(866\) | 10.6307 | 0.361245 | ||||||||
\(867\) | −40.1771 | −1.36449 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 10.8769 | 0.368973 | ||||||||
\(870\) | −22.2462 | −0.754217 | ||||||||
\(871\) | −86.4773 | −2.93017 | ||||||||
\(872\) | 25.7538 | 0.872133 | ||||||||
\(873\) | −15.3693 | −0.520173 | ||||||||
\(874\) | −2.24621 | −0.0759792 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.57671 | 0.0870589 | ||||||||
\(877\) | −24.0540 | −0.812245 | −0.406123 | − | 0.913819i | \(-0.633119\pi\) | ||||
−0.406123 | + | 0.913819i | \(0.633119\pi\) | |||||||
\(878\) | −24.3845 | −0.822936 | ||||||||
\(879\) | 24.0540 | 0.811320 | ||||||||
\(880\) | −14.6307 | −0.493200 | ||||||||
\(881\) | −5.31534 | −0.179078 | −0.0895392 | − | 0.995983i | \(-0.528539\pi\) | ||||
−0.0895392 | + | 0.995983i | \(0.528539\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.06913 | −0.0696318 | −0.0348159 | − | 0.999394i | \(-0.511084\pi\) | ||||
−0.0348159 | + | 0.999394i | \(0.511084\pi\) | |||||||
\(884\) | 20.3002 | 0.682769 | ||||||||
\(885\) | −14.2462 | −0.478881 | ||||||||
\(886\) | 20.7926 | 0.698541 | ||||||||
\(887\) | −0.630683 | −0.0211763 | −0.0105881 | − | 0.999944i | \(-0.503370\pi\) | ||||
−0.0105881 | + | 0.999944i | \(0.503370\pi\) | |||||||
\(888\) | 8.38447 | 0.281364 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −24.3845 | −0.817369 | ||||||||
\(891\) | −2.00000 | −0.0670025 | ||||||||
\(892\) | 8.98485 | 0.300835 | ||||||||
\(893\) | 9.61553 | 0.321771 | ||||||||
\(894\) | 2.05398 | 0.0686952 | ||||||||
\(895\) | −10.8229 | −0.361770 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.12311 | −0.204445 | ||||||||
\(898\) | −21.8617 | −0.729536 | ||||||||
\(899\) | 51.8617 | 1.72969 | ||||||||
\(900\) | −1.12311 | −0.0374369 | ||||||||
\(901\) | −59.0388 | −1.96687 | ||||||||
\(902\) | −32.0000 | −1.06548 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −23.9157 | −0.795425 | ||||||||
\(905\) | −12.3845 | −0.411674 | ||||||||
\(906\) | 28.4924 | 0.946597 | ||||||||
\(907\) | 7.73863 | 0.256957 | 0.128479 | − | 0.991712i | \(-0.458991\pi\) | ||||
0.128479 | + | 0.991712i | \(0.458991\pi\) | |||||||
\(908\) | −0.876894 | −0.0291008 | ||||||||
\(909\) | 0.876894 | 0.0290848 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40.4924 | 1.34157 | 0.670787 | − | 0.741650i | \(-0.265957\pi\) | ||||
0.670787 | + | 0.741650i | \(0.265957\pi\) | |||||||
\(912\) | −6.73863 | −0.223138 | ||||||||
\(913\) | 9.75379 | 0.322803 | ||||||||
\(914\) | 2.24621 | 0.0742981 | ||||||||
\(915\) | −9.36932 | −0.309740 | ||||||||
\(916\) | 12.8466 | 0.424463 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −11.8078 | −0.389714 | ||||||||
\(919\) | −39.4924 | −1.30273 | −0.651367 | − | 0.758762i | \(-0.725804\pi\) | ||||
−0.651367 | + | 0.758762i | \(0.725804\pi\) | |||||||
\(920\) | 3.80776 | 0.125538 | ||||||||
\(921\) | 11.6847 | 0.385023 | ||||||||
\(922\) | 6.63068 | 0.218370 | ||||||||
\(923\) | 84.5464 | 2.78288 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.80776 | −0.289597 | ||||||||
\(926\) | 30.7386 | 1.01013 | ||||||||
\(927\) | −14.1231 | −0.463864 | ||||||||
\(928\) | 22.2462 | 0.730268 | ||||||||
\(929\) | −3.50758 | −0.115080 | −0.0575399 | − | 0.998343i | \(-0.518326\pi\) | ||||
−0.0575399 | + | 0.998343i | \(0.518326\pi\) | |||||||
\(930\) | −13.8617 | −0.454544 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −4.76894 | −0.156212 | ||||||||
\(933\) | 7.56155 | 0.247554 | ||||||||
\(934\) | −1.75379 | −0.0573857 | ||||||||
\(935\) | 23.6155 | 0.772310 | ||||||||
\(936\) | −14.9309 | −0.488031 | ||||||||
\(937\) | 1.93087 | 0.0630788 | 0.0315394 | − | 0.999503i | \(-0.489959\pi\) | ||||
0.0315394 | + | 0.999503i | \(0.489959\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 29.3002 | 0.956175 | ||||||||
\(940\) | 4.57671 | 0.149276 | ||||||||
\(941\) | 15.1231 | 0.492999 | 0.246500 | − | 0.969143i | \(-0.420720\pi\) | ||||
0.246500 | + | 0.969143i | \(0.420720\pi\) | |||||||
\(942\) | 6.63068 | 0.216039 | ||||||||
\(943\) | 10.2462 | 0.333663 | ||||||||
\(944\) | 42.7386 | 1.39102 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.984845 | 0.0320201 | ||||||||
\(947\) | −17.3153 | −0.562673 | −0.281336 | − | 0.959609i | \(-0.590778\pi\) | ||||
−0.281336 | + | 0.959609i | \(0.590778\pi\) | |||||||
\(948\) | 2.38447 | 0.0774440 | ||||||||
\(949\) | −35.9848 | −1.16812 | ||||||||
\(950\) | 5.75379 | 0.186678 | ||||||||
\(951\) | 11.7538 | 0.381143 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.00000 | 0.194359 | 0.0971795 | − | 0.995267i | \(-0.469018\pi\) | ||||
0.0971795 | + | 0.995267i | \(0.469018\pi\) | |||||||
\(954\) | −12.1922 | −0.394738 | ||||||||
\(955\) | 1.75379 | 0.0567513 | ||||||||
\(956\) | −8.00000 | −0.258738 | ||||||||
\(957\) | −18.2462 | −0.589816 | ||||||||
\(958\) | 30.2462 | 0.977211 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 8.68466 | 0.280296 | ||||||||
\(961\) | 1.31534 | 0.0424304 | ||||||||
\(962\) | 32.8769 | 1.05999 | ||||||||
\(963\) | −6.24621 | −0.201281 | ||||||||
\(964\) | −0.876894 | −0.0282429 | ||||||||
\(965\) | −12.3002 | −0.395957 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −40.8078 | −1.31229 | −0.656145 | − | 0.754635i | \(-0.727814\pi\) | ||||
−0.656145 | + | 0.754635i | \(0.727814\pi\) | |||||||
\(968\) | 17.0691 | 0.548623 | ||||||||
\(969\) | 10.8769 | 0.349416 | ||||||||
\(970\) | 37.4773 | 1.20332 | ||||||||
\(971\) | 9.12311 | 0.292774 | 0.146387 | − | 0.989227i | \(-0.453235\pi\) | ||||
0.146387 | + | 0.989227i | \(0.453235\pi\) | |||||||
\(972\) | −0.438447 | −0.0140632 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 35.0152 | 1.12196 | ||||||||
\(975\) | 15.6847 | 0.502311 | ||||||||
\(976\) | 28.1080 | 0.899714 | ||||||||
\(977\) | −8.43845 | −0.269970 | −0.134985 | − | 0.990848i | \(-0.543099\pi\) | ||||
−0.134985 | + | 0.990848i | \(0.543099\pi\) | |||||||
\(978\) | −6.24621 | −0.199732 | ||||||||
\(979\) | −20.0000 | −0.639203 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.5616 | −0.337204 | ||||||||
\(982\) | −47.9157 | −1.52905 | ||||||||
\(983\) | −5.36932 | −0.171255 | −0.0856273 | − | 0.996327i | \(-0.527289\pi\) | ||||
−0.0856273 | + | 0.996327i | \(0.527289\pi\) | |||||||
\(984\) | 24.9848 | 0.796488 | ||||||||
\(985\) | 33.3693 | 1.06323 | ||||||||
\(986\) | −107.723 | −3.43061 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.86174 | −0.122858 | ||||||||
\(989\) | −0.315342 | −0.0100273 | ||||||||
\(990\) | 4.87689 | 0.154998 | ||||||||
\(991\) | −7.30019 | −0.231898 | −0.115949 | − | 0.993255i | \(-0.536991\pi\) | ||||
−0.115949 | + | 0.993255i | \(0.536991\pi\) | |||||||
\(992\) | 13.8617 | 0.440111 | ||||||||
\(993\) | 15.4384 | 0.489924 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −12.4924 | −0.396036 | ||||||||
\(996\) | 2.13826 | 0.0677534 | ||||||||
\(997\) | −31.3002 | −0.991287 | −0.495643 | − | 0.868526i | \(-0.665068\pi\) | ||||
−0.495643 | + | 0.868526i | \(0.665068\pi\) | |||||||
\(998\) | −55.7235 | −1.76390 | ||||||||
\(999\) | −3.43845 | −0.108788 |
(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 | 3381.2.a.q.1.2 | 2 | ||
7.3 | odd | 6 | 483.2.i.e.415.1 | yes | 4 | ||
7.5 | odd | 6 | 483.2.i.e.277.1 | ✓ | 4 | ||
7.6 | odd | 2 | 3381.2.a.s.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
483.2.i.e.277.1 | ✓ | 4 | 7.5 | odd | 6 | ||
483.2.i.e.415.1 | yes | 4 | 7.3 | odd | 6 | ||
3381.2.a.q.1.2 | 2 | 1.1 | even | 1 | trivial | ||
3381.2.a.s.1.2 | 2 | 7.6 | odd | 2 |