Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4017,2,Mod(1,4017)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4017, 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("4017.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4017 = 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4017.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.0759064919\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4017.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.41421 | −1.70711 | −0.853553 | − | 0.521005i | \(-0.825557\pi\) | ||||
−0.853553 | + | 0.521005i | \(0.825557\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 3.82843 | 1.91421 | ||||||||
\(5\) | −3.41421 | −1.52688 | −0.763441 | − | 0.645877i | \(-0.776492\pi\) | ||||
−0.763441 | + | 0.645877i | \(0.776492\pi\) | |||||||
\(6\) | 2.41421 | 0.985599 | ||||||||
\(7\) | 2.82843 | 1.06904 | 0.534522 | − | 0.845154i | \(-0.320491\pi\) | ||||
0.534522 | + | 0.845154i | \(0.320491\pi\) | |||||||
\(8\) | −4.41421 | −1.56066 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 8.24264 | 2.60655 | ||||||||
\(11\) | 1.41421 | 0.426401 | 0.213201 | − | 0.977008i | \(-0.431611\pi\) | ||||
0.213201 | + | 0.977008i | \(0.431611\pi\) | |||||||
\(12\) | −3.82843 | −1.10517 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | −6.82843 | −1.82497 | ||||||||
\(15\) | 3.41421 | 0.881546 | ||||||||
\(16\) | 3.00000 | 0.750000 | ||||||||
\(17\) | 1.17157 | 0.284148 | 0.142074 | − | 0.989856i | \(-0.454623\pi\) | ||||
0.142074 | + | 0.989856i | \(0.454623\pi\) | |||||||
\(18\) | −2.41421 | −0.569036 | ||||||||
\(19\) | 5.65685 | 1.29777 | 0.648886 | − | 0.760886i | \(-0.275235\pi\) | ||||
0.648886 | + | 0.760886i | \(0.275235\pi\) | |||||||
\(20\) | −13.0711 | −2.92278 | ||||||||
\(21\) | −2.82843 | −0.617213 | ||||||||
\(22\) | −3.41421 | −0.727913 | ||||||||
\(23\) | −3.65685 | −0.762507 | −0.381253 | − | 0.924471i | \(-0.624507\pi\) | ||||
−0.381253 | + | 0.924471i | \(0.624507\pi\) | |||||||
\(24\) | 4.41421 | 0.901048 | ||||||||
\(25\) | 6.65685 | 1.33137 | ||||||||
\(26\) | −2.41421 | −0.473466 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 10.8284 | 2.04638 | ||||||||
\(29\) | −7.65685 | −1.42184 | −0.710921 | − | 0.703272i | \(-0.751722\pi\) | ||||
−0.710921 | + | 0.703272i | \(0.751722\pi\) | |||||||
\(30\) | −8.24264 | −1.50489 | ||||||||
\(31\) | −7.41421 | −1.33163 | −0.665816 | − | 0.746116i | \(-0.731916\pi\) | ||||
−0.665816 | + | 0.746116i | \(0.731916\pi\) | |||||||
\(32\) | 1.58579 | 0.280330 | ||||||||
\(33\) | −1.41421 | −0.246183 | ||||||||
\(34\) | −2.82843 | −0.485071 | ||||||||
\(35\) | −9.65685 | −1.63231 | ||||||||
\(36\) | 3.82843 | 0.638071 | ||||||||
\(37\) | −3.07107 | −0.504880 | −0.252440 | − | 0.967612i | \(-0.581233\pi\) | ||||
−0.252440 | + | 0.967612i | \(0.581233\pi\) | |||||||
\(38\) | −13.6569 | −2.21543 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 15.0711 | 2.38295 | ||||||||
\(41\) | 6.82843 | 1.06642 | 0.533211 | − | 0.845983i | \(-0.320985\pi\) | ||||
0.533211 | + | 0.845983i | \(0.320985\pi\) | |||||||
\(42\) | 6.82843 | 1.05365 | ||||||||
\(43\) | 2.82843 | 0.431331 | 0.215666 | − | 0.976467i | \(-0.430808\pi\) | ||||
0.215666 | + | 0.976467i | \(0.430808\pi\) | |||||||
\(44\) | 5.41421 | 0.816223 | ||||||||
\(45\) | −3.41421 | −0.508961 | ||||||||
\(46\) | 8.82843 | 1.30168 | ||||||||
\(47\) | −7.07107 | −1.03142 | −0.515711 | − | 0.856763i | \(-0.672472\pi\) | ||||
−0.515711 | + | 0.856763i | \(0.672472\pi\) | |||||||
\(48\) | −3.00000 | −0.433013 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −16.0711 | −2.27279 | ||||||||
\(51\) | −1.17157 | −0.164053 | ||||||||
\(52\) | 3.82843 | 0.530907 | ||||||||
\(53\) | 7.65685 | 1.05175 | 0.525875 | − | 0.850562i | \(-0.323738\pi\) | ||||
0.525875 | + | 0.850562i | \(0.323738\pi\) | |||||||
\(54\) | 2.41421 | 0.328533 | ||||||||
\(55\) | −4.82843 | −0.651065 | ||||||||
\(56\) | −12.4853 | −1.66842 | ||||||||
\(57\) | −5.65685 | −0.749269 | ||||||||
\(58\) | 18.4853 | 2.42724 | ||||||||
\(59\) | −6.00000 | −0.781133 | −0.390567 | − | 0.920575i | \(-0.627721\pi\) | ||||
−0.390567 | + | 0.920575i | \(0.627721\pi\) | |||||||
\(60\) | 13.0711 | 1.68747 | ||||||||
\(61\) | 4.00000 | 0.512148 | 0.256074 | − | 0.966657i | \(-0.417571\pi\) | ||||
0.256074 | + | 0.966657i | \(0.417571\pi\) | |||||||
\(62\) | 17.8995 | 2.27324 | ||||||||
\(63\) | 2.82843 | 0.356348 | ||||||||
\(64\) | −9.82843 | −1.22855 | ||||||||
\(65\) | −3.41421 | −0.423481 | ||||||||
\(66\) | 3.41421 | 0.420261 | ||||||||
\(67\) | −7.41421 | −0.905790 | −0.452895 | − | 0.891564i | \(-0.649609\pi\) | ||||
−0.452895 | + | 0.891564i | \(0.649609\pi\) | |||||||
\(68\) | 4.48528 | 0.543920 | ||||||||
\(69\) | 3.65685 | 0.440234 | ||||||||
\(70\) | 23.3137 | 2.78652 | ||||||||
\(71\) | −4.24264 | −0.503509 | −0.251754 | − | 0.967791i | \(-0.581008\pi\) | ||||
−0.251754 | + | 0.967791i | \(0.581008\pi\) | |||||||
\(72\) | −4.41421 | −0.520220 | ||||||||
\(73\) | −16.2426 | −1.90106 | −0.950529 | − | 0.310637i | \(-0.899458\pi\) | ||||
−0.950529 | + | 0.310637i | \(0.899458\pi\) | |||||||
\(74\) | 7.41421 | 0.861885 | ||||||||
\(75\) | −6.65685 | −0.768667 | ||||||||
\(76\) | 21.6569 | 2.48421 | ||||||||
\(77\) | 4.00000 | 0.455842 | ||||||||
\(78\) | 2.41421 | 0.273356 | ||||||||
\(79\) | 10.4853 | 1.17969 | 0.589843 | − | 0.807518i | \(-0.299190\pi\) | ||||
0.589843 | + | 0.807518i | \(0.299190\pi\) | |||||||
\(80\) | −10.2426 | −1.14516 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −16.4853 | −1.82049 | ||||||||
\(83\) | 4.82843 | 0.529989 | 0.264994 | − | 0.964250i | \(-0.414630\pi\) | ||||
0.264994 | + | 0.964250i | \(0.414630\pi\) | |||||||
\(84\) | −10.8284 | −1.18148 | ||||||||
\(85\) | −4.00000 | −0.433861 | ||||||||
\(86\) | −6.82843 | −0.736328 | ||||||||
\(87\) | 7.65685 | 0.820901 | ||||||||
\(88\) | −6.24264 | −0.665468 | ||||||||
\(89\) | 14.2426 | 1.50972 | 0.754858 | − | 0.655888i | \(-0.227706\pi\) | ||||
0.754858 | + | 0.655888i | \(0.227706\pi\) | |||||||
\(90\) | 8.24264 | 0.868851 | ||||||||
\(91\) | 2.82843 | 0.296500 | ||||||||
\(92\) | −14.0000 | −1.45960 | ||||||||
\(93\) | 7.41421 | 0.768818 | ||||||||
\(94\) | 17.0711 | 1.76075 | ||||||||
\(95\) | −19.3137 | −1.98154 | ||||||||
\(96\) | −1.58579 | −0.161849 | ||||||||
\(97\) | 11.6569 | 1.18357 | 0.591787 | − | 0.806094i | \(-0.298423\pi\) | ||||
0.591787 | + | 0.806094i | \(0.298423\pi\) | |||||||
\(98\) | −2.41421 | −0.243872 | ||||||||
\(99\) | 1.41421 | 0.142134 | ||||||||
\(100\) | 25.4853 | 2.54853 | ||||||||
\(101\) | 7.65685 | 0.761885 | 0.380943 | − | 0.924599i | \(-0.375599\pi\) | ||||
0.380943 | + | 0.924599i | \(0.375599\pi\) | |||||||
\(102\) | 2.82843 | 0.280056 | ||||||||
\(103\) | 1.00000 | 0.0985329 | ||||||||
\(104\) | −4.41421 | −0.432849 | ||||||||
\(105\) | 9.65685 | 0.942412 | ||||||||
\(106\) | −18.4853 | −1.79545 | ||||||||
\(107\) | 13.6569 | 1.32026 | 0.660129 | − | 0.751152i | \(-0.270502\pi\) | ||||
0.660129 | + | 0.751152i | \(0.270502\pi\) | |||||||
\(108\) | −3.82843 | −0.368391 | ||||||||
\(109\) | −16.7279 | −1.60224 | −0.801122 | − | 0.598501i | \(-0.795763\pi\) | ||||
−0.801122 | + | 0.598501i | \(0.795763\pi\) | |||||||
\(110\) | 11.6569 | 1.11144 | ||||||||
\(111\) | 3.07107 | 0.291493 | ||||||||
\(112\) | 8.48528 | 0.801784 | ||||||||
\(113\) | −10.0000 | −0.940721 | −0.470360 | − | 0.882474i | \(-0.655876\pi\) | ||||
−0.470360 | + | 0.882474i | \(0.655876\pi\) | |||||||
\(114\) | 13.6569 | 1.27908 | ||||||||
\(115\) | 12.4853 | 1.16426 | ||||||||
\(116\) | −29.3137 | −2.72171 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | 14.4853 | 1.33348 | ||||||||
\(119\) | 3.31371 | 0.303767 | ||||||||
\(120\) | −15.0711 | −1.37579 | ||||||||
\(121\) | −9.00000 | −0.818182 | ||||||||
\(122\) | −9.65685 | −0.874291 | ||||||||
\(123\) | −6.82843 | −0.615699 | ||||||||
\(124\) | −28.3848 | −2.54903 | ||||||||
\(125\) | −5.65685 | −0.505964 | ||||||||
\(126\) | −6.82843 | −0.608325 | ||||||||
\(127\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(128\) | 20.5563 | 1.81694 | ||||||||
\(129\) | −2.82843 | −0.249029 | ||||||||
\(130\) | 8.24264 | 0.722927 | ||||||||
\(131\) | −6.00000 | −0.524222 | −0.262111 | − | 0.965038i | \(-0.584419\pi\) | ||||
−0.262111 | + | 0.965038i | \(0.584419\pi\) | |||||||
\(132\) | −5.41421 | −0.471247 | ||||||||
\(133\) | 16.0000 | 1.38738 | ||||||||
\(134\) | 17.8995 | 1.54628 | ||||||||
\(135\) | 3.41421 | 0.293849 | ||||||||
\(136\) | −5.17157 | −0.443459 | ||||||||
\(137\) | −8.00000 | −0.683486 | −0.341743 | − | 0.939793i | \(-0.611017\pi\) | ||||
−0.341743 | + | 0.939793i | \(0.611017\pi\) | |||||||
\(138\) | −8.82843 | −0.751526 | ||||||||
\(139\) | 20.1421 | 1.70843 | 0.854217 | − | 0.519917i | \(-0.174037\pi\) | ||||
0.854217 | + | 0.519917i | \(0.174037\pi\) | |||||||
\(140\) | −36.9706 | −3.12458 | ||||||||
\(141\) | 7.07107 | 0.595491 | ||||||||
\(142\) | 10.2426 | 0.859543 | ||||||||
\(143\) | 1.41421 | 0.118262 | ||||||||
\(144\) | 3.00000 | 0.250000 | ||||||||
\(145\) | 26.1421 | 2.17099 | ||||||||
\(146\) | 39.2132 | 3.24531 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | −11.7574 | −0.966449 | ||||||||
\(149\) | −4.00000 | −0.327693 | −0.163846 | − | 0.986486i | \(-0.552390\pi\) | ||||
−0.163846 | + | 0.986486i | \(0.552390\pi\) | |||||||
\(150\) | 16.0711 | 1.31220 | ||||||||
\(151\) | 2.72792 | 0.221995 | 0.110998 | − | 0.993821i | \(-0.464595\pi\) | ||||
0.110998 | + | 0.993821i | \(0.464595\pi\) | |||||||
\(152\) | −24.9706 | −2.02538 | ||||||||
\(153\) | 1.17157 | 0.0947161 | ||||||||
\(154\) | −9.65685 | −0.778171 | ||||||||
\(155\) | 25.3137 | 2.03325 | ||||||||
\(156\) | −3.82843 | −0.306519 | ||||||||
\(157\) | −16.1421 | −1.28828 | −0.644141 | − | 0.764906i | \(-0.722785\pi\) | ||||
−0.644141 | + | 0.764906i | \(0.722785\pi\) | |||||||
\(158\) | −25.3137 | −2.01385 | ||||||||
\(159\) | −7.65685 | −0.607228 | ||||||||
\(160\) | −5.41421 | −0.428031 | ||||||||
\(161\) | −10.3431 | −0.815154 | ||||||||
\(162\) | −2.41421 | −0.189679 | ||||||||
\(163\) | 5.65685 | 0.443079 | 0.221540 | − | 0.975151i | \(-0.428892\pi\) | ||||
0.221540 | + | 0.975151i | \(0.428892\pi\) | |||||||
\(164\) | 26.1421 | 2.04136 | ||||||||
\(165\) | 4.82843 | 0.375893 | ||||||||
\(166\) | −11.6569 | −0.904747 | ||||||||
\(167\) | −24.1421 | −1.86817 | −0.934087 | − | 0.357045i | \(-0.883784\pi\) | ||||
−0.934087 | + | 0.357045i | \(0.883784\pi\) | |||||||
\(168\) | 12.4853 | 0.963260 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 9.65685 | 0.740647 | ||||||||
\(171\) | 5.65685 | 0.432590 | ||||||||
\(172\) | 10.8284 | 0.825660 | ||||||||
\(173\) | −25.7990 | −1.96146 | −0.980730 | − | 0.195366i | \(-0.937411\pi\) | ||||
−0.980730 | + | 0.195366i | \(0.937411\pi\) | |||||||
\(174\) | −18.4853 | −1.40137 | ||||||||
\(175\) | 18.8284 | 1.42330 | ||||||||
\(176\) | 4.24264 | 0.319801 | ||||||||
\(177\) | 6.00000 | 0.450988 | ||||||||
\(178\) | −34.3848 | −2.57725 | ||||||||
\(179\) | 13.3137 | 0.995113 | 0.497557 | − | 0.867431i | \(-0.334231\pi\) | ||||
0.497557 | + | 0.867431i | \(0.334231\pi\) | |||||||
\(180\) | −13.0711 | −0.974260 | ||||||||
\(181\) | 15.6569 | 1.16376 | 0.581882 | − | 0.813273i | \(-0.302316\pi\) | ||||
0.581882 | + | 0.813273i | \(0.302316\pi\) | |||||||
\(182\) | −6.82843 | −0.506157 | ||||||||
\(183\) | −4.00000 | −0.295689 | ||||||||
\(184\) | 16.1421 | 1.19001 | ||||||||
\(185\) | 10.4853 | 0.770893 | ||||||||
\(186\) | −17.8995 | −1.31245 | ||||||||
\(187\) | 1.65685 | 0.121161 | ||||||||
\(188\) | −27.0711 | −1.97436 | ||||||||
\(189\) | −2.82843 | −0.205738 | ||||||||
\(190\) | 46.6274 | 3.38271 | ||||||||
\(191\) | 24.9706 | 1.80681 | 0.903403 | − | 0.428792i | \(-0.141061\pi\) | ||||
0.903403 | + | 0.428792i | \(0.141061\pi\) | |||||||
\(192\) | 9.82843 | 0.709306 | ||||||||
\(193\) | 8.72792 | 0.628250 | 0.314125 | − | 0.949382i | \(-0.398289\pi\) | ||||
0.314125 | + | 0.949382i | \(0.398289\pi\) | |||||||
\(194\) | −28.1421 | −2.02049 | ||||||||
\(195\) | 3.41421 | 0.244497 | ||||||||
\(196\) | 3.82843 | 0.273459 | ||||||||
\(197\) | 7.89949 | 0.562816 | 0.281408 | − | 0.959588i | \(-0.409199\pi\) | ||||
0.281408 | + | 0.959588i | \(0.409199\pi\) | |||||||
\(198\) | −3.41421 | −0.242638 | ||||||||
\(199\) | −4.00000 | −0.283552 | −0.141776 | − | 0.989899i | \(-0.545281\pi\) | ||||
−0.141776 | + | 0.989899i | \(0.545281\pi\) | |||||||
\(200\) | −29.3848 | −2.07782 | ||||||||
\(201\) | 7.41421 | 0.522958 | ||||||||
\(202\) | −18.4853 | −1.30062 | ||||||||
\(203\) | −21.6569 | −1.52001 | ||||||||
\(204\) | −4.48528 | −0.314033 | ||||||||
\(205\) | −23.3137 | −1.62830 | ||||||||
\(206\) | −2.41421 | −0.168206 | ||||||||
\(207\) | −3.65685 | −0.254169 | ||||||||
\(208\) | 3.00000 | 0.208013 | ||||||||
\(209\) | 8.00000 | 0.553372 | ||||||||
\(210\) | −23.3137 | −1.60880 | ||||||||
\(211\) | 10.8284 | 0.745460 | 0.372730 | − | 0.927940i | \(-0.378422\pi\) | ||||
0.372730 | + | 0.927940i | \(0.378422\pi\) | |||||||
\(212\) | 29.3137 | 2.01327 | ||||||||
\(213\) | 4.24264 | 0.290701 | ||||||||
\(214\) | −32.9706 | −2.25382 | ||||||||
\(215\) | −9.65685 | −0.658592 | ||||||||
\(216\) | 4.41421 | 0.300349 | ||||||||
\(217\) | −20.9706 | −1.42357 | ||||||||
\(218\) | 40.3848 | 2.73520 | ||||||||
\(219\) | 16.2426 | 1.09758 | ||||||||
\(220\) | −18.4853 | −1.24628 | ||||||||
\(221\) | 1.17157 | 0.0788085 | ||||||||
\(222\) | −7.41421 | −0.497609 | ||||||||
\(223\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(224\) | 4.48528 | 0.299685 | ||||||||
\(225\) | 6.65685 | 0.443790 | ||||||||
\(226\) | 24.1421 | 1.60591 | ||||||||
\(227\) | −16.2426 | −1.07806 | −0.539031 | − | 0.842286i | \(-0.681209\pi\) | ||||
−0.539031 | + | 0.842286i | \(0.681209\pi\) | |||||||
\(228\) | −21.6569 | −1.43426 | ||||||||
\(229\) | −6.68629 | −0.441843 | −0.220921 | − | 0.975292i | \(-0.570906\pi\) | ||||
−0.220921 | + | 0.975292i | \(0.570906\pi\) | |||||||
\(230\) | −30.1421 | −1.98751 | ||||||||
\(231\) | −4.00000 | −0.263181 | ||||||||
\(232\) | 33.7990 | 2.21901 | ||||||||
\(233\) | −28.6274 | −1.87544 | −0.937722 | − | 0.347386i | \(-0.887069\pi\) | ||||
−0.937722 | + | 0.347386i | \(0.887069\pi\) | |||||||
\(234\) | −2.41421 | −0.157822 | ||||||||
\(235\) | 24.1421 | 1.57486 | ||||||||
\(236\) | −22.9706 | −1.49526 | ||||||||
\(237\) | −10.4853 | −0.681092 | ||||||||
\(238\) | −8.00000 | −0.518563 | ||||||||
\(239\) | 12.3431 | 0.798412 | 0.399206 | − | 0.916861i | \(-0.369286\pi\) | ||||
0.399206 | + | 0.916861i | \(0.369286\pi\) | |||||||
\(240\) | 10.2426 | 0.661160 | ||||||||
\(241\) | −20.7279 | −1.33520 | −0.667601 | − | 0.744519i | \(-0.732679\pi\) | ||||
−0.667601 | + | 0.744519i | \(0.732679\pi\) | |||||||
\(242\) | 21.7279 | 1.39672 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 15.3137 | 0.980360 | ||||||||
\(245\) | −3.41421 | −0.218126 | ||||||||
\(246\) | 16.4853 | 1.05106 | ||||||||
\(247\) | 5.65685 | 0.359937 | ||||||||
\(248\) | 32.7279 | 2.07823 | ||||||||
\(249\) | −4.82843 | −0.305989 | ||||||||
\(250\) | 13.6569 | 0.863735 | ||||||||
\(251\) | 24.4853 | 1.54550 | 0.772749 | − | 0.634712i | \(-0.218881\pi\) | ||||
0.772749 | + | 0.634712i | \(0.218881\pi\) | |||||||
\(252\) | 10.8284 | 0.682127 | ||||||||
\(253\) | −5.17157 | −0.325134 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.00000 | 0.250490 | ||||||||
\(256\) | −29.9706 | −1.87316 | ||||||||
\(257\) | 30.9706 | 1.93189 | 0.965945 | − | 0.258746i | \(-0.0833094\pi\) | ||||
0.965945 | + | 0.258746i | \(0.0833094\pi\) | |||||||
\(258\) | 6.82843 | 0.425119 | ||||||||
\(259\) | −8.68629 | −0.539740 | ||||||||
\(260\) | −13.0711 | −0.810633 | ||||||||
\(261\) | −7.65685 | −0.473947 | ||||||||
\(262\) | 14.4853 | 0.894904 | ||||||||
\(263\) | −1.17157 | −0.0722423 | −0.0361211 | − | 0.999347i | \(-0.511500\pi\) | ||||
−0.0361211 | + | 0.999347i | \(0.511500\pi\) | |||||||
\(264\) | 6.24264 | 0.384208 | ||||||||
\(265\) | −26.1421 | −1.60590 | ||||||||
\(266\) | −38.6274 | −2.36840 | ||||||||
\(267\) | −14.2426 | −0.871635 | ||||||||
\(268\) | −28.3848 | −1.73388 | ||||||||
\(269\) | 2.82843 | 0.172452 | 0.0862261 | − | 0.996276i | \(-0.472519\pi\) | ||||
0.0862261 | + | 0.996276i | \(0.472519\pi\) | |||||||
\(270\) | −8.24264 | −0.501631 | ||||||||
\(271\) | −20.5858 | −1.25050 | −0.625249 | − | 0.780426i | \(-0.715002\pi\) | ||||
−0.625249 | + | 0.780426i | \(0.715002\pi\) | |||||||
\(272\) | 3.51472 | 0.213111 | ||||||||
\(273\) | −2.82843 | −0.171184 | ||||||||
\(274\) | 19.3137 | 1.16678 | ||||||||
\(275\) | 9.41421 | 0.567698 | ||||||||
\(276\) | 14.0000 | 0.842701 | ||||||||
\(277\) | 3.17157 | 0.190561 | 0.0952807 | − | 0.995450i | \(-0.469625\pi\) | ||||
0.0952807 | + | 0.995450i | \(0.469625\pi\) | |||||||
\(278\) | −48.6274 | −2.91648 | ||||||||
\(279\) | −7.41421 | −0.443877 | ||||||||
\(280\) | 42.6274 | 2.54748 | ||||||||
\(281\) | −0.100505 | −0.00599563 | −0.00299781 | − | 0.999996i | \(-0.500954\pi\) | ||||
−0.00299781 | + | 0.999996i | \(0.500954\pi\) | |||||||
\(282\) | −17.0711 | −1.01657 | ||||||||
\(283\) | −10.1421 | −0.602887 | −0.301444 | − | 0.953484i | \(-0.597469\pi\) | ||||
−0.301444 | + | 0.953484i | \(0.597469\pi\) | |||||||
\(284\) | −16.2426 | −0.963823 | ||||||||
\(285\) | 19.3137 | 1.14405 | ||||||||
\(286\) | −3.41421 | −0.201887 | ||||||||
\(287\) | 19.3137 | 1.14005 | ||||||||
\(288\) | 1.58579 | 0.0934434 | ||||||||
\(289\) | −15.6274 | −0.919260 | ||||||||
\(290\) | −63.1127 | −3.70611 | ||||||||
\(291\) | −11.6569 | −0.683337 | ||||||||
\(292\) | −62.1838 | −3.63903 | ||||||||
\(293\) | −9.55635 | −0.558288 | −0.279144 | − | 0.960249i | \(-0.590051\pi\) | ||||
−0.279144 | + | 0.960249i | \(0.590051\pi\) | |||||||
\(294\) | 2.41421 | 0.140800 | ||||||||
\(295\) | 20.4853 | 1.19270 | ||||||||
\(296\) | 13.5563 | 0.787947 | ||||||||
\(297\) | −1.41421 | −0.0820610 | ||||||||
\(298\) | 9.65685 | 0.559407 | ||||||||
\(299\) | −3.65685 | −0.211481 | ||||||||
\(300\) | −25.4853 | −1.47139 | ||||||||
\(301\) | 8.00000 | 0.461112 | ||||||||
\(302\) | −6.58579 | −0.378969 | ||||||||
\(303\) | −7.65685 | −0.439875 | ||||||||
\(304\) | 16.9706 | 0.973329 | ||||||||
\(305\) | −13.6569 | −0.781989 | ||||||||
\(306\) | −2.82843 | −0.161690 | ||||||||
\(307\) | −21.0711 | −1.20259 | −0.601295 | − | 0.799027i | \(-0.705348\pi\) | ||||
−0.601295 | + | 0.799027i | \(0.705348\pi\) | |||||||
\(308\) | 15.3137 | 0.872580 | ||||||||
\(309\) | −1.00000 | −0.0568880 | ||||||||
\(310\) | −61.1127 | −3.47097 | ||||||||
\(311\) | −22.3431 | −1.26696 | −0.633482 | − | 0.773758i | \(-0.718375\pi\) | ||||
−0.633482 | + | 0.773758i | \(0.718375\pi\) | |||||||
\(312\) | 4.41421 | 0.249906 | ||||||||
\(313\) | 6.68629 | 0.377932 | 0.188966 | − | 0.981984i | \(-0.439486\pi\) | ||||
0.188966 | + | 0.981984i | \(0.439486\pi\) | |||||||
\(314\) | 38.9706 | 2.19924 | ||||||||
\(315\) | −9.65685 | −0.544102 | ||||||||
\(316\) | 40.1421 | 2.25817 | ||||||||
\(317\) | −25.4558 | −1.42974 | −0.714871 | − | 0.699256i | \(-0.753515\pi\) | ||||
−0.714871 | + | 0.699256i | \(0.753515\pi\) | |||||||
\(318\) | 18.4853 | 1.03660 | ||||||||
\(319\) | −10.8284 | −0.606276 | ||||||||
\(320\) | 33.5563 | 1.87586 | ||||||||
\(321\) | −13.6569 | −0.762251 | ||||||||
\(322\) | 24.9706 | 1.39156 | ||||||||
\(323\) | 6.62742 | 0.368759 | ||||||||
\(324\) | 3.82843 | 0.212690 | ||||||||
\(325\) | 6.65685 | 0.369256 | ||||||||
\(326\) | −13.6569 | −0.756383 | ||||||||
\(327\) | 16.7279 | 0.925056 | ||||||||
\(328\) | −30.1421 | −1.66432 | ||||||||
\(329\) | −20.0000 | −1.10264 | ||||||||
\(330\) | −11.6569 | −0.641689 | ||||||||
\(331\) | 5.07107 | 0.278731 | 0.139366 | − | 0.990241i | \(-0.455494\pi\) | ||||
0.139366 | + | 0.990241i | \(0.455494\pi\) | |||||||
\(332\) | 18.4853 | 1.01451 | ||||||||
\(333\) | −3.07107 | −0.168293 | ||||||||
\(334\) | 58.2843 | 3.18917 | ||||||||
\(335\) | 25.3137 | 1.38304 | ||||||||
\(336\) | −8.48528 | −0.462910 | ||||||||
\(337\) | 12.6274 | 0.687859 | 0.343930 | − | 0.938995i | \(-0.388242\pi\) | ||||
0.343930 | + | 0.938995i | \(0.388242\pi\) | |||||||
\(338\) | −2.41421 | −0.131316 | ||||||||
\(339\) | 10.0000 | 0.543125 | ||||||||
\(340\) | −15.3137 | −0.830502 | ||||||||
\(341\) | −10.4853 | −0.567810 | ||||||||
\(342\) | −13.6569 | −0.738478 | ||||||||
\(343\) | −16.9706 | −0.916324 | ||||||||
\(344\) | −12.4853 | −0.673161 | ||||||||
\(345\) | −12.4853 | −0.672185 | ||||||||
\(346\) | 62.2843 | 3.34842 | ||||||||
\(347\) | 28.0000 | 1.50312 | 0.751559 | − | 0.659665i | \(-0.229302\pi\) | ||||
0.751559 | + | 0.659665i | \(0.229302\pi\) | |||||||
\(348\) | 29.3137 | 1.57138 | ||||||||
\(349\) | 30.8701 | 1.65244 | 0.826218 | − | 0.563350i | \(-0.190488\pi\) | ||||
0.826218 | + | 0.563350i | \(0.190488\pi\) | |||||||
\(350\) | −45.4558 | −2.42972 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 2.24264 | 0.119533 | ||||||||
\(353\) | −14.9289 | −0.794587 | −0.397293 | − | 0.917692i | \(-0.630050\pi\) | ||||
−0.397293 | + | 0.917692i | \(0.630050\pi\) | |||||||
\(354\) | −14.4853 | −0.769884 | ||||||||
\(355\) | 14.4853 | 0.768799 | ||||||||
\(356\) | 54.5269 | 2.88992 | ||||||||
\(357\) | −3.31371 | −0.175380 | ||||||||
\(358\) | −32.1421 | −1.69876 | ||||||||
\(359\) | 22.4853 | 1.18673 | 0.593364 | − | 0.804934i | \(-0.297800\pi\) | ||||
0.593364 | + | 0.804934i | \(0.297800\pi\) | |||||||
\(360\) | 15.0711 | 0.794315 | ||||||||
\(361\) | 13.0000 | 0.684211 | ||||||||
\(362\) | −37.7990 | −1.98667 | ||||||||
\(363\) | 9.00000 | 0.472377 | ||||||||
\(364\) | 10.8284 | 0.567564 | ||||||||
\(365\) | 55.4558 | 2.90269 | ||||||||
\(366\) | 9.65685 | 0.504772 | ||||||||
\(367\) | −15.1716 | −0.791950 | −0.395975 | − | 0.918261i | \(-0.629593\pi\) | ||||
−0.395975 | + | 0.918261i | \(0.629593\pi\) | |||||||
\(368\) | −10.9706 | −0.571880 | ||||||||
\(369\) | 6.82843 | 0.355474 | ||||||||
\(370\) | −25.3137 | −1.31600 | ||||||||
\(371\) | 21.6569 | 1.12437 | ||||||||
\(372\) | 28.3848 | 1.47168 | ||||||||
\(373\) | 1.65685 | 0.0857887 | 0.0428943 | − | 0.999080i | \(-0.486342\pi\) | ||||
0.0428943 | + | 0.999080i | \(0.486342\pi\) | |||||||
\(374\) | −4.00000 | −0.206835 | ||||||||
\(375\) | 5.65685 | 0.292119 | ||||||||
\(376\) | 31.2132 | 1.60970 | ||||||||
\(377\) | −7.65685 | −0.394348 | ||||||||
\(378\) | 6.82843 | 0.351216 | ||||||||
\(379\) | −4.58579 | −0.235556 | −0.117778 | − | 0.993040i | \(-0.537577\pi\) | ||||
−0.117778 | + | 0.993040i | \(0.537577\pi\) | |||||||
\(380\) | −73.9411 | −3.79310 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −60.2843 | −3.08441 | ||||||||
\(383\) | −2.58579 | −0.132128 | −0.0660638 | − | 0.997815i | \(-0.521044\pi\) | ||||
−0.0660638 | + | 0.997815i | \(0.521044\pi\) | |||||||
\(384\) | −20.5563 | −1.04901 | ||||||||
\(385\) | −13.6569 | −0.696018 | ||||||||
\(386\) | −21.0711 | −1.07249 | ||||||||
\(387\) | 2.82843 | 0.143777 | ||||||||
\(388\) | 44.6274 | 2.26561 | ||||||||
\(389\) | 10.4853 | 0.531625 | 0.265812 | − | 0.964025i | \(-0.414360\pi\) | ||||
0.265812 | + | 0.964025i | \(0.414360\pi\) | |||||||
\(390\) | −8.24264 | −0.417382 | ||||||||
\(391\) | −4.28427 | −0.216665 | ||||||||
\(392\) | −4.41421 | −0.222951 | ||||||||
\(393\) | 6.00000 | 0.302660 | ||||||||
\(394\) | −19.0711 | −0.960787 | ||||||||
\(395\) | −35.7990 | −1.80124 | ||||||||
\(396\) | 5.41421 | 0.272074 | ||||||||
\(397\) | −26.8701 | −1.34857 | −0.674285 | − | 0.738471i | \(-0.735548\pi\) | ||||
−0.674285 | + | 0.738471i | \(0.735548\pi\) | |||||||
\(398\) | 9.65685 | 0.484054 | ||||||||
\(399\) | −16.0000 | −0.801002 | ||||||||
\(400\) | 19.9706 | 0.998528 | ||||||||
\(401\) | −25.1716 | −1.25701 | −0.628504 | − | 0.777806i | \(-0.716332\pi\) | ||||
−0.628504 | + | 0.777806i | \(0.716332\pi\) | |||||||
\(402\) | −17.8995 | −0.892746 | ||||||||
\(403\) | −7.41421 | −0.369328 | ||||||||
\(404\) | 29.3137 | 1.45841 | ||||||||
\(405\) | −3.41421 | −0.169654 | ||||||||
\(406\) | 52.2843 | 2.59482 | ||||||||
\(407\) | −4.34315 | −0.215282 | ||||||||
\(408\) | 5.17157 | 0.256031 | ||||||||
\(409\) | 15.1716 | 0.750186 | 0.375093 | − | 0.926987i | \(-0.377611\pi\) | ||||
0.375093 | + | 0.926987i | \(0.377611\pi\) | |||||||
\(410\) | 56.2843 | 2.77968 | ||||||||
\(411\) | 8.00000 | 0.394611 | ||||||||
\(412\) | 3.82843 | 0.188613 | ||||||||
\(413\) | −16.9706 | −0.835067 | ||||||||
\(414\) | 8.82843 | 0.433894 | ||||||||
\(415\) | −16.4853 | −0.809231 | ||||||||
\(416\) | 1.58579 | 0.0777496 | ||||||||
\(417\) | −20.1421 | −0.986365 | ||||||||
\(418\) | −19.3137 | −0.944664 | ||||||||
\(419\) | −29.6569 | −1.44883 | −0.724416 | − | 0.689363i | \(-0.757891\pi\) | ||||
−0.724416 | + | 0.689363i | \(0.757891\pi\) | |||||||
\(420\) | 36.9706 | 1.80398 | ||||||||
\(421\) | −10.4853 | −0.511021 | −0.255511 | − | 0.966806i | \(-0.582244\pi\) | ||||
−0.255511 | + | 0.966806i | \(0.582244\pi\) | |||||||
\(422\) | −26.1421 | −1.27258 | ||||||||
\(423\) | −7.07107 | −0.343807 | ||||||||
\(424\) | −33.7990 | −1.64142 | ||||||||
\(425\) | 7.79899 | 0.378307 | ||||||||
\(426\) | −10.2426 | −0.496258 | ||||||||
\(427\) | 11.3137 | 0.547509 | ||||||||
\(428\) | 52.2843 | 2.52726 | ||||||||
\(429\) | −1.41421 | −0.0682789 | ||||||||
\(430\) | 23.3137 | 1.12429 | ||||||||
\(431\) | −30.4853 | −1.46842 | −0.734212 | − | 0.678920i | \(-0.762448\pi\) | ||||
−0.734212 | + | 0.678920i | \(0.762448\pi\) | |||||||
\(432\) | −3.00000 | −0.144338 | ||||||||
\(433\) | −3.65685 | −0.175737 | −0.0878686 | − | 0.996132i | \(-0.528006\pi\) | ||||
−0.0878686 | + | 0.996132i | \(0.528006\pi\) | |||||||
\(434\) | 50.6274 | 2.43019 | ||||||||
\(435\) | −26.1421 | −1.25342 | ||||||||
\(436\) | −64.0416 | −3.06704 | ||||||||
\(437\) | −20.6863 | −0.989560 | ||||||||
\(438\) | −39.2132 | −1.87368 | ||||||||
\(439\) | −25.4558 | −1.21494 | −0.607471 | − | 0.794342i | \(-0.707816\pi\) | ||||
−0.607471 | + | 0.794342i | \(0.707816\pi\) | |||||||
\(440\) | 21.3137 | 1.01609 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −2.82843 | −0.134535 | ||||||||
\(443\) | −2.82843 | −0.134383 | −0.0671913 | − | 0.997740i | \(-0.521404\pi\) | ||||
−0.0671913 | + | 0.997740i | \(0.521404\pi\) | |||||||
\(444\) | 11.7574 | 0.557980 | ||||||||
\(445\) | −48.6274 | −2.30516 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.00000 | 0.189194 | ||||||||
\(448\) | −27.7990 | −1.31338 | ||||||||
\(449\) | −12.1005 | −0.571058 | −0.285529 | − | 0.958370i | \(-0.592169\pi\) | ||||
−0.285529 | + | 0.958370i | \(0.592169\pi\) | |||||||
\(450\) | −16.0711 | −0.757597 | ||||||||
\(451\) | 9.65685 | 0.454724 | ||||||||
\(452\) | −38.2843 | −1.80074 | ||||||||
\(453\) | −2.72792 | −0.128169 | ||||||||
\(454\) | 39.2132 | 1.84037 | ||||||||
\(455\) | −9.65685 | −0.452720 | ||||||||
\(456\) | 24.9706 | 1.16935 | ||||||||
\(457\) | −29.4142 | −1.37594 | −0.687969 | − | 0.725740i | \(-0.741498\pi\) | ||||
−0.687969 | + | 0.725740i | \(0.741498\pi\) | |||||||
\(458\) | 16.1421 | 0.754272 | ||||||||
\(459\) | −1.17157 | −0.0546843 | ||||||||
\(460\) | 47.7990 | 2.22864 | ||||||||
\(461\) | −37.9411 | −1.76709 | −0.883547 | − | 0.468342i | \(-0.844851\pi\) | ||||
−0.883547 | + | 0.468342i | \(0.844851\pi\) | |||||||
\(462\) | 9.65685 | 0.449278 | ||||||||
\(463\) | −18.2426 | −0.847807 | −0.423904 | − | 0.905707i | \(-0.639341\pi\) | ||||
−0.423904 | + | 0.905707i | \(0.639341\pi\) | |||||||
\(464\) | −22.9706 | −1.06638 | ||||||||
\(465\) | −25.3137 | −1.17390 | ||||||||
\(466\) | 69.1127 | 3.20158 | ||||||||
\(467\) | 12.6863 | 0.587052 | 0.293526 | − | 0.955951i | \(-0.405171\pi\) | ||||
0.293526 | + | 0.955951i | \(0.405171\pi\) | |||||||
\(468\) | 3.82843 | 0.176969 | ||||||||
\(469\) | −20.9706 | −0.968331 | ||||||||
\(470\) | −58.2843 | −2.68845 | ||||||||
\(471\) | 16.1421 | 0.743790 | ||||||||
\(472\) | 26.4853 | 1.21908 | ||||||||
\(473\) | 4.00000 | 0.183920 | ||||||||
\(474\) | 25.3137 | 1.16270 | ||||||||
\(475\) | 37.6569 | 1.72781 | ||||||||
\(476\) | 12.6863 | 0.581475 | ||||||||
\(477\) | 7.65685 | 0.350583 | ||||||||
\(478\) | −29.7990 | −1.36297 | ||||||||
\(479\) | −5.41421 | −0.247382 | −0.123691 | − | 0.992321i | \(-0.539473\pi\) | ||||
−0.123691 | + | 0.992321i | \(0.539473\pi\) | |||||||
\(480\) | 5.41421 | 0.247124 | ||||||||
\(481\) | −3.07107 | −0.140029 | ||||||||
\(482\) | 50.0416 | 2.27933 | ||||||||
\(483\) | 10.3431 | 0.470629 | ||||||||
\(484\) | −34.4558 | −1.56617 | ||||||||
\(485\) | −39.7990 | −1.80718 | ||||||||
\(486\) | 2.41421 | 0.109511 | ||||||||
\(487\) | −1.55635 | −0.0705249 | −0.0352625 | − | 0.999378i | \(-0.511227\pi\) | ||||
−0.0352625 | + | 0.999378i | \(0.511227\pi\) | |||||||
\(488\) | −17.6569 | −0.799288 | ||||||||
\(489\) | −5.65685 | −0.255812 | ||||||||
\(490\) | 8.24264 | 0.372365 | ||||||||
\(491\) | −29.6569 | −1.33840 | −0.669198 | − | 0.743085i | \(-0.733362\pi\) | ||||
−0.669198 | + | 0.743085i | \(0.733362\pi\) | |||||||
\(492\) | −26.1421 | −1.17858 | ||||||||
\(493\) | −8.97056 | −0.404014 | ||||||||
\(494\) | −13.6569 | −0.614451 | ||||||||
\(495\) | −4.82843 | −0.217022 | ||||||||
\(496\) | −22.2426 | −0.998724 | ||||||||
\(497\) | −12.0000 | −0.538274 | ||||||||
\(498\) | 11.6569 | 0.522356 | ||||||||
\(499\) | −0.585786 | −0.0262234 | −0.0131117 | − | 0.999914i | \(-0.504174\pi\) | ||||
−0.0131117 | + | 0.999914i | \(0.504174\pi\) | |||||||
\(500\) | −21.6569 | −0.968524 | ||||||||
\(501\) | 24.1421 | 1.07859 | ||||||||
\(502\) | −59.1127 | −2.63833 | ||||||||
\(503\) | 18.2843 | 0.815255 | 0.407628 | − | 0.913148i | \(-0.366356\pi\) | ||||
0.407628 | + | 0.913148i | \(0.366356\pi\) | |||||||
\(504\) | −12.4853 | −0.556139 | ||||||||
\(505\) | −26.1421 | −1.16331 | ||||||||
\(506\) | 12.4853 | 0.555038 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 21.4558 | 0.951014 | 0.475507 | − | 0.879712i | \(-0.342265\pi\) | ||||
0.475507 | + | 0.879712i | \(0.342265\pi\) | |||||||
\(510\) | −9.65685 | −0.427613 | ||||||||
\(511\) | −45.9411 | −2.03232 | ||||||||
\(512\) | 31.2426 | 1.38074 | ||||||||
\(513\) | −5.65685 | −0.249756 | ||||||||
\(514\) | −74.7696 | −3.29794 | ||||||||
\(515\) | −3.41421 | −0.150448 | ||||||||
\(516\) | −10.8284 | −0.476695 | ||||||||
\(517\) | −10.0000 | −0.439799 | ||||||||
\(518\) | 20.9706 | 0.921394 | ||||||||
\(519\) | 25.7990 | 1.13245 | ||||||||
\(520\) | 15.0711 | 0.660910 | ||||||||
\(521\) | 13.7990 | 0.604545 | 0.302272 | − | 0.953222i | \(-0.402255\pi\) | ||||
0.302272 | + | 0.953222i | \(0.402255\pi\) | |||||||
\(522\) | 18.4853 | 0.809079 | ||||||||
\(523\) | −28.1421 | −1.23057 | −0.615285 | − | 0.788305i | \(-0.710959\pi\) | ||||
−0.615285 | + | 0.788305i | \(0.710959\pi\) | |||||||
\(524\) | −22.9706 | −1.00347 | ||||||||
\(525\) | −18.8284 | −0.821740 | ||||||||
\(526\) | 2.82843 | 0.123325 | ||||||||
\(527\) | −8.68629 | −0.378381 | ||||||||
\(528\) | −4.24264 | −0.184637 | ||||||||
\(529\) | −9.62742 | −0.418583 | ||||||||
\(530\) | 63.1127 | 2.74144 | ||||||||
\(531\) | −6.00000 | −0.260378 | ||||||||
\(532\) | 61.2548 | 2.65573 | ||||||||
\(533\) | 6.82843 | 0.295772 | ||||||||
\(534\) | 34.3848 | 1.48797 | ||||||||
\(535\) | −46.6274 | −2.01588 | ||||||||
\(536\) | 32.7279 | 1.41363 | ||||||||
\(537\) | −13.3137 | −0.574529 | ||||||||
\(538\) | −6.82843 | −0.294394 | ||||||||
\(539\) | 1.41421 | 0.0609145 | ||||||||
\(540\) | 13.0711 | 0.562489 | ||||||||
\(541\) | 37.1127 | 1.59560 | 0.797800 | − | 0.602922i | \(-0.205997\pi\) | ||||
0.797800 | + | 0.602922i | \(0.205997\pi\) | |||||||
\(542\) | 49.6985 | 2.13473 | ||||||||
\(543\) | −15.6569 | −0.671900 | ||||||||
\(544\) | 1.85786 | 0.0796553 | ||||||||
\(545\) | 57.1127 | 2.44644 | ||||||||
\(546\) | 6.82843 | 0.292230 | ||||||||
\(547\) | −7.17157 | −0.306634 | −0.153317 | − | 0.988177i | \(-0.548996\pi\) | ||||
−0.153317 | + | 0.988177i | \(0.548996\pi\) | |||||||
\(548\) | −30.6274 | −1.30834 | ||||||||
\(549\) | 4.00000 | 0.170716 | ||||||||
\(550\) | −22.7279 | −0.969122 | ||||||||
\(551\) | −43.3137 | −1.84523 | ||||||||
\(552\) | −16.1421 | −0.687055 | ||||||||
\(553\) | 29.6569 | 1.26114 | ||||||||
\(554\) | −7.65685 | −0.325309 | ||||||||
\(555\) | −10.4853 | −0.445075 | ||||||||
\(556\) | 77.1127 | 3.27031 | ||||||||
\(557\) | −18.9289 | −0.802045 | −0.401022 | − | 0.916068i | \(-0.631345\pi\) | ||||
−0.401022 | + | 0.916068i | \(0.631345\pi\) | |||||||
\(558\) | 17.8995 | 0.757746 | ||||||||
\(559\) | 2.82843 | 0.119630 | ||||||||
\(560\) | −28.9706 | −1.22423 | ||||||||
\(561\) | −1.65685 | −0.0699524 | ||||||||
\(562\) | 0.242641 | 0.0102352 | ||||||||
\(563\) | 3.31371 | 0.139656 | 0.0698281 | − | 0.997559i | \(-0.477755\pi\) | ||||
0.0698281 | + | 0.997559i | \(0.477755\pi\) | |||||||
\(564\) | 27.0711 | 1.13990 | ||||||||
\(565\) | 34.1421 | 1.43637 | ||||||||
\(566\) | 24.4853 | 1.02919 | ||||||||
\(567\) | 2.82843 | 0.118783 | ||||||||
\(568\) | 18.7279 | 0.785806 | ||||||||
\(569\) | −20.1421 | −0.844402 | −0.422201 | − | 0.906502i | \(-0.638742\pi\) | ||||
−0.422201 | + | 0.906502i | \(0.638742\pi\) | |||||||
\(570\) | −46.6274 | −1.95301 | ||||||||
\(571\) | −10.6274 | −0.444744 | −0.222372 | − | 0.974962i | \(-0.571380\pi\) | ||||
−0.222372 | + | 0.974962i | \(0.571380\pi\) | |||||||
\(572\) | 5.41421 | 0.226380 | ||||||||
\(573\) | −24.9706 | −1.04316 | ||||||||
\(574\) | −46.6274 | −1.94619 | ||||||||
\(575\) | −24.3431 | −1.01518 | ||||||||
\(576\) | −9.82843 | −0.409518 | ||||||||
\(577\) | 18.3848 | 0.765368 | 0.382684 | − | 0.923879i | \(-0.375000\pi\) | ||||
0.382684 | + | 0.923879i | \(0.375000\pi\) | |||||||
\(578\) | 37.7279 | 1.56927 | ||||||||
\(579\) | −8.72792 | −0.362720 | ||||||||
\(580\) | 100.083 | 4.15573 | ||||||||
\(581\) | 13.6569 | 0.566582 | ||||||||
\(582\) | 28.1421 | 1.16653 | ||||||||
\(583\) | 10.8284 | 0.448468 | ||||||||
\(584\) | 71.6985 | 2.96690 | ||||||||
\(585\) | −3.41421 | −0.141160 | ||||||||
\(586\) | 23.0711 | 0.953057 | ||||||||
\(587\) | 16.8284 | 0.694584 | 0.347292 | − | 0.937757i | \(-0.387101\pi\) | ||||
0.347292 | + | 0.937757i | \(0.387101\pi\) | |||||||
\(588\) | −3.82843 | −0.157882 | ||||||||
\(589\) | −41.9411 | −1.72815 | ||||||||
\(590\) | −49.4558 | −2.03606 | ||||||||
\(591\) | −7.89949 | −0.324942 | ||||||||
\(592\) | −9.21320 | −0.378660 | ||||||||
\(593\) | −18.9289 | −0.777318 | −0.388659 | − | 0.921382i | \(-0.627062\pi\) | ||||
−0.388659 | + | 0.921382i | \(0.627062\pi\) | |||||||
\(594\) | 3.41421 | 0.140087 | ||||||||
\(595\) | −11.3137 | −0.463817 | ||||||||
\(596\) | −15.3137 | −0.627274 | ||||||||
\(597\) | 4.00000 | 0.163709 | ||||||||
\(598\) | 8.82843 | 0.361021 | ||||||||
\(599\) | −35.1127 | −1.43467 | −0.717333 | − | 0.696731i | \(-0.754637\pi\) | ||||
−0.717333 | + | 0.696731i | \(0.754637\pi\) | |||||||
\(600\) | 29.3848 | 1.19963 | ||||||||
\(601\) | 5.31371 | 0.216751 | 0.108375 | − | 0.994110i | \(-0.465435\pi\) | ||||
0.108375 | + | 0.994110i | \(0.465435\pi\) | |||||||
\(602\) | −19.3137 | −0.787168 | ||||||||
\(603\) | −7.41421 | −0.301930 | ||||||||
\(604\) | 10.4437 | 0.424946 | ||||||||
\(605\) | 30.7279 | 1.24927 | ||||||||
\(606\) | 18.4853 | 0.750913 | ||||||||
\(607\) | −19.3137 | −0.783919 | −0.391960 | − | 0.919982i | \(-0.628203\pi\) | ||||
−0.391960 | + | 0.919982i | \(0.628203\pi\) | |||||||
\(608\) | 8.97056 | 0.363804 | ||||||||
\(609\) | 21.6569 | 0.877580 | ||||||||
\(610\) | 32.9706 | 1.33494 | ||||||||
\(611\) | −7.07107 | −0.286065 | ||||||||
\(612\) | 4.48528 | 0.181307 | ||||||||
\(613\) | −9.79899 | −0.395777 | −0.197889 | − | 0.980224i | \(-0.563408\pi\) | ||||
−0.197889 | + | 0.980224i | \(0.563408\pi\) | |||||||
\(614\) | 50.8701 | 2.05295 | ||||||||
\(615\) | 23.3137 | 0.940099 | ||||||||
\(616\) | −17.6569 | −0.711415 | ||||||||
\(617\) | −10.0416 | −0.404261 | −0.202130 | − | 0.979359i | \(-0.564786\pi\) | ||||
−0.202130 | + | 0.979359i | \(0.564786\pi\) | |||||||
\(618\) | 2.41421 | 0.0971139 | ||||||||
\(619\) | −33.1716 | −1.33328 | −0.666639 | − | 0.745381i | \(-0.732268\pi\) | ||||
−0.666639 | + | 0.745381i | \(0.732268\pi\) | |||||||
\(620\) | 96.9117 | 3.89207 | ||||||||
\(621\) | 3.65685 | 0.146745 | ||||||||
\(622\) | 53.9411 | 2.16284 | ||||||||
\(623\) | 40.2843 | 1.61396 | ||||||||
\(624\) | −3.00000 | −0.120096 | ||||||||
\(625\) | −13.9706 | −0.558823 | ||||||||
\(626\) | −16.1421 | −0.645169 | ||||||||
\(627\) | −8.00000 | −0.319489 | ||||||||
\(628\) | −61.7990 | −2.46605 | ||||||||
\(629\) | −3.59798 | −0.143461 | ||||||||
\(630\) | 23.3137 | 0.928840 | ||||||||
\(631\) | −28.4853 | −1.13398 | −0.566991 | − | 0.823724i | \(-0.691892\pi\) | ||||
−0.566991 | + | 0.823724i | \(0.691892\pi\) | |||||||
\(632\) | −46.2843 | −1.84109 | ||||||||
\(633\) | −10.8284 | −0.430391 | ||||||||
\(634\) | 61.4558 | 2.44072 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −29.3137 | −1.16236 | ||||||||
\(637\) | 1.00000 | 0.0396214 | ||||||||
\(638\) | 26.1421 | 1.03498 | ||||||||
\(639\) | −4.24264 | −0.167836 | ||||||||
\(640\) | −70.1838 | −2.77426 | ||||||||
\(641\) | −18.6863 | −0.738064 | −0.369032 | − | 0.929417i | \(-0.620311\pi\) | ||||
−0.369032 | + | 0.929417i | \(0.620311\pi\) | |||||||
\(642\) | 32.9706 | 1.30124 | ||||||||
\(643\) | −17.4558 | −0.688391 | −0.344196 | − | 0.938898i | \(-0.611848\pi\) | ||||
−0.344196 | + | 0.938898i | \(0.611848\pi\) | |||||||
\(644\) | −39.5980 | −1.56038 | ||||||||
\(645\) | 9.65685 | 0.380238 | ||||||||
\(646\) | −16.0000 | −0.629512 | ||||||||
\(647\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(648\) | −4.41421 | −0.173407 | ||||||||
\(649\) | −8.48528 | −0.333076 | ||||||||
\(650\) | −16.0711 | −0.630359 | ||||||||
\(651\) | 20.9706 | 0.821901 | ||||||||
\(652\) | 21.6569 | 0.848148 | ||||||||
\(653\) | −16.8284 | −0.658547 | −0.329274 | − | 0.944235i | \(-0.606804\pi\) | ||||
−0.329274 | + | 0.944235i | \(0.606804\pi\) | |||||||
\(654\) | −40.3848 | −1.57917 | ||||||||
\(655\) | 20.4853 | 0.800426 | ||||||||
\(656\) | 20.4853 | 0.799816 | ||||||||
\(657\) | −16.2426 | −0.633686 | ||||||||
\(658\) | 48.2843 | 1.88232 | ||||||||
\(659\) | 36.6274 | 1.42680 | 0.713401 | − | 0.700756i | \(-0.247154\pi\) | ||||
0.713401 | + | 0.700756i | \(0.247154\pi\) | |||||||
\(660\) | 18.4853 | 0.719539 | ||||||||
\(661\) | 8.92893 | 0.347295 | 0.173648 | − | 0.984808i | \(-0.444445\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444445\pi\) | |||||||
\(662\) | −12.2426 | −0.475824 | ||||||||
\(663\) | −1.17157 | −0.0455001 | ||||||||
\(664\) | −21.3137 | −0.827132 | ||||||||
\(665\) | −54.6274 | −2.11836 | ||||||||
\(666\) | 7.41421 | 0.287295 | ||||||||
\(667\) | 28.0000 | 1.08416 | ||||||||
\(668\) | −92.4264 | −3.57609 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −61.1127 | −2.36099 | ||||||||
\(671\) | 5.65685 | 0.218380 | ||||||||
\(672\) | −4.48528 | −0.173023 | ||||||||
\(673\) | 18.6863 | 0.720304 | 0.360152 | − | 0.932894i | \(-0.382725\pi\) | ||||
0.360152 | + | 0.932894i | \(0.382725\pi\) | |||||||
\(674\) | −30.4853 | −1.17425 | ||||||||
\(675\) | −6.65685 | −0.256222 | ||||||||
\(676\) | 3.82843 | 0.147247 | ||||||||
\(677\) | 25.3137 | 0.972885 | 0.486442 | − | 0.873713i | \(-0.338294\pi\) | ||||
0.486442 | + | 0.873713i | \(0.338294\pi\) | |||||||
\(678\) | −24.1421 | −0.927173 | ||||||||
\(679\) | 32.9706 | 1.26529 | ||||||||
\(680\) | 17.6569 | 0.677109 | ||||||||
\(681\) | 16.2426 | 0.622419 | ||||||||
\(682\) | 25.3137 | 0.969312 | ||||||||
\(683\) | 41.6985 | 1.59555 | 0.797774 | − | 0.602956i | \(-0.206011\pi\) | ||||
0.797774 | + | 0.602956i | \(0.206011\pi\) | |||||||
\(684\) | 21.6569 | 0.828071 | ||||||||
\(685\) | 27.3137 | 1.04360 | ||||||||
\(686\) | 40.9706 | 1.56426 | ||||||||
\(687\) | 6.68629 | 0.255098 | ||||||||
\(688\) | 8.48528 | 0.323498 | ||||||||
\(689\) | 7.65685 | 0.291703 | ||||||||
\(690\) | 30.1421 | 1.14749 | ||||||||
\(691\) | 44.8701 | 1.70694 | 0.853469 | − | 0.521144i | \(-0.174495\pi\) | ||||
0.853469 | + | 0.521144i | \(0.174495\pi\) | |||||||
\(692\) | −98.7696 | −3.75466 | ||||||||
\(693\) | 4.00000 | 0.151947 | ||||||||
\(694\) | −67.5980 | −2.56598 | ||||||||
\(695\) | −68.7696 | −2.60858 | ||||||||
\(696\) | −33.7990 | −1.28115 | ||||||||
\(697\) | 8.00000 | 0.303022 | ||||||||
\(698\) | −74.5269 | −2.82089 | ||||||||
\(699\) | 28.6274 | 1.08279 | ||||||||
\(700\) | 72.0833 | 2.72449 | ||||||||
\(701\) | −27.1127 | −1.02403 | −0.512016 | − | 0.858976i | \(-0.671101\pi\) | ||||
−0.512016 | + | 0.858976i | \(0.671101\pi\) | |||||||
\(702\) | 2.41421 | 0.0911186 | ||||||||
\(703\) | −17.3726 | −0.655219 | ||||||||
\(704\) | −13.8995 | −0.523857 | ||||||||
\(705\) | −24.1421 | −0.909245 | ||||||||
\(706\) | 36.0416 | 1.35644 | ||||||||
\(707\) | 21.6569 | 0.814490 | ||||||||
\(708\) | 22.9706 | 0.863287 | ||||||||
\(709\) | 30.0000 | 1.12667 | 0.563337 | − | 0.826227i | \(-0.309517\pi\) | ||||
0.563337 | + | 0.826227i | \(0.309517\pi\) | |||||||
\(710\) | −34.9706 | −1.31242 | ||||||||
\(711\) | 10.4853 | 0.393229 | ||||||||
\(712\) | −62.8701 | −2.35616 | ||||||||
\(713\) | 27.1127 | 1.01538 | ||||||||
\(714\) | 8.00000 | 0.299392 | ||||||||
\(715\) | −4.82843 | −0.180573 | ||||||||
\(716\) | 50.9706 | 1.90486 | ||||||||
\(717\) | −12.3431 | −0.460963 | ||||||||
\(718\) | −54.2843 | −2.02587 | ||||||||
\(719\) | 4.20101 | 0.156671 | 0.0783356 | − | 0.996927i | \(-0.475039\pi\) | ||||
0.0783356 | + | 0.996927i | \(0.475039\pi\) | |||||||
\(720\) | −10.2426 | −0.381721 | ||||||||
\(721\) | 2.82843 | 0.105336 | ||||||||
\(722\) | −31.3848 | −1.16802 | ||||||||
\(723\) | 20.7279 | 0.770880 | ||||||||
\(724\) | 59.9411 | 2.22769 | ||||||||
\(725\) | −50.9706 | −1.89300 | ||||||||
\(726\) | −21.7279 | −0.806399 | ||||||||
\(727\) | −19.0294 | −0.705763 | −0.352881 | − | 0.935668i | \(-0.614798\pi\) | ||||
−0.352881 | + | 0.935668i | \(0.614798\pi\) | |||||||
\(728\) | −12.4853 | −0.462735 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −133.882 | −4.95520 | ||||||||
\(731\) | 3.31371 | 0.122562 | ||||||||
\(732\) | −15.3137 | −0.566011 | ||||||||
\(733\) | −10.7868 | −0.398419 | −0.199210 | − | 0.979957i | \(-0.563837\pi\) | ||||
−0.199210 | + | 0.979957i | \(0.563837\pi\) | |||||||
\(734\) | 36.6274 | 1.35194 | ||||||||
\(735\) | 3.41421 | 0.125935 | ||||||||
\(736\) | −5.79899 | −0.213754 | ||||||||
\(737\) | −10.4853 | −0.386230 | ||||||||
\(738\) | −16.4853 | −0.606832 | ||||||||
\(739\) | −10.6274 | −0.390936 | −0.195468 | − | 0.980710i | \(-0.562623\pi\) | ||||
−0.195468 | + | 0.980710i | \(0.562623\pi\) | |||||||
\(740\) | 40.1421 | 1.47565 | ||||||||
\(741\) | −5.65685 | −0.207810 | ||||||||
\(742\) | −52.2843 | −1.91942 | ||||||||
\(743\) | −10.1005 | −0.370552 | −0.185276 | − | 0.982687i | \(-0.559318\pi\) | ||||
−0.185276 | + | 0.982687i | \(0.559318\pi\) | |||||||
\(744\) | −32.7279 | −1.19986 | ||||||||
\(745\) | 13.6569 | 0.500348 | ||||||||
\(746\) | −4.00000 | −0.146450 | ||||||||
\(747\) | 4.82843 | 0.176663 | ||||||||
\(748\) | 6.34315 | 0.231928 | ||||||||
\(749\) | 38.6274 | 1.41142 | ||||||||
\(750\) | −13.6569 | −0.498678 | ||||||||
\(751\) | 8.82843 | 0.322154 | 0.161077 | − | 0.986942i | \(-0.448503\pi\) | ||||
0.161077 | + | 0.986942i | \(0.448503\pi\) | |||||||
\(752\) | −21.2132 | −0.773566 | ||||||||
\(753\) | −24.4853 | −0.892293 | ||||||||
\(754\) | 18.4853 | 0.673194 | ||||||||
\(755\) | −9.31371 | −0.338961 | ||||||||
\(756\) | −10.8284 | −0.393826 | ||||||||
\(757\) | −12.3431 | −0.448619 | −0.224310 | − | 0.974518i | \(-0.572013\pi\) | ||||
−0.224310 | + | 0.974518i | \(0.572013\pi\) | |||||||
\(758\) | 11.0711 | 0.402119 | ||||||||
\(759\) | 5.17157 | 0.187716 | ||||||||
\(760\) | 85.2548 | 3.09252 | ||||||||
\(761\) | −11.4142 | −0.413765 | −0.206882 | − | 0.978366i | \(-0.566332\pi\) | ||||
−0.206882 | + | 0.978366i | \(0.566332\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −47.3137 | −1.71287 | ||||||||
\(764\) | 95.5980 | 3.45861 | ||||||||
\(765\) | −4.00000 | −0.144620 | ||||||||
\(766\) | 6.24264 | 0.225556 | ||||||||
\(767\) | −6.00000 | −0.216647 | ||||||||
\(768\) | 29.9706 | 1.08147 | ||||||||
\(769\) | 5.41421 | 0.195242 | 0.0976208 | − | 0.995224i | \(-0.468877\pi\) | ||||
0.0976208 | + | 0.995224i | \(0.468877\pi\) | |||||||
\(770\) | 32.9706 | 1.18818 | ||||||||
\(771\) | −30.9706 | −1.11538 | ||||||||
\(772\) | 33.4142 | 1.20260 | ||||||||
\(773\) | −12.0000 | −0.431610 | −0.215805 | − | 0.976436i | \(-0.569238\pi\) | ||||
−0.215805 | + | 0.976436i | \(0.569238\pi\) | |||||||
\(774\) | −6.82843 | −0.245443 | ||||||||
\(775\) | −49.3553 | −1.77290 | ||||||||
\(776\) | −51.4558 | −1.84716 | ||||||||
\(777\) | 8.68629 | 0.311619 | ||||||||
\(778\) | −25.3137 | −0.907540 | ||||||||
\(779\) | 38.6274 | 1.38397 | ||||||||
\(780\) | 13.0711 | 0.468019 | ||||||||
\(781\) | −6.00000 | −0.214697 | ||||||||
\(782\) | 10.3431 | 0.369870 | ||||||||
\(783\) | 7.65685 | 0.273634 | ||||||||
\(784\) | 3.00000 | 0.107143 | ||||||||
\(785\) | 55.1127 | 1.96706 | ||||||||
\(786\) | −14.4853 | −0.516673 | ||||||||
\(787\) | −10.3431 | −0.368693 | −0.184347 | − | 0.982861i | \(-0.559017\pi\) | ||||
−0.184347 | + | 0.982861i | \(0.559017\pi\) | |||||||
\(788\) | 30.2426 | 1.07735 | ||||||||
\(789\) | 1.17157 | 0.0417091 | ||||||||
\(790\) | 86.4264 | 3.07491 | ||||||||
\(791\) | −28.2843 | −1.00567 | ||||||||
\(792\) | −6.24264 | −0.221823 | ||||||||
\(793\) | 4.00000 | 0.142044 | ||||||||
\(794\) | 64.8701 | 2.30215 | ||||||||
\(795\) | 26.1421 | 0.927166 | ||||||||
\(796\) | −15.3137 | −0.542780 | ||||||||
\(797\) | 18.6863 | 0.661902 | 0.330951 | − | 0.943648i | \(-0.392630\pi\) | ||||
0.330951 | + | 0.943648i | \(0.392630\pi\) | |||||||
\(798\) | 38.6274 | 1.36740 | ||||||||
\(799\) | −8.28427 | −0.293076 | ||||||||
\(800\) | 10.5563 | 0.373223 | ||||||||
\(801\) | 14.2426 | 0.503239 | ||||||||
\(802\) | 60.7696 | 2.14585 | ||||||||
\(803\) | −22.9706 | −0.810614 | ||||||||
\(804\) | 28.3848 | 1.00105 | ||||||||
\(805\) | 35.3137 | 1.24464 | ||||||||
\(806\) | 17.8995 | 0.630483 | ||||||||
\(807\) | −2.82843 | −0.0995654 | ||||||||
\(808\) | −33.7990 | −1.18904 | ||||||||
\(809\) | 7.85786 | 0.276268 | 0.138134 | − | 0.990414i | \(-0.455890\pi\) | ||||
0.138134 | + | 0.990414i | \(0.455890\pi\) | |||||||
\(810\) | 8.24264 | 0.289617 | ||||||||
\(811\) | 33.0711 | 1.16128 | 0.580641 | − | 0.814160i | \(-0.302802\pi\) | ||||
0.580641 | + | 0.814160i | \(0.302802\pi\) | |||||||
\(812\) | −82.9117 | −2.90963 | ||||||||
\(813\) | 20.5858 | 0.721975 | ||||||||
\(814\) | 10.4853 | 0.367509 | ||||||||
\(815\) | −19.3137 | −0.676530 | ||||||||
\(816\) | −3.51472 | −0.123040 | ||||||||
\(817\) | 16.0000 | 0.559769 | ||||||||
\(818\) | −36.6274 | −1.28065 | ||||||||
\(819\) | 2.82843 | 0.0988332 | ||||||||
\(820\) | −89.2548 | −3.11691 | ||||||||
\(821\) | −7.31371 | −0.255250 | −0.127625 | − | 0.991822i | \(-0.540735\pi\) | ||||
−0.127625 | + | 0.991822i | \(0.540735\pi\) | |||||||
\(822\) | −19.3137 | −0.673643 | ||||||||
\(823\) | −44.4853 | −1.55066 | −0.775330 | − | 0.631557i | \(-0.782416\pi\) | ||||
−0.775330 | + | 0.631557i | \(0.782416\pi\) | |||||||
\(824\) | −4.41421 | −0.153776 | ||||||||
\(825\) | −9.41421 | −0.327761 | ||||||||
\(826\) | 40.9706 | 1.42555 | ||||||||
\(827\) | 32.5269 | 1.13107 | 0.565536 | − | 0.824724i | \(-0.308669\pi\) | ||||
0.565536 | + | 0.824724i | \(0.308669\pi\) | |||||||
\(828\) | −14.0000 | −0.486534 | ||||||||
\(829\) | −20.6274 | −0.716420 | −0.358210 | − | 0.933641i | \(-0.616613\pi\) | ||||
−0.358210 | + | 0.933641i | \(0.616613\pi\) | |||||||
\(830\) | 39.7990 | 1.38144 | ||||||||
\(831\) | −3.17157 | −0.110021 | ||||||||
\(832\) | −9.82843 | −0.340739 | ||||||||
\(833\) | 1.17157 | 0.0405926 | ||||||||
\(834\) | 48.6274 | 1.68383 | ||||||||
\(835\) | 82.4264 | 2.85248 | ||||||||
\(836\) | 30.6274 | 1.05927 | ||||||||
\(837\) | 7.41421 | 0.256273 | ||||||||
\(838\) | 71.5980 | 2.47331 | ||||||||
\(839\) | 11.6569 | 0.402439 | 0.201220 | − | 0.979546i | \(-0.435510\pi\) | ||||
0.201220 | + | 0.979546i | \(0.435510\pi\) | |||||||
\(840\) | −42.6274 | −1.47079 | ||||||||
\(841\) | 29.6274 | 1.02164 | ||||||||
\(842\) | 25.3137 | 0.872368 | ||||||||
\(843\) | 0.100505 | 0.00346158 | ||||||||
\(844\) | 41.4558 | 1.42697 | ||||||||
\(845\) | −3.41421 | −0.117453 | ||||||||
\(846\) | 17.0711 | 0.586915 | ||||||||
\(847\) | −25.4558 | −0.874673 | ||||||||
\(848\) | 22.9706 | 0.788812 | ||||||||
\(849\) | 10.1421 | 0.348077 | ||||||||
\(850\) | −18.8284 | −0.645810 | ||||||||
\(851\) | 11.2304 | 0.384975 | ||||||||
\(852\) | 16.2426 | 0.556464 | ||||||||
\(853\) | 42.9706 | 1.47128 | 0.735642 | − | 0.677371i | \(-0.236881\pi\) | ||||
0.735642 | + | 0.677371i | \(0.236881\pi\) | |||||||
\(854\) | −27.3137 | −0.934656 | ||||||||
\(855\) | −19.3137 | −0.660515 | ||||||||
\(856\) | −60.2843 | −2.06047 | ||||||||
\(857\) | 0.485281 | 0.0165769 | 0.00828845 | − | 0.999966i | \(-0.497362\pi\) | ||||
0.00828845 | + | 0.999966i | \(0.497362\pi\) | |||||||
\(858\) | 3.41421 | 0.116559 | ||||||||
\(859\) | 4.48528 | 0.153036 | 0.0765179 | − | 0.997068i | \(-0.475620\pi\) | ||||
0.0765179 | + | 0.997068i | \(0.475620\pi\) | |||||||
\(860\) | −36.9706 | −1.26069 | ||||||||
\(861\) | −19.3137 | −0.658209 | ||||||||
\(862\) | 73.5980 | 2.50676 | ||||||||
\(863\) | −47.5563 | −1.61884 | −0.809418 | − | 0.587232i | \(-0.800218\pi\) | ||||
−0.809418 | + | 0.587232i | \(0.800218\pi\) | |||||||
\(864\) | −1.58579 | −0.0539496 | ||||||||
\(865\) | 88.0833 | 2.99492 | ||||||||
\(866\) | 8.82843 | 0.300002 | ||||||||
\(867\) | 15.6274 | 0.530735 | ||||||||
\(868\) | −80.2843 | −2.72503 | ||||||||
\(869\) | 14.8284 | 0.503020 | ||||||||
\(870\) | 63.1127 | 2.13972 | ||||||||
\(871\) | −7.41421 | −0.251221 | ||||||||
\(872\) | 73.8406 | 2.50056 | ||||||||
\(873\) | 11.6569 | 0.394525 | ||||||||
\(874\) | 49.9411 | 1.68928 | ||||||||
\(875\) | −16.0000 | −0.540899 | ||||||||
\(876\) | 62.1838 | 2.10099 | ||||||||
\(877\) | 25.2132 | 0.851389 | 0.425695 | − | 0.904867i | \(-0.360030\pi\) | ||||
0.425695 | + | 0.904867i | \(0.360030\pi\) | |||||||
\(878\) | 61.4558 | 2.07403 | ||||||||
\(879\) | 9.55635 | 0.322328 | ||||||||
\(880\) | −14.4853 | −0.488299 | ||||||||
\(881\) | 34.4853 | 1.16184 | 0.580919 | − | 0.813961i | \(-0.302693\pi\) | ||||
0.580919 | + | 0.813961i | \(0.302693\pi\) | |||||||
\(882\) | −2.41421 | −0.0812908 | ||||||||
\(883\) | 9.11270 | 0.306667 | 0.153333 | − | 0.988175i | \(-0.450999\pi\) | ||||
0.153333 | + | 0.988175i | \(0.450999\pi\) | |||||||
\(884\) | 4.48528 | 0.150856 | ||||||||
\(885\) | −20.4853 | −0.688605 | ||||||||
\(886\) | 6.82843 | 0.229405 | ||||||||
\(887\) | −12.2843 | −0.412465 | −0.206233 | − | 0.978503i | \(-0.566120\pi\) | ||||
−0.206233 | + | 0.978503i | \(0.566120\pi\) | |||||||
\(888\) | −13.5563 | −0.454921 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 117.397 | 3.93516 | ||||||||
\(891\) | 1.41421 | 0.0473779 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −40.0000 | −1.33855 | ||||||||
\(894\) | −9.65685 | −0.322974 | ||||||||
\(895\) | −45.4558 | −1.51942 | ||||||||
\(896\) | 58.1421 | 1.94239 | ||||||||
\(897\) | 3.65685 | 0.122099 | ||||||||
\(898\) | 29.2132 | 0.974857 | ||||||||
\(899\) | 56.7696 | 1.89337 | ||||||||
\(900\) | 25.4853 | 0.849509 | ||||||||
\(901\) | 8.97056 | 0.298853 | ||||||||
\(902\) | −23.3137 | −0.776262 | ||||||||
\(903\) | −8.00000 | −0.266223 | ||||||||
\(904\) | 44.1421 | 1.46815 | ||||||||
\(905\) | −53.4558 | −1.77693 | ||||||||
\(906\) | 6.58579 | 0.218798 | ||||||||
\(907\) | 24.6863 | 0.819695 | 0.409847 | − | 0.912154i | \(-0.365582\pi\) | ||||
0.409847 | + | 0.912154i | \(0.365582\pi\) | |||||||
\(908\) | −62.1838 | −2.06364 | ||||||||
\(909\) | 7.65685 | 0.253962 | ||||||||
\(910\) | 23.3137 | 0.772842 | ||||||||
\(911\) | 42.6274 | 1.41231 | 0.706155 | − | 0.708058i | \(-0.250428\pi\) | ||||
0.706155 | + | 0.708058i | \(0.250428\pi\) | |||||||
\(912\) | −16.9706 | −0.561951 | ||||||||
\(913\) | 6.82843 | 0.225988 | ||||||||
\(914\) | 71.0122 | 2.34887 | ||||||||
\(915\) | 13.6569 | 0.451482 | ||||||||
\(916\) | −25.5980 | −0.845781 | ||||||||
\(917\) | −16.9706 | −0.560417 | ||||||||
\(918\) | 2.82843 | 0.0933520 | ||||||||
\(919\) | 41.1716 | 1.35812 | 0.679062 | − | 0.734081i | \(-0.262387\pi\) | ||||
0.679062 | + | 0.734081i | \(0.262387\pi\) | |||||||
\(920\) | −55.1127 | −1.81701 | ||||||||
\(921\) | 21.0711 | 0.694315 | ||||||||
\(922\) | 91.5980 | 3.01662 | ||||||||
\(923\) | −4.24264 | −0.139648 | ||||||||
\(924\) | −15.3137 | −0.503784 | ||||||||
\(925\) | −20.4437 | −0.672183 | ||||||||
\(926\) | 44.0416 | 1.44730 | ||||||||
\(927\) | 1.00000 | 0.0328443 | ||||||||
\(928\) | −12.1421 | −0.398585 | ||||||||
\(929\) | 40.2843 | 1.32168 | 0.660842 | − | 0.750525i | \(-0.270199\pi\) | ||||
0.660842 | + | 0.750525i | \(0.270199\pi\) | |||||||
\(930\) | 61.1127 | 2.00396 | ||||||||
\(931\) | 5.65685 | 0.185396 | ||||||||
\(932\) | −109.598 | −3.59000 | ||||||||
\(933\) | 22.3431 | 0.731482 | ||||||||
\(934\) | −30.6274 | −1.00216 | ||||||||
\(935\) | −5.65685 | −0.184999 | ||||||||
\(936\) | −4.41421 | −0.144283 | ||||||||
\(937\) | 7.85786 | 0.256705 | 0.128353 | − | 0.991729i | \(-0.459031\pi\) | ||||
0.128353 | + | 0.991729i | \(0.459031\pi\) | |||||||
\(938\) | 50.6274 | 1.65304 | ||||||||
\(939\) | −6.68629 | −0.218199 | ||||||||
\(940\) | 92.4264 | 3.01462 | ||||||||
\(941\) | −0.686292 | −0.0223725 | −0.0111862 | − | 0.999937i | \(-0.503561\pi\) | ||||
−0.0111862 | + | 0.999937i | \(0.503561\pi\) | |||||||
\(942\) | −38.9706 | −1.26973 | ||||||||
\(943\) | −24.9706 | −0.813153 | ||||||||
\(944\) | −18.0000 | −0.585850 | ||||||||
\(945\) | 9.65685 | 0.314137 | ||||||||
\(946\) | −9.65685 | −0.313971 | ||||||||
\(947\) | −38.3848 | −1.24734 | −0.623669 | − | 0.781689i | \(-0.714359\pi\) | ||||
−0.623669 | + | 0.781689i | \(0.714359\pi\) | |||||||
\(948\) | −40.1421 | −1.30376 | ||||||||
\(949\) | −16.2426 | −0.527258 | ||||||||
\(950\) | −90.9117 | −2.94956 | ||||||||
\(951\) | 25.4558 | 0.825462 | ||||||||
\(952\) | −14.6274 | −0.474077 | ||||||||
\(953\) | −1.85786 | −0.0601821 | −0.0300911 | − | 0.999547i | \(-0.509580\pi\) | ||||
−0.0300911 | + | 0.999547i | \(0.509580\pi\) | |||||||
\(954\) | −18.4853 | −0.598483 | ||||||||
\(955\) | −85.2548 | −2.75878 | ||||||||
\(956\) | 47.2548 | 1.52833 | ||||||||
\(957\) | 10.8284 | 0.350033 | ||||||||
\(958\) | 13.0711 | 0.422307 | ||||||||
\(959\) | −22.6274 | −0.730677 | ||||||||
\(960\) | −33.5563 | −1.08303 | ||||||||
\(961\) | 23.9706 | 0.773244 | ||||||||
\(962\) | 7.41421 | 0.239044 | ||||||||
\(963\) | 13.6569 | 0.440086 | ||||||||
\(964\) | −79.3553 | −2.55586 | ||||||||
\(965\) | −29.7990 | −0.959263 | ||||||||
\(966\) | −24.9706 | −0.803415 | ||||||||
\(967\) | −42.7279 | −1.37404 | −0.687019 | − | 0.726640i | \(-0.741081\pi\) | ||||
−0.687019 | + | 0.726640i | \(0.741081\pi\) | |||||||
\(968\) | 39.7279 | 1.27690 | ||||||||
\(969\) | −6.62742 | −0.212903 | ||||||||
\(970\) | 96.0833 | 3.08505 | ||||||||
\(971\) | 24.2843 | 0.779319 | 0.389660 | − | 0.920959i | \(-0.372593\pi\) | ||||
0.389660 | + | 0.920959i | \(0.372593\pi\) | |||||||
\(972\) | −3.82843 | −0.122797 | ||||||||
\(973\) | 56.9706 | 1.82639 | ||||||||
\(974\) | 3.75736 | 0.120394 | ||||||||
\(975\) | −6.65685 | −0.213190 | ||||||||
\(976\) | 12.0000 | 0.384111 | ||||||||
\(977\) | −42.1421 | −1.34825 | −0.674123 | − | 0.738619i | \(-0.735478\pi\) | ||||
−0.674123 | + | 0.738619i | \(0.735478\pi\) | |||||||
\(978\) | 13.6569 | 0.436698 | ||||||||
\(979\) | 20.1421 | 0.643745 | ||||||||
\(980\) | −13.0711 | −0.417540 | ||||||||
\(981\) | −16.7279 | −0.534081 | ||||||||
\(982\) | 71.5980 | 2.28478 | ||||||||
\(983\) | 3.45584 | 0.110224 | 0.0551122 | − | 0.998480i | \(-0.482448\pi\) | ||||
0.0551122 | + | 0.998480i | \(0.482448\pi\) | |||||||
\(984\) | 30.1421 | 0.960896 | ||||||||
\(985\) | −26.9706 | −0.859354 | ||||||||
\(986\) | 21.6569 | 0.689695 | ||||||||
\(987\) | 20.0000 | 0.636607 | ||||||||
\(988\) | 21.6569 | 0.688996 | ||||||||
\(989\) | −10.3431 | −0.328893 | ||||||||
\(990\) | 11.6569 | 0.370479 | ||||||||
\(991\) | 8.82843 | 0.280444 | 0.140222 | − | 0.990120i | \(-0.455218\pi\) | ||||
0.140222 | + | 0.990120i | \(0.455218\pi\) | |||||||
\(992\) | −11.7574 | −0.373297 | ||||||||
\(993\) | −5.07107 | −0.160925 | ||||||||
\(994\) | 28.9706 | 0.918890 | ||||||||
\(995\) | 13.6569 | 0.432951 | ||||||||
\(996\) | −18.4853 | −0.585729 | ||||||||
\(997\) | −35.6569 | −1.12926 | −0.564632 | − | 0.825343i | \(-0.690982\pi\) | ||||
−0.564632 | + | 0.825343i | \(0.690982\pi\) | |||||||
\(998\) | 1.41421 | 0.0447661 | ||||||||
\(999\) | 3.07107 | 0.0971643 |
(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 | 4017.2.a.d.1.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4017.2.a.d.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial |