Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8048,2,Mod(1,8048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8048, 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("8048.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8048 = 2^{4} \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8048.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.2636035467\) |
Analytic rank: | \(0\) |
Dimension: | \(33\) |
Twist minimal: | no (minimal twist has level 4024) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 8048.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.07783 | −0.622284 | −0.311142 | − | 0.950364i | \(-0.600711\pi\) | ||||
−0.311142 | + | 0.950364i | \(0.600711\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.09164 | −0.488197 | −0.244098 | − | 0.969750i | \(-0.578492\pi\) | ||||
−0.244098 | + | 0.969750i | \(0.578492\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.08785 | −0.789131 | −0.394566 | − | 0.918868i | \(-0.629105\pi\) | ||||
−0.394566 | + | 0.918868i | \(0.629105\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.83829 | −0.612763 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.69673 | 0.813095 | 0.406548 | − | 0.913630i | \(-0.366733\pi\) | ||||
0.406548 | + | 0.913630i | \(0.366733\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.315489 | 0.0875010 | 0.0437505 | − | 0.999042i | \(-0.486069\pi\) | ||||
0.0437505 | + | 0.999042i | \(0.486069\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.17660 | 0.303797 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.53047 | 0.856265 | 0.428132 | − | 0.903716i | \(-0.359172\pi\) | ||||
0.428132 | + | 0.903716i | \(0.359172\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.12979 | −1.63569 | −0.817843 | − | 0.575442i | \(-0.804830\pi\) | ||||
−0.817843 | + | 0.575442i | \(0.804830\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.25034 | 0.491064 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.16379 | −0.659697 | −0.329848 | − | 0.944034i | \(-0.606998\pi\) | ||||
−0.329848 | + | 0.944034i | \(0.606998\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.80832 | −0.761664 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.21484 | 1.00360 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.04684 | 0.937175 | 0.468587 | − | 0.883417i | \(-0.344763\pi\) | ||||
0.468587 | + | 0.883417i | \(0.344763\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.99293 | 0.717152 | 0.358576 | − | 0.933500i | \(-0.383262\pi\) | ||||
0.358576 | + | 0.933500i | \(0.383262\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.90661 | −0.505976 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.27918 | 0.385251 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.32100 | −0.217171 | −0.108586 | − | 0.994087i | \(-0.534632\pi\) | ||||
−0.108586 | + | 0.994087i | \(0.534632\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.340043 | −0.0544504 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.528913 | −0.0826024 | −0.0413012 | − | 0.999147i | \(-0.513150\pi\) | ||||
−0.0413012 | + | 0.999147i | \(0.513150\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.6427 | −1.77550 | −0.887750 | − | 0.460326i | \(-0.847733\pi\) | ||||
−0.887750 | + | 0.460326i | \(0.847733\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.00675 | 0.299149 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.96128 | −0.286083 | −0.143041 | − | 0.989717i | \(-0.545688\pi\) | ||||
−0.143041 | + | 0.989717i | \(0.545688\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.64090 | −0.377272 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.80524 | −0.532840 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.54974 | 0.350234 | 0.175117 | − | 0.984548i | \(-0.443970\pi\) | ||||
0.175117 | + | 0.984548i | \(0.443970\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.94386 | −0.396950 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.68467 | 1.01786 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.20847 | 0.547896 | 0.273948 | − | 0.961745i | \(-0.411670\pi\) | ||||
0.273948 | + | 0.961745i | \(0.411670\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14.7620 | −1.89009 | −0.945043 | − | 0.326946i | \(-0.893981\pi\) | ||||
−0.945043 | + | 0.326946i | \(0.893981\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.83806 | 0.483551 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.344401 | −0.0427177 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.34098 | 0.774674 | 0.387337 | − | 0.921938i | \(-0.373395\pi\) | ||||
0.387337 | + | 0.921938i | \(0.373395\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.41002 | 0.410518 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.3257 | −1.22544 | −0.612720 | − | 0.790300i | \(-0.709925\pi\) | ||||
−0.612720 | + | 0.790300i | \(0.709925\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.4248 | 1.33717 | 0.668587 | − | 0.743634i | \(-0.266899\pi\) | ||||
0.668587 | + | 0.743634i | \(0.266899\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.10471 | 0.473971 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.63036 | −0.641639 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.9631 | −1.45846 | −0.729229 | − | 0.684270i | \(-0.760121\pi\) | ||||
−0.729229 | + | 0.684270i | \(0.760121\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.105823 | −0.0117581 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −13.8083 | −1.51566 | −0.757831 | − | 0.652451i | \(-0.773741\pi\) | ||||
−0.757831 | + | 0.652451i | \(0.773741\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.85401 | −0.418026 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.43962 | −0.583188 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.2851 | 1.09022 | 0.545110 | − | 0.838365i | \(-0.316488\pi\) | ||||
0.545110 | + | 0.838365i | \(0.316488\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.658693 | −0.0690498 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.30369 | −0.446272 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.78316 | 0.798536 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.53931 | 0.562432 | 0.281216 | − | 0.959644i | \(-0.409262\pi\) | ||||
0.281216 | + | 0.959644i | \(0.409262\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.95737 | −0.498235 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.3127 | 1.12565 | 0.562825 | − | 0.826576i | \(-0.309714\pi\) | ||||
0.562825 | + | 0.826576i | \(0.309714\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.3946 | 1.02421 | 0.512106 | − | 0.858922i | \(-0.328865\pi\) | ||||
0.512106 | + | 0.858922i | \(0.328865\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.45656 | −0.239736 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −13.4790 | −1.30307 | −0.651533 | − | 0.758620i | \(-0.725874\pi\) | ||||
−0.651533 | + | 0.758620i | \(0.725874\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.03302 | −0.386293 | −0.193146 | − | 0.981170i | \(-0.561869\pi\) | ||||
−0.193146 | + | 0.981170i | \(0.561869\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.42381 | 0.135142 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.93417 | 0.840456 | 0.420228 | − | 0.907419i | \(-0.361950\pi\) | ||||
0.420228 | + | 0.907419i | \(0.361950\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.45373 | 0.322062 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.579960 | −0.0536174 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.37108 | −0.675706 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.72764 | −0.338876 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.570077 | 0.0514021 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.61552 | 0.860038 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.2938 | −1.44584 | −0.722920 | − | 0.690932i | \(-0.757201\pi\) | ||||
−0.722920 | + | 0.690932i | \(0.757201\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 12.5488 | 1.10486 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.452067 | −0.0394972 | −0.0197486 | − | 0.999805i | \(-0.506287\pi\) | ||||
−0.0197486 | + | 0.999805i | \(0.506287\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 14.8859 | 1.29077 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.69273 | −0.489952 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.0610484 | −0.00521572 | −0.00260786 | − | 0.999997i | \(-0.500830\pi\) | ||||
−0.00260786 | + | 0.999997i | \(0.500830\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.756749 | −0.0641866 | −0.0320933 | − | 0.999485i | \(-0.510217\pi\) | ||||
−0.0320933 | + | 0.999485i | \(0.510217\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.11392 | 0.178024 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.850790 | 0.0711466 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.50934 | −0.457526 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.84643 | 0.234770 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 14.5148 | 1.18910 | 0.594549 | − | 0.804060i | \(-0.297331\pi\) | ||||
0.594549 | + | 0.804060i | \(0.297331\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.746583 | 0.0607561 | 0.0303780 | − | 0.999538i | \(-0.490329\pi\) | ||||
0.0303780 | + | 0.999538i | \(0.490329\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.49003 | −0.524688 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.35885 | −0.350111 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.21886 | −0.576128 | −0.288064 | − | 0.957611i | \(-0.593012\pi\) | ||||
−0.288064 | + | 0.957611i | \(0.593012\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.74818 | −0.217945 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.60551 | 0.520587 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −22.5224 | −1.76409 | −0.882045 | − | 0.471166i | \(-0.843833\pi\) | ||||
−0.882045 | + | 0.471166i | \(0.843833\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.17297 | 0.247016 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.7352 | 1.44977 | 0.724887 | − | 0.688867i | \(-0.241892\pi\) | ||||
0.724887 | + | 0.688867i | \(0.241892\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9005 | −0.992344 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 13.1066 | 1.00229 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.74517 | −0.360768 | −0.180384 | − | 0.983596i | \(-0.557734\pi\) | ||||
−0.180384 | + | 0.983596i | \(0.557734\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.95119 | 0.601053 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.53600 | −0.340947 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 24.6303 | 1.84095 | 0.920476 | − | 0.390799i | \(-0.127801\pi\) | ||||
0.920476 | + | 0.390799i | \(0.127801\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.6193 | 1.53262 | 0.766309 | − | 0.642472i | \(-0.222091\pi\) | ||||
0.766309 | + | 0.642472i | \(0.222091\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 15.9109 | 1.17617 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.44206 | 0.106022 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.52073 | 0.696225 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −10.8878 | −0.791969 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.84208 | −0.712148 | −0.356074 | − | 0.934458i | \(-0.615885\pi\) | ||||
−0.356074 | + | 0.934458i | \(0.615885\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −20.8828 | −1.50318 | −0.751589 | − | 0.659632i | \(-0.770712\pi\) | ||||
−0.751589 | + | 0.659632i | \(0.770712\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.371204 | 0.0265825 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.6869 | 0.761412 | 0.380706 | − | 0.924696i | \(-0.375681\pi\) | ||||
0.380706 | + | 0.924696i | \(0.375681\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.79192 | 0.552355 | 0.276177 | − | 0.961107i | \(-0.410932\pi\) | ||||
0.276177 | + | 0.961107i | \(0.410932\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.83448 | −0.482067 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −10.5370 | −0.739554 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.577383 | 0.0403262 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.81597 | 0.404238 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −19.2271 | −1.32997 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 27.2693 | 1.87730 | 0.938649 | − | 0.344874i | \(-0.112078\pi\) | ||||
0.938649 | + | 0.344874i | \(0.112078\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 11.1294 | 0.762571 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 12.7097 | 0.866793 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.33663 | −0.565927 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −12.3140 | −0.832102 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.11383 | 0.0749240 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.4941 | −1.10453 | −0.552265 | − | 0.833669i | \(-0.686236\pi\) | ||||
−0.552265 | + | 0.833669i | \(0.686236\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.00080 | 0.466720 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.235622 | −0.0156388 | −0.00781940 | − | 0.999969i | \(-0.502489\pi\) | ||||
−0.00781940 | + | 0.999969i | \(0.502489\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.6417 | 1.29796 | 0.648981 | − | 0.760805i | \(-0.275195\pi\) | ||||
0.648981 | + | 0.760805i | \(0.275195\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.06855 | 0.399281 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 24.4561 | 1.60217 | 0.801087 | − | 0.598548i | \(-0.204255\pi\) | ||||
0.801087 | + | 0.598548i | \(0.204255\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.14102 | 0.139665 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 13.9719 | 0.907574 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.5322 | 0.745956 | 0.372978 | − | 0.927840i | \(-0.378337\pi\) | ||||
0.372978 | + | 0.927840i | \(0.378337\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −23.2970 | −1.50069 | −0.750345 | − | 0.661047i | \(-0.770112\pi\) | ||||
−0.750345 | + | 0.661047i | \(0.770112\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.5305 | −0.996279 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.88291 | 0.184183 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.24937 | −0.143124 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 14.8830 | 0.943172 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −17.6645 | −1.11497 | −0.557487 | − | 0.830186i | \(-0.688234\pi\) | ||||
−0.557487 | + | 0.830186i | \(0.688234\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.53190 | −0.536396 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.15395 | 0.260130 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 27.1780 | 1.69532 | 0.847659 | − | 0.530542i | \(-0.178012\pi\) | ||||
0.847659 | + | 0.530542i | \(0.178012\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.75805 | 0.171377 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.27755 | −0.574266 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.44008 | 0.582100 | 0.291050 | − | 0.956708i | \(-0.405995\pi\) | ||||
0.291050 | + | 0.956708i | \(0.405995\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.78341 | −0.170983 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −11.0856 | −0.678426 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 18.6112 | 1.13474 | 0.567371 | − | 0.823462i | \(-0.307961\pi\) | ||||
0.567371 | + | 0.823462i | \(0.307961\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.7573 | −1.07868 | −0.539341 | − | 0.842088i | \(-0.681327\pi\) | ||||
−0.539341 | + | 0.842088i | \(0.681327\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.709957 | 0.0429685 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −10.2700 | −0.619305 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 21.4657 | 1.28975 | 0.644874 | − | 0.764289i | \(-0.276910\pi\) | ||||
0.644874 | + | 0.764289i | \(0.276910\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.34017 | −0.439445 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −26.2281 | −1.56464 | −0.782318 | − | 0.622880i | \(-0.785963\pi\) | ||||
−0.782318 | + | 0.622880i | \(0.785963\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.7796 | 0.938000 | 0.469000 | − | 0.883198i | \(-0.344614\pi\) | ||||
0.469000 | + | 0.883198i | \(0.344614\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −8.38890 | −0.496916 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.10429 | 0.0651841 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.53578 | −0.266810 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.97042 | −0.349992 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.48083 | −0.144932 | −0.0724659 | − | 0.997371i | \(-0.523087\pi\) | ||||
−0.0724659 | + | 0.997371i | \(0.523087\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.59414 | −0.267481 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 14.0630 | 0.816019 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.998143 | −0.0577241 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 24.3082 | 1.40110 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −12.1931 | −0.700474 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 16.1148 | 0.922734 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 27.1739 | 1.55090 | 0.775448 | − | 0.631411i | \(-0.217524\pi\) | ||||
0.775448 | + | 0.631411i | \(0.217524\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.2036 | −0.637350 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.61285 | 0.431685 | 0.215843 | − | 0.976428i | \(-0.430750\pi\) | ||||
0.215843 | + | 0.976428i | \(0.430750\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.4041 | −0.927215 | −0.463608 | − | 0.886041i | \(-0.653445\pi\) | ||||
−0.463608 | + | 0.886041i | \(0.653445\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.18979 | −0.236068 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 17.3242 | 0.973025 | 0.486512 | − | 0.873674i | \(-0.338269\pi\) | ||||
0.486512 | + | 0.873674i | \(0.338269\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 13.6100 | 0.762012 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 14.5281 | 0.810877 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −25.1715 | −1.40058 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.20148 | −0.0666463 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.34689 | 0.240384 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.09486 | 0.225757 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 31.7355 | 1.74434 | 0.872170 | − | 0.489203i | \(-0.162712\pi\) | ||||
0.872170 | + | 0.489203i | \(0.162712\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.42838 | 0.133075 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.92207 | −0.378193 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.54463 | −0.0841412 | −0.0420706 | − | 0.999115i | \(-0.513395\pi\) | ||||
−0.0420706 | + | 0.999115i | \(0.513395\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.62949 | −0.523002 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.7679 | 0.583113 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.1287 | 1.08685 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.72252 | −0.200414 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.697526 | −0.0374452 | −0.0187226 | − | 0.999825i | \(-0.505960\pi\) | ||||
−0.0187226 | + | 0.999825i | \(0.505960\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.1003 | 1.23653 | 0.618265 | − | 0.785970i | \(-0.287836\pi\) | ||||
0.618265 | + | 0.785970i | \(0.287836\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.64522 | 0.0878156 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.46525 | 0.450560 | 0.225280 | − | 0.974294i | \(-0.427670\pi\) | ||||
0.225280 | + | 0.974294i | \(0.427670\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11.2720 | 0.598256 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 7.94474 | 0.420480 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 19.9446 | 1.05264 | 0.526319 | − | 0.850287i | \(-0.323572\pi\) | ||||
0.526319 | + | 0.850287i | \(0.323572\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 31.8339 | 1.67547 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.01775 | 0.210877 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12.4718 | −0.652804 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.0930 | 0.579052 | 0.289526 | − | 0.957170i | \(-0.406502\pi\) | ||||
0.289526 | + | 0.957170i | \(0.406502\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.972296 | 0.0506157 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.32347 | −0.276381 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.19976 | −0.217455 | −0.108728 | − | 0.994072i | \(-0.534678\pi\) | ||||
−0.108728 | + | 0.994072i | \(0.534678\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −10.3639 | −0.535188 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.59222 | 0.0820037 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.71111 | 0.293360 | 0.146680 | − | 0.989184i | \(-0.453141\pi\) | ||||
0.146680 | + | 0.989184i | \(0.453141\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 17.5619 | 0.899723 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 17.3126 | 0.884633 | 0.442316 | − | 0.896859i | \(-0.354157\pi\) | ||||
0.442316 | + | 0.896859i | \(0.354157\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.14633 | 0.313246 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 21.4027 | 1.08796 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 27.8613 | 1.41262 | 0.706311 | − | 0.707901i | \(-0.250358\pi\) | ||||
0.706311 | + | 0.707901i | \(0.250358\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.1697 | −0.564875 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.487249 | 0.0245785 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 14.1510 | 0.712014 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −30.3468 | −1.52306 | −0.761531 | − | 0.648129i | \(-0.775552\pi\) | ||||
−0.761531 | + | 0.648129i | \(0.775552\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −16.0444 | −0.803225 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 21.6813 | 1.08271 | 0.541355 | − | 0.840794i | \(-0.317911\pi\) | ||||
0.541355 | + | 0.840794i | \(0.317911\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.25973 | 0.0627515 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.115521 | 0.00574026 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.56239 | −0.176581 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −20.9451 | −1.03567 | −0.517834 | − | 0.855481i | \(-0.673261\pi\) | ||||
−0.517834 | + | 0.855481i | \(0.673261\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.0657996 | 0.00324566 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8.78663 | −0.432362 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15.0737 | 0.739941 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.815644 | 0.0399423 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.85144 | 0.139302 | 0.0696509 | − | 0.997571i | \(-0.477811\pi\) | ||||
0.0696509 | + | 0.997571i | \(0.477811\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.1212 | 1.12686 | 0.563430 | − | 0.826164i | \(-0.309481\pi\) | ||||
0.563430 | + | 0.826164i | \(0.309481\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.60541 | 0.175301 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −13.4452 | −0.652186 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 30.8209 | 1.49153 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.917004 | −0.0442734 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14.2031 | −0.684138 | −0.342069 | − | 0.939675i | \(-0.611128\pi\) | ||||
−0.342069 | + | 0.939675i | \(0.611128\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.5386 | 1.17925 | 0.589624 | − | 0.807678i | \(-0.299276\pi\) | ||||
0.589624 | + | 0.807678i | \(0.299276\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.93811 | 0.284711 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 22.5572 | 1.07906 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.3497 | 1.25760 | 0.628800 | − | 0.777567i | \(-0.283546\pi\) | ||||
0.628800 | + | 0.777567i | \(0.283546\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.85474 | 0.231178 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 18.0001 | 0.855209 | 0.427604 | − | 0.903966i | \(-0.359358\pi\) | ||||
0.427604 | + | 0.903966i | \(0.359358\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11.2276 | −0.532242 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −15.6444 | −0.739956 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −20.4589 | −0.965517 | −0.482758 | − | 0.875754i | \(-0.660365\pi\) | ||||
−0.482758 | + | 0.875754i | \(0.660365\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.42634 | −0.0671636 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.804687 | −0.0378075 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.719056 | 0.0337099 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.03988 | 0.188978 | 0.0944888 | − | 0.995526i | \(-0.469878\pi\) | ||||
0.0944888 | + | 0.995526i | \(0.469878\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 18.4108 | 0.859344 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −31.2568 | −1.45577 | −0.727887 | − | 0.685697i | \(-0.759498\pi\) | ||||
−0.727887 | + | 0.685697i | \(0.759498\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −27.7833 | −1.29120 | −0.645600 | − | 0.763676i | \(-0.723393\pi\) | ||||
−0.645600 | + | 0.763676i | \(0.723393\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.69809 | 0.217868 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9.91012 | −0.458586 | −0.229293 | − | 0.973357i | \(-0.573641\pi\) | ||||
−0.229293 | + | 0.973357i | \(0.573641\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13.2390 | −0.611320 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.78069 | 0.358515 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −31.3973 | −1.44365 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 27.1525 | 1.24584 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.68717 | −0.214611 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −17.8938 | −0.817589 | −0.408795 | − | 0.912626i | \(-0.634051\pi\) | ||||
−0.408795 | + | 0.912626i | \(0.634051\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.416762 | −0.0190027 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −7.11960 | −0.323953 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.04694 | −0.274577 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 29.2727 | 1.32647 | 0.663237 | − | 0.748409i | \(-0.269182\pi\) | ||||
0.663237 | + | 0.748409i | \(0.269182\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 24.2752 | 1.09776 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 36.3888 | 1.64221 | 0.821103 | − | 0.570780i | \(-0.193359\pi\) | ||||
0.821103 | + | 0.570780i | \(0.193359\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 17.8177 | 0.802470 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.41167 | 0.243236 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 21.5586 | 0.967033 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19.5482 | −0.875100 | −0.437550 | − | 0.899194i | \(-0.644154\pi\) | ||||
−0.437550 | + | 0.899194i | \(0.644154\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −20.1933 | −0.902171 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.00000 | 0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.3494 | −0.549539 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 13.9045 | 0.617519 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −35.6532 | −1.58030 | −0.790149 | − | 0.612915i | \(-0.789997\pi\) | ||||
−0.790149 | + | 0.612915i | \(0.789997\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −23.8533 | −1.05521 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −37.1807 | −1.64157 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11.3472 | −0.500017 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.28905 | −0.232612 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.11447 | 0.224500 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19.7841 | −0.866755 | −0.433378 | − | 0.901212i | \(-0.642678\pi\) | ||||
−0.433378 | + | 0.901212i | \(0.642678\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −30.9566 | −1.35364 | −0.676819 | − | 0.736149i | \(-0.736642\pi\) | ||||
−0.676819 | + | 0.736149i | \(0.736642\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −8.57000 | −0.374025 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 14.0969 | 0.614072 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12.9904 | −0.564800 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.73638 | −0.335730 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.166866 | −0.00722779 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14.7143 | 0.636153 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −26.5472 | −1.14559 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7.12180 | −0.306758 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.7017 | −0.804050 | −0.402025 | − | 0.915629i | \(-0.631694\pi\) | ||||
−0.402025 | + | 0.915629i | \(0.631694\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −22.2240 | −0.953723 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.40260 | 0.188587 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.5786 | 0.837120 | 0.418560 | − | 0.908189i | \(-0.362535\pi\) | ||||
0.418560 | + | 0.908189i | \(0.362535\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 27.1369 | 1.15818 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −35.9829 | −1.53292 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 27.0649 | 1.15092 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.55429 | −0.0659760 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 26.7877 | 1.13503 | 0.567516 | − | 0.823362i | \(-0.307904\pi\) | ||||
0.567516 | + | 0.823362i | \(0.307904\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.67316 | −0.155358 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −10.2617 | −0.433249 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −37.8793 | −1.59642 | −0.798211 | − | 0.602378i | \(-0.794220\pi\) | ||||
−0.798211 | + | 0.602378i | \(0.794220\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.75290 | −0.410308 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.220942 | 0.00927868 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −33.9553 | −1.42348 | −0.711740 | − | 0.702443i | \(-0.752093\pi\) | ||||
−0.711740 | + | 0.702443i | \(0.752093\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.8686 | −0.873324 | −0.436662 | − | 0.899626i | \(-0.643839\pi\) | ||||
−0.436662 | + | 0.899626i | \(0.643839\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10.6081 | 0.443158 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 12.0487 | 0.502467 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 36.3441 | 1.51303 | 0.756513 | − | 0.653978i | \(-0.226901\pi\) | ||||
0.756513 | + | 0.653978i | \(0.226901\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 22.5081 | 0.935403 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 28.8297 | 1.19606 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.87598 | 0.284774 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.633108 | 0.0261758 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.30158 | 0.383917 | 0.191959 | − | 0.981403i | \(-0.438516\pi\) | ||||
0.191959 | + | 0.981403i | \(0.438516\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −28.4688 | −1.17304 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −11.5187 | −0.473814 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −31.0040 | −1.27318 | −0.636592 | − | 0.771201i | \(-0.719656\pi\) | ||||
−0.636592 | + | 0.771201i | \(0.719656\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.04657 | 0.329877 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.39834 | −0.343721 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 41.3474 | 1.68941 | 0.844705 | − | 0.535231i | \(-0.179776\pi\) | ||||
0.844705 | + | 0.535231i | \(0.179776\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.0347 | −0.654071 | −0.327035 | − | 0.945012i | \(-0.606050\pi\) | ||||
−0.327035 | + | 0.945012i | \(0.606050\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −11.6566 | −0.474692 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.06924 | 0.165438 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −23.6655 | −0.960552 | −0.480276 | − | 0.877117i | \(-0.659463\pi\) | ||||
−0.480276 | + | 0.877117i | \(0.659463\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 11.3571 | 0.460212 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.618764 | −0.0250325 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 31.4762 | 1.27131 | 0.635657 | − | 0.771972i | \(-0.280729\pi\) | ||||
0.635657 | + | 0.771972i | \(0.280729\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.622319 | −0.0250943 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 48.3544 | 1.94668 | 0.973338 | − | 0.229376i | \(-0.0736685\pi\) | ||||
0.973338 | + | 0.229376i | \(0.0736685\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15.4928 | 0.622709 | 0.311355 | − | 0.950294i | \(-0.399217\pi\) | ||||
0.311355 | + | 0.950294i | \(0.399217\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −16.4987 | −0.662069 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −21.4737 | −0.860327 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8.54491 | 0.341796 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 20.7235 | 0.827617 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.66376 | −0.185956 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.5340 | 0.618400 | 0.309200 | − | 0.950997i | \(-0.399939\pi\) | ||||
0.309200 | + | 0.950997i | \(0.399939\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −29.3916 | −1.16821 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 17.7870 | 0.705854 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.833176 | −0.0330116 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 18.9817 | 0.750905 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −28.2557 | −1.11603 | −0.558017 | − | 0.829829i | \(-0.688438\pi\) | ||||
−0.558017 | + | 0.829829i | \(0.688438\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 35.9951 | 1.41951 | 0.709754 | − | 0.704449i | \(-0.248806\pi\) | ||||
0.709754 | + | 0.704449i | \(0.248806\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −13.6988 | −0.539391 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 15.1203 | 0.594441 | 0.297220 | − | 0.954809i | \(-0.403940\pi\) | ||||
0.297220 | + | 0.954809i | \(0.403940\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.3491 | 0.445492 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.98544 | 0.352167 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 38.3334 | 1.50010 | 0.750052 | − | 0.661379i | \(-0.230029\pi\) | ||||
0.750052 | + | 0.661379i | \(0.230029\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.493494 | 0.0192824 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −21.0021 | −0.819371 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15.8517 | −0.617496 | −0.308748 | − | 0.951144i | \(-0.599910\pi\) | ||||
−0.308748 | + | 0.951144i | \(0.599910\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.53797 | 0.293193 | 0.146597 | − | 0.989196i | \(-0.453168\pi\) | ||||
0.146597 | + | 0.989196i | \(0.453168\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.20051 | −0.0466240 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −16.2500 | −0.630150 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −15.9672 | −0.618251 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 17.7778 | 0.687330 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −39.8093 | −1.53682 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.74054 | −0.221282 | −0.110641 | − | 0.993860i | \(-0.535290\pi\) | ||||
−0.110641 | + | 0.993860i | \(0.535290\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −19.8598 | −0.764403 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 20.2200 | 0.777118 | 0.388559 | − | 0.921424i | \(-0.372973\pi\) | ||||
0.388559 | + | 0.921424i | \(0.372973\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −11.5652 | −0.443833 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.253960 | 0.00973177 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −16.1656 | −0.618559 | −0.309279 | − | 0.950971i | \(-0.600088\pi\) | ||||
−0.309279 | + | 0.950971i | \(0.600088\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.0666430 | 0.00254630 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −21.1704 | −0.807700 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.804417 | 0.0306458 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23.7362 | −0.902968 | −0.451484 | − | 0.892279i | \(-0.649105\pi\) | ||||
−0.451484 | + | 0.892279i | \(0.649105\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 10.3502 | 0.393173 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.826098 | 0.0313357 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.86731 | −0.0707295 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −26.3595 | −0.997007 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −38.1029 | −1.43913 | −0.719563 | − | 0.694427i | \(-0.755658\pi\) | ||||
−0.719563 | + | 0.694427i | \(0.755658\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.41846 | 0.355224 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.30764 | −0.0869109 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −23.6191 | −0.888286 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 47.4945 | 1.78370 | 0.891848 | − | 0.452336i | \(-0.149409\pi\) | ||||
0.891848 | + | 0.452336i | \(0.149409\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 23.8299 | 0.893689 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −12.6328 | −0.473103 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.928756 | −0.0347335 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −12.4297 | −0.464196 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 42.3751 | 1.58033 | 0.790163 | − | 0.612897i | \(-0.209996\pi\) | ||||
0.790163 | + | 0.612897i | \(0.209996\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −21.7024 | −0.808238 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 25.1101 | 0.933854 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −19.2200 | −0.713812 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20.3476 | −0.754651 | −0.377326 | − | 0.926081i | \(-0.623156\pi\) | ||||
−0.377326 | + | 0.926081i | \(0.623156\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 17.0566 | 0.631726 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −41.1043 | −1.52030 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21.2441 | −0.784668 | −0.392334 | − | 0.919823i | \(-0.628332\pi\) | ||||
−0.392334 | + | 0.919823i | \(0.628332\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.10728 | −0.114614 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 17.0999 | 0.629884 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 36.1913 | 1.33132 | 0.665659 | − | 0.746256i | \(-0.268150\pi\) | ||||
0.665659 | + | 0.746256i | \(0.268150\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.42443 | 0.0890637 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 29.8356 | 1.09456 | 0.547281 | − | 0.836949i | \(-0.315663\pi\) | ||||
0.547281 | + | 0.836949i | \(0.315663\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15.8449 | −0.580513 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 25.3837 | 0.928742 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 28.1421 | 1.02829 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17.7038 | 0.646019 | 0.323010 | − | 0.946396i | \(-0.395305\pi\) | ||||
0.323010 | + | 0.946396i | \(0.395305\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 19.0393 | 0.693829 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.815001 | −0.0296609 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.818007 | −0.0297310 | −0.0148655 | − | 0.999890i | \(-0.504732\pi\) | ||||
−0.0148655 | + | 0.999890i | \(0.504732\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 9.19591 | 0.333791 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12.8127 | −0.464459 | −0.232229 | − | 0.972661i | \(-0.574602\pi\) | ||||
−0.232229 | + | 0.972661i | \(0.574602\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.42032 | 0.304836 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 7.08478 | 0.256151 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.32773 | 0.0479414 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.17687 | 0.0424389 | 0.0212194 | − | 0.999775i | \(-0.493245\pi\) | ||||
0.0212194 | + | 0.999775i | \(0.493245\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −29.2932 | −1.05497 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 10.2684 | 0.369329 | 0.184664 | − | 0.982802i | \(-0.440880\pi\) | ||||
0.184664 | + | 0.982802i | \(0.440880\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −15.2064 | −0.546229 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.97270 | −0.106645 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.77104 | 0.135111 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −27.8457 | −0.996399 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 26.3185 | 0.940545 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.88041 | 0.281264 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17.5512 | −0.625633 | −0.312816 | − | 0.949814i | \(-0.601272\pi\) | ||||
−0.312816 | + | 0.949814i | \(0.601272\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −10.1748 | −0.362231 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −18.6532 | −0.663230 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.65727 | −0.165384 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.00003 | 0.106400 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 20.6806 | 0.732546 | 0.366273 | − | 0.930507i | \(-0.380634\pi\) | ||||
0.366273 | + | 0.930507i | \(0.380634\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.92425 | −0.244962 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −18.9070 | −0.668047 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 30.8097 | 1.08725 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.21085 | −0.254149 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −20.0596 | −0.706131 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −15.1849 | −0.533871 | −0.266936 | − | 0.963714i | \(-0.586011\pi\) | ||||
−0.266936 | + | 0.963714i | \(0.586011\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.41204 | 0.119813 | 0.0599064 | − | 0.998204i | \(-0.480920\pi\) | ||||
0.0599064 | + | 0.998204i | \(0.480920\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 19.1393 | 0.671246 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 24.5864 | 0.861222 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 83.0102 | 2.90416 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.21087 | 0.0423112 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 24.7846 | 0.864990 | 0.432495 | − | 0.901636i | \(-0.357633\pi\) | ||||
0.432495 | + | 0.901636i | \(0.357633\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27.9361 | 0.973793 | 0.486896 | − | 0.873460i | \(-0.338129\pi\) | ||||
0.486896 | + | 0.873460i | \(0.338129\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 11.0693 | 0.385384 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 39.9686 | 1.38984 | 0.694922 | − | 0.719085i | \(-0.255439\pi\) | ||||
0.694922 | + | 0.719085i | \(0.255439\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.18764 | 0.284368 | 0.142184 | − | 0.989840i | \(-0.454587\pi\) | ||||
0.142184 | + | 0.989840i | \(0.454587\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −23.1363 | −0.802589 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −9.32362 | −0.323044 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −20.4521 | −0.707775 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 20.8225 | 0.719731 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 34.9548 | 1.20678 | 0.603388 | − | 0.797448i | \(-0.293817\pi\) | ||||
0.603388 | + | 0.797448i | \(0.293817\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.52940 | −0.121703 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 28.2693 | 0.973647 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 14.0827 | 0.484459 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.78274 | 0.267418 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −17.0077 | −0.583702 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.17938 | 0.143267 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.87862 | 0.235519 | 0.117760 | − | 0.993042i | \(-0.462429\pi\) | ||||
0.117760 | + | 0.993042i | \(0.462429\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −14.3077 | −0.489313 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −6.03666 | −0.206208 | −0.103104 | − | 0.994671i | \(-0.532877\pi\) | ||||
−0.103104 | + | 0.994671i | \(0.532877\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 40.9708 | 1.39791 | 0.698953 | − | 0.715168i | \(-0.253650\pi\) | ||||
0.698953 | + | 0.715168i | \(0.253650\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.19023 | −0.0405630 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 37.8792 | 1.28942 | 0.644712 | − | 0.764426i | \(-0.276977\pi\) | ||||
0.644712 | + | 0.764426i | \(0.276977\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.18002 | 0.176126 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.88878 | 0.166032 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −34.9579 | −1.18586 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.00051 | 0.0677847 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −10.1829 | −0.344638 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −20.0757 | −0.678683 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.111887 | −0.00377816 | −0.00188908 | − | 0.999998i | \(-0.500601\pi\) | ||||
−0.00188908 | + | 0.999998i | \(0.500601\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.67391 | 0.0901887 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −54.6495 | −1.84119 | −0.920595 | − | 0.390519i | \(-0.872296\pi\) | ||||
−0.920595 | + | 0.390519i | \(0.872296\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 54.6962 | 1.84067 | 0.920336 | − | 0.391128i | \(-0.127915\pi\) | ||||
0.920336 | + | 0.391128i | \(0.127915\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.95168 | 0.166449 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −53.3624 | −1.79173 | −0.895867 | − | 0.444322i | \(-0.853445\pi\) | ||||
−0.895867 | + | 0.444322i | \(0.853445\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 34.0189 | 1.14096 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.285376 | −0.00956045 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 13.9835 | 0.467941 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −26.8874 | −0.898747 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.07583 | 0.0359208 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 20.1517 | 0.672097 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.00180 | 0.299893 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −26.2001 | −0.871883 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −22.5088 | −0.748219 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.24736 | 0.174236 | 0.0871179 | − | 0.996198i | \(-0.472234\pi\) | ||||
0.0871179 | + | 0.996198i | \(0.472234\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −20.7959 | −0.689757 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 32.8403 | 1.08805 | 0.544023 | − | 0.839070i | \(-0.316900\pi\) | ||||
0.544023 | + | 0.839070i | \(0.316900\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −37.2374 | −1.23238 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −17.3690 | −0.574202 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.943845 | 0.0311685 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −52.6044 | −1.73526 | −0.867630 | − | 0.497211i | \(-0.834358\pi\) | ||||
−0.867630 | + | 0.497211i | \(0.834358\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −29.2888 | −0.965097 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.25766 | −0.107227 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.03080 | 0.165412 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −19.1083 | −0.627600 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.31771 | −0.108850 | −0.0544252 | − | 0.998518i | \(-0.517333\pi\) | ||||
−0.0544252 | + | 0.998518i | \(0.517333\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18.8291 | 0.617097 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8.20534 | −0.268631 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −10.3932 | −0.339895 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −35.1170 | −1.14722 | −0.573612 | − | 0.819127i | \(-0.694458\pi\) | ||||
−0.573612 | + | 0.819127i | \(0.694458\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 17.6808 | 0.576991 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 29.8064 | 0.971661 | 0.485831 | − | 0.874053i | \(-0.338517\pi\) | ||||
0.485831 | + | 0.874053i | \(0.338517\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.67337 | 0.0544925 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 11.8855 | 0.386637 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 22.6189 | 0.735015 | 0.367508 | − | 0.930020i | \(-0.380211\pi\) | ||||
0.367508 | + | 0.930020i | \(0.380211\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.60441 | 0.117004 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −18.6725 | −0.605497 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.46365 | −0.176985 | −0.0884926 | − | 0.996077i | \(-0.528205\pi\) | ||||
−0.0884926 | + | 0.996077i | \(0.528205\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10.7440 | 0.347668 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −14.6692 | −0.474188 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.127460 | 0.00411589 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0565 | −0.485693 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 24.7784 | 0.798471 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 22.7965 | 0.733846 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −58.7962 | −1.89076 | −0.945379 | − | 0.325974i | \(-0.894308\pi\) | ||||
−0.945379 | + | 0.325974i | \(0.894308\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 27.1305 | 0.871558 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6.30246 | −0.202256 | −0.101128 | − | 0.994873i | \(-0.532245\pi\) | ||||
−0.101128 | + | 0.994873i | \(0.532245\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.57998 | 0.0506517 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.29499 | 0.0414729 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 22.5507 | 0.721461 | 0.360730 | − | 0.932670i | \(-0.382527\pi\) | ||||
0.360730 | + | 0.932670i | \(0.382527\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 27.7362 | 0.886452 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.41385 | 0.236706 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −40.0002 | −1.27581 | −0.637904 | − | 0.770116i | \(-0.720198\pi\) | ||||
−0.637904 | + | 0.770116i | \(0.720198\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.6663 | −0.371719 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.41355 | −0.140485 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 36.8352 | 1.17129 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.53861 | −0.175940 | −0.0879699 | − | 0.996123i | \(-0.528038\pi\) | ||||
−0.0879699 | + | 0.996123i | \(0.528038\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −34.2053 | −1.08547 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.50598 | −0.269658 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 56.4989 | 1.78934 | 0.894669 | − | 0.446729i | \(-0.147411\pi\) | ||||
0.894669 | + | 0.446729i | \(0.147411\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.88881 | −0.217952 |
(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 | 8048.2.a.y.1.12 | 33 | ||
4.3 | odd | 2 | 4024.2.a.f.1.22 | ✓ | 33 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4024.2.a.f.1.22 | ✓ | 33 | 4.3 | odd | 2 | ||
8048.2.a.y.1.12 | 33 | 1.1 | even | 1 | trivial |