Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1875,2,Mod(1249,1875)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1875, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1875.1249");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1875 = 3 \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1875.b (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(14.9719503790\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 25x^{14} + 246x^{12} + 1220x^{10} + 3281x^{8} + 4880x^{6} + 3936x^{4} + 1600x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1249.15 | ||
Root | \(0.770071i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1875.1249 |
Dual form | 1875.2.b.g.1249.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1875\mathbb{Z}\right)^\times\).
\(n\) | \(626\) | \(1252\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.59716i | 1.83647i | 0.396035 | + | 0.918235i | \(0.370386\pi\) | ||||
−0.396035 | + | 0.918235i | \(0.629614\pi\) | |||||||
\(3\) | − 1.00000i | − 0.577350i | ||||||||
\(4\) | −4.74525 | −2.37263 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.59716 | 1.06029 | ||||||||
\(7\) | 3.28414i | 1.24129i | 0.784093 | + | 0.620643i | \(0.213129\pi\) | ||||
−0.784093 | + | 0.620643i | \(0.786871\pi\) | |||||||
\(8\) | − 7.12986i | − 2.52079i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.30834 | 1.29901 | 0.649507 | − | 0.760356i | \(-0.274975\pi\) | ||||
0.649507 | + | 0.760356i | \(0.274975\pi\) | |||||||
\(12\) | 4.74525i | 1.36984i | ||||||||
\(13\) | 3.46120i | 0.959964i | 0.877278 | + | 0.479982i | \(0.159357\pi\) | ||||
−0.877278 | + | 0.479982i | \(0.840643\pi\) | |||||||
\(14\) | −8.52943 | −2.27959 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 9.02691 | 2.25673 | ||||||||
\(17\) | − 5.44757i | − 1.32123i | −0.750725 | − | 0.660615i | \(-0.770295\pi\) | ||||
0.750725 | − | 0.660615i | \(-0.229705\pi\) | |||||||
\(18\) | − 2.59716i | − 0.612157i | ||||||||
\(19\) | 7.63427 | 1.75142 | 0.875711 | − | 0.482835i | \(-0.160393\pi\) | ||||
0.875711 | + | 0.482835i | \(0.160393\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.28414 | 0.716657 | ||||||||
\(22\) | 11.1895i | 2.38560i | ||||||||
\(23\) | 5.04986i | 1.05297i | 0.850185 | + | 0.526484i | \(0.176490\pi\) | ||||
−0.850185 | + | 0.526484i | \(0.823510\pi\) | |||||||
\(24\) | −7.12986 | −1.45538 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −8.98929 | −1.76295 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | − 15.5841i | − 2.94511i | ||||||||
\(29\) | 3.12329 | 0.579981 | 0.289990 | − | 0.957030i | \(-0.406348\pi\) | ||||
0.289990 | + | 0.957030i | \(0.406348\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.06658 | −0.371169 | −0.185584 | − | 0.982628i | \(-0.559418\pi\) | ||||
−0.185584 | + | 0.982628i | \(0.559418\pi\) | |||||||
\(32\) | 9.18462i | 1.62363i | ||||||||
\(33\) | − 4.30834i | − 0.749986i | ||||||||
\(34\) | 14.1482 | 2.42640 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.74525 | 0.790875 | ||||||||
\(37\) | − 1.89142i | − 0.310947i | −0.987840 | − | 0.155474i | \(-0.950310\pi\) | ||||
0.987840 | − | 0.155474i | \(-0.0496904\pi\) | |||||||
\(38\) | 19.8274i | 3.21644i | ||||||||
\(39\) | 3.46120 | 0.554235 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.89896 | 0.608915 | 0.304457 | − | 0.952526i | \(-0.401525\pi\) | ||||
0.304457 | + | 0.952526i | \(0.401525\pi\) | |||||||
\(42\) | 8.52943i | 1.31612i | ||||||||
\(43\) | 3.20815i | 0.489238i | 0.969619 | + | 0.244619i | \(0.0786629\pi\) | ||||
−0.969619 | + | 0.244619i | \(0.921337\pi\) | |||||||
\(44\) | −20.4442 | −3.08207 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −13.1153 | −1.93375 | ||||||||
\(47\) | 6.28577i | 0.916874i | 0.888727 | + | 0.458437i | \(0.151591\pi\) | ||||
−0.888727 | + | 0.458437i | \(0.848409\pi\) | |||||||
\(48\) | − 9.02691i | − 1.30292i | ||||||||
\(49\) | −3.78555 | −0.540793 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.44757 | −0.762813 | ||||||||
\(52\) | − 16.4243i | − 2.27763i | ||||||||
\(53\) | 2.51480i | 0.345434i | 0.984971 | + | 0.172717i | \(0.0552546\pi\) | ||||
−0.984971 | + | 0.172717i | \(0.944745\pi\) | |||||||
\(54\) | −2.59716 | −0.353429 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 23.4154 | 3.12902 | ||||||||
\(57\) | − 7.63427i | − 1.01118i | ||||||||
\(58\) | 8.11170i | 1.06512i | ||||||||
\(59\) | −7.72948 | −1.00629 | −0.503146 | − | 0.864201i | \(-0.667824\pi\) | ||||
−0.503146 | + | 0.864201i | \(0.667824\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.95661 | −0.378555 | −0.189278 | − | 0.981924i | \(-0.560615\pi\) | ||||
−0.189278 | + | 0.981924i | \(0.560615\pi\) | |||||||
\(62\) | − 5.36725i | − 0.681641i | ||||||||
\(63\) | − 3.28414i | − 0.413762i | ||||||||
\(64\) | −5.80013 | −0.725016 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 11.1895 | 1.37733 | ||||||||
\(67\) | 12.9952i | 1.58762i | 0.608165 | + | 0.793811i | \(0.291906\pi\) | ||||
−0.608165 | + | 0.793811i | \(0.708094\pi\) | |||||||
\(68\) | 25.8501i | 3.13479i | ||||||||
\(69\) | 5.04986 | 0.607931 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.72665 | −0.560950 | −0.280475 | − | 0.959861i | \(-0.590492\pi\) | ||||
−0.280475 | + | 0.959861i | \(0.590492\pi\) | |||||||
\(72\) | 7.12986i | 0.840262i | ||||||||
\(73\) | 1.64933i | 0.193040i | 0.995331 | + | 0.0965198i | \(0.0307711\pi\) | ||||
−0.995331 | + | 0.0965198i | \(0.969229\pi\) | |||||||
\(74\) | 4.91232 | 0.571046 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −36.2265 | −4.15547 | ||||||||
\(77\) | 14.1492i | 1.61245i | ||||||||
\(78\) | 8.98929i | 1.01784i | ||||||||
\(79\) | −13.7349 | −1.54530 | −0.772648 | − | 0.634835i | \(-0.781068\pi\) | ||||
−0.772648 | + | 0.634835i | \(0.781068\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 10.1262i | 1.11825i | ||||||||
\(83\) | 5.01687i | 0.550673i | 0.961348 | + | 0.275336i | \(0.0887893\pi\) | ||||
−0.961348 | + | 0.275336i | \(0.911211\pi\) | |||||||
\(84\) | −15.5841 | −1.70036 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −8.33208 | −0.898472 | ||||||||
\(87\) | − 3.12329i | − 0.334852i | ||||||||
\(88\) | − 30.7179i | − 3.27454i | ||||||||
\(89\) | 9.00209 | 0.954220 | 0.477110 | − | 0.878844i | \(-0.341684\pi\) | ||||
0.477110 | + | 0.878844i | \(0.341684\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −11.3670 | −1.19159 | ||||||||
\(92\) | − 23.9628i | − 2.49830i | ||||||||
\(93\) | 2.06658i | 0.214294i | ||||||||
\(94\) | −16.3252 | −1.68381 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 9.18462 | 0.937401 | ||||||||
\(97\) | 2.57278i | 0.261226i | 0.991433 | + | 0.130613i | \(0.0416945\pi\) | ||||
−0.991433 | + | 0.130613i | \(0.958305\pi\) | |||||||
\(98\) | − 9.83169i | − 0.993150i | ||||||||
\(99\) | −4.30834 | −0.433005 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.87863 | 0.783953 | 0.391976 | − | 0.919975i | \(-0.371791\pi\) | ||||
0.391976 | + | 0.919975i | \(0.371791\pi\) | |||||||
\(102\) | − 14.1482i | − 1.40088i | ||||||||
\(103\) | − 12.4046i | − 1.22226i | −0.791530 | − | 0.611131i | \(-0.790715\pi\) | ||||
0.791530 | − | 0.611131i | \(-0.209285\pi\) | |||||||
\(104\) | 24.6779 | 2.41986 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.53134 | −0.634380 | ||||||||
\(107\) | 8.52094i | 0.823750i | 0.911240 | + | 0.411875i | \(0.135126\pi\) | ||||
−0.911240 | + | 0.411875i | \(0.864874\pi\) | |||||||
\(108\) | − 4.74525i | − 0.456612i | ||||||||
\(109\) | −17.5139 | −1.67752 | −0.838762 | − | 0.544499i | \(-0.816720\pi\) | ||||
−0.838762 | + | 0.544499i | \(0.816720\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.89142 | −0.179526 | ||||||||
\(112\) | 29.6456i | 2.80125i | ||||||||
\(113\) | − 4.17711i | − 0.392949i | −0.980509 | − | 0.196475i | \(-0.937051\pi\) | ||||
0.980509 | − | 0.196475i | \(-0.0629493\pi\) | |||||||
\(114\) | 19.8274 | 1.85701 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −14.8208 | −1.37608 | ||||||||
\(117\) | − 3.46120i | − 0.319988i | ||||||||
\(118\) | − 20.0747i | − 1.84803i | ||||||||
\(119\) | 17.8906 | 1.64003 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.56181 | 0.687438 | ||||||||
\(122\) | − 7.67880i | − 0.695206i | ||||||||
\(123\) | − 3.89896i | − 0.351557i | ||||||||
\(124\) | 9.80645 | 0.880645 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 8.52943 | 0.759862 | ||||||||
\(127\) | 10.2112i | 0.906097i | 0.891486 | + | 0.453049i | \(0.149664\pi\) | ||||
−0.891486 | + | 0.453049i | \(0.850336\pi\) | |||||||
\(128\) | 3.30537i | 0.292156i | ||||||||
\(129\) | 3.20815 | 0.282462 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.91686 | −0.429588 | −0.214794 | − | 0.976659i | \(-0.568908\pi\) | ||||
−0.214794 | + | 0.976659i | \(0.568908\pi\) | |||||||
\(132\) | 20.4442i | 1.77944i | ||||||||
\(133\) | 25.0720i | 2.17402i | ||||||||
\(134\) | −33.7508 | −2.91562 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −38.8404 | −3.33054 | ||||||||
\(137\) | − 12.3817i | − 1.05784i | −0.848672 | − | 0.528919i | \(-0.822597\pi\) | ||||
0.848672 | − | 0.528919i | \(-0.177403\pi\) | |||||||
\(138\) | 13.1153i | 1.11645i | ||||||||
\(139\) | −13.2420 | −1.12317 | −0.561584 | − | 0.827420i | \(-0.689808\pi\) | ||||
−0.561584 | + | 0.827420i | \(0.689808\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.28577 | 0.529357 | ||||||||
\(142\) | − 12.2759i | − 1.03017i | ||||||||
\(143\) | 14.9120i | 1.24701i | ||||||||
\(144\) | −9.02691 | −0.752242 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.28358 | −0.354512 | ||||||||
\(147\) | 3.78555i | 0.312227i | ||||||||
\(148\) | 8.97526i | 0.737762i | ||||||||
\(149\) | −5.20686 | −0.426563 | −0.213281 | − | 0.976991i | \(-0.568415\pi\) | ||||
−0.213281 | + | 0.976991i | \(0.568415\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.78162 | 0.633259 | 0.316630 | − | 0.948549i | \(-0.397449\pi\) | ||||
0.316630 | + | 0.948549i | \(0.397449\pi\) | |||||||
\(152\) | − 54.4313i | − 4.41496i | ||||||||
\(153\) | 5.44757i | 0.440410i | ||||||||
\(154\) | −36.7477 | −2.96122 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −16.4243 | −1.31499 | ||||||||
\(157\) | − 16.4474i | − 1.31264i | −0.754481 | − | 0.656322i | \(-0.772111\pi\) | ||||
0.754481 | − | 0.656322i | \(-0.227889\pi\) | |||||||
\(158\) | − 35.6717i | − 2.83789i | ||||||||
\(159\) | 2.51480 | 0.199436 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −16.5844 | −1.30704 | ||||||||
\(162\) | 2.59716i | 0.204052i | ||||||||
\(163\) | − 7.81342i | − 0.611994i | −0.952032 | − | 0.305997i | \(-0.901010\pi\) | ||||
0.952032 | − | 0.305997i | \(-0.0989898\pi\) | |||||||
\(164\) | −18.5015 | −1.44473 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −13.0296 | −1.01129 | ||||||||
\(167\) | − 2.77030i | − 0.214372i | −0.994239 | − | 0.107186i | \(-0.965816\pi\) | ||||
0.994239 | − | 0.107186i | \(-0.0341841\pi\) | |||||||
\(168\) | − 23.4154i | − 1.80654i | ||||||||
\(169\) | 1.02011 | 0.0784700 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.63427 | −0.583807 | ||||||||
\(172\) | − 15.2235i | − 1.16078i | ||||||||
\(173\) | 16.9573i | 1.28924i | 0.764503 | + | 0.644620i | \(0.222985\pi\) | ||||
−0.764503 | + | 0.644620i | \(0.777015\pi\) | |||||||
\(174\) | 8.11170 | 0.614946 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 38.8910 | 2.93152 | ||||||||
\(177\) | 7.72948i | 0.580983i | ||||||||
\(178\) | 23.3799i | 1.75240i | ||||||||
\(179\) | −1.56173 | −0.116729 | −0.0583645 | − | 0.998295i | \(-0.518589\pi\) | ||||
−0.0583645 | + | 0.998295i | \(0.518589\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.55277 | 0.115416 | 0.0577081 | − | 0.998333i | \(-0.481621\pi\) | ||||
0.0577081 | + | 0.998333i | \(0.481621\pi\) | |||||||
\(182\) | − 29.5221i | − 2.18832i | ||||||||
\(183\) | 2.95661i | 0.218559i | ||||||||
\(184\) | 36.0048 | 2.65431 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −5.36725 | −0.393546 | ||||||||
\(187\) | − 23.4700i | − 1.71630i | ||||||||
\(188\) | − 29.8276i | − 2.17540i | ||||||||
\(189\) | −3.28414 | −0.238886 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 26.5640 | 1.92211 | 0.961054 | − | 0.276362i | \(-0.0891290\pi\) | ||||
0.961054 | + | 0.276362i | \(0.0891290\pi\) | |||||||
\(192\) | 5.80013i | 0.418588i | ||||||||
\(193\) | 13.7642i | 0.990772i | 0.868673 | + | 0.495386i | \(0.164973\pi\) | ||||
−0.868673 | + | 0.495386i | \(0.835027\pi\) | |||||||
\(194\) | −6.68192 | −0.479734 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 17.9634 | 1.28310 | ||||||||
\(197\) | 6.25851i | 0.445901i | 0.974830 | + | 0.222950i | \(0.0715688\pi\) | ||||
−0.974830 | + | 0.222950i | \(0.928431\pi\) | |||||||
\(198\) | − 11.1895i | − 0.795201i | ||||||||
\(199\) | −3.35009 | −0.237482 | −0.118741 | − | 0.992925i | \(-0.537886\pi\) | ||||
−0.118741 | + | 0.992925i | \(0.537886\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.9952 | 0.916614 | ||||||||
\(202\) | 20.4621i | 1.43971i | ||||||||
\(203\) | 10.2573i | 0.719923i | ||||||||
\(204\) | 25.8501 | 1.80987 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 32.2168 | 2.24465 | ||||||||
\(207\) | − 5.04986i | − 0.350989i | ||||||||
\(208\) | 31.2439i | 2.16638i | ||||||||
\(209\) | 32.8911 | 2.27512 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.0984 | 1.65900 | 0.829502 | − | 0.558504i | \(-0.188624\pi\) | ||||
0.829502 | + | 0.558504i | \(0.188624\pi\) | |||||||
\(212\) | − 11.9333i | − 0.819586i | ||||||||
\(213\) | 4.72665i | 0.323865i | ||||||||
\(214\) | −22.1303 | −1.51279 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 7.12986 | 0.485126 | ||||||||
\(217\) | − 6.78693i | − 0.460727i | ||||||||
\(218\) | − 45.4863i | − 3.08072i | ||||||||
\(219\) | 1.64933 | 0.111452 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 18.8551 | 1.26833 | ||||||||
\(222\) | − 4.91232i | − 0.329693i | ||||||||
\(223\) | 18.2697i | 1.22343i | 0.791079 | + | 0.611714i | \(0.209520\pi\) | ||||
−0.791079 | + | 0.611714i | \(0.790480\pi\) | |||||||
\(224\) | −30.1635 | −2.01539 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 10.8486 | 0.721640 | ||||||||
\(227\) | − 17.9602i | − 1.19206i | −0.802962 | − | 0.596031i | \(-0.796744\pi\) | ||||
0.802962 | − | 0.596031i | \(-0.203256\pi\) | |||||||
\(228\) | 36.2265i | 2.39916i | ||||||||
\(229\) | −6.00658 | −0.396926 | −0.198463 | − | 0.980108i | \(-0.563595\pi\) | ||||
−0.198463 | + | 0.980108i | \(0.563595\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 14.1492 | 0.930948 | ||||||||
\(232\) | − 22.2687i | − 1.46201i | ||||||||
\(233\) | 20.8526i | 1.36610i | 0.730373 | + | 0.683049i | \(0.239346\pi\) | ||||
−0.730373 | + | 0.683049i | \(0.760654\pi\) | |||||||
\(234\) | 8.98929 | 0.587648 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 36.6783 | 2.38755 | ||||||||
\(237\) | 13.7349i | 0.892177i | ||||||||
\(238\) | 46.4647i | 3.01186i | ||||||||
\(239\) | 27.8722 | 1.80290 | 0.901452 | − | 0.432880i | \(-0.142503\pi\) | ||||
0.901452 | + | 0.432880i | \(0.142503\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.7159 | −1.20560 | −0.602798 | − | 0.797894i | \(-0.705947\pi\) | ||||
−0.602798 | + | 0.797894i | \(0.705947\pi\) | |||||||
\(242\) | 19.6393i | 1.26246i | ||||||||
\(243\) | − 1.00000i | − 0.0641500i | ||||||||
\(244\) | 14.0299 | 0.898170 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 10.1262 | 0.645624 | ||||||||
\(247\) | 26.4237i | 1.68130i | ||||||||
\(248\) | 14.7344i | 0.935638i | ||||||||
\(249\) | 5.01687 | 0.317931 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.0995 | 0.700594 | 0.350297 | − | 0.936639i | \(-0.386081\pi\) | ||||
0.350297 | + | 0.936639i | \(0.386081\pi\) | |||||||
\(252\) | 15.5841i | 0.981703i | ||||||||
\(253\) | 21.7565i | 1.36782i | ||||||||
\(254\) | −26.5201 | −1.66402 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −20.1848 | −1.26155 | ||||||||
\(257\) | − 17.8844i | − 1.11560i | −0.829975 | − | 0.557800i | \(-0.811646\pi\) | ||||
0.829975 | − | 0.557800i | \(-0.188354\pi\) | |||||||
\(258\) | 8.33208i | 0.518733i | ||||||||
\(259\) | 6.21168 | 0.385975 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.12329 | −0.193327 | ||||||||
\(262\) | − 12.7699i | − 0.788927i | ||||||||
\(263\) | 18.1341i | 1.11819i | 0.829102 | + | 0.559097i | \(0.188852\pi\) | ||||
−0.829102 | + | 0.559097i | \(0.811148\pi\) | |||||||
\(264\) | −30.7179 | −1.89056 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −65.1160 | −3.99252 | ||||||||
\(267\) | − 9.00209i | − 0.550919i | ||||||||
\(268\) | − 61.6657i | − 3.76683i | ||||||||
\(269\) | 22.2963 | 1.35943 | 0.679714 | − | 0.733477i | \(-0.262104\pi\) | ||||
0.679714 | + | 0.733477i | \(0.262104\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.8621 | 1.02430 | 0.512149 | − | 0.858896i | \(-0.328849\pi\) | ||||
0.512149 | + | 0.858896i | \(0.328849\pi\) | |||||||
\(272\) | − 49.1747i | − 2.98166i | ||||||||
\(273\) | 11.3670i | 0.687965i | ||||||||
\(274\) | 32.1572 | 1.94269 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −23.9628 | −1.44239 | ||||||||
\(277\) | − 18.6929i | − 1.12315i | −0.827426 | − | 0.561575i | \(-0.810196\pi\) | ||||
0.827426 | − | 0.561575i | \(-0.189804\pi\) | |||||||
\(278\) | − 34.3915i | − 2.06266i | ||||||||
\(279\) | 2.06658 | 0.123723 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 25.9852 | 1.55015 | 0.775075 | − | 0.631870i | \(-0.217712\pi\) | ||||
0.775075 | + | 0.631870i | \(0.217712\pi\) | |||||||
\(282\) | 16.3252i | 0.972150i | ||||||||
\(283\) | − 16.9219i | − 1.00591i | −0.864314 | − | 0.502953i | \(-0.832247\pi\) | ||||
0.864314 | − | 0.502953i | \(-0.167753\pi\) | |||||||
\(284\) | 22.4291 | 1.33092 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −38.7289 | −2.29009 | ||||||||
\(287\) | 12.8047i | 0.755838i | ||||||||
\(288\) | − 9.18462i | − 0.541209i | ||||||||
\(289\) | −12.6760 | −0.745650 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.57278 | 0.150819 | ||||||||
\(292\) | − 7.82649i | − 0.458011i | ||||||||
\(293\) | − 1.05979i | − 0.0619134i | −0.999521 | − | 0.0309567i | \(-0.990145\pi\) | ||||
0.999521 | − | 0.0309567i | \(-0.00985540\pi\) | |||||||
\(294\) | −9.83169 | −0.573396 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −13.4856 | −0.783832 | ||||||||
\(297\) | 4.30834i | 0.249995i | ||||||||
\(298\) | − 13.5231i | − 0.783370i | ||||||||
\(299\) | −17.4786 | −1.01081 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.5360 | −0.607285 | ||||||||
\(302\) | 20.2101i | 1.16296i | ||||||||
\(303\) | − 7.87863i | − 0.452615i | ||||||||
\(304\) | 68.9139 | 3.95248 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −14.1482 | −0.808800 | ||||||||
\(307\) | 29.7239i | 1.69643i | 0.529652 | + | 0.848215i | \(0.322323\pi\) | ||||
−0.529652 | + | 0.848215i | \(0.677677\pi\) | |||||||
\(308\) | − 67.1414i | − 3.82574i | ||||||||
\(309\) | −12.4046 | −0.705673 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.08513 | 0.288351 | 0.144176 | − | 0.989552i | \(-0.453947\pi\) | ||||
0.144176 | + | 0.989552i | \(0.453947\pi\) | |||||||
\(312\) | − 24.6779i | − 1.39711i | ||||||||
\(313\) | − 25.9388i | − 1.46615i | −0.680149 | − | 0.733074i | \(-0.738085\pi\) | ||||
0.680149 | − | 0.733074i | \(-0.261915\pi\) | |||||||
\(314\) | 42.7165 | 2.41063 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 65.1755 | 3.66641 | ||||||||
\(317\) | 19.7727i | 1.11054i | 0.831669 | + | 0.555271i | \(0.187386\pi\) | ||||
−0.831669 | + | 0.555271i | \(0.812614\pi\) | |||||||
\(318\) | 6.53134i | 0.366259i | ||||||||
\(319\) | 13.4562 | 0.753403 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8.52094 | 0.475592 | ||||||||
\(322\) | − 43.0724i | − 2.40033i | ||||||||
\(323\) | − 41.5883i | − 2.31403i | ||||||||
\(324\) | −4.74525 | −0.263625 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 20.2927 | 1.12391 | ||||||||
\(327\) | 17.5139i | 0.968519i | ||||||||
\(328\) | − 27.7990i | − 1.53494i | ||||||||
\(329\) | −20.6433 | −1.13810 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −23.9589 | −1.31690 | −0.658449 | − | 0.752625i | \(-0.728787\pi\) | ||||
−0.658449 | + | 0.752625i | \(0.728787\pi\) | |||||||
\(332\) | − 23.8063i | − 1.30654i | ||||||||
\(333\) | 1.89142i | 0.103649i | ||||||||
\(334\) | 7.19492 | 0.393689 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 29.6456 | 1.61730 | ||||||||
\(337\) | − 27.6779i | − 1.50771i | −0.657039 | − | 0.753857i | \(-0.728191\pi\) | ||||
0.657039 | − | 0.753857i | \(-0.271809\pi\) | |||||||
\(338\) | 2.64939i | 0.144108i | ||||||||
\(339\) | −4.17711 | −0.226869 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.90354 | −0.482154 | ||||||||
\(342\) | − 19.8274i | − 1.07215i | ||||||||
\(343\) | 10.5567i | 0.570008i | ||||||||
\(344\) | 22.8737 | 1.23327 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −44.0409 | −2.36765 | ||||||||
\(347\) | − 13.4880i | − 0.724075i | −0.932164 | − | 0.362037i | \(-0.882081\pi\) | ||||
0.932164 | − | 0.362037i | \(-0.117919\pi\) | |||||||
\(348\) | 14.8208i | 0.794479i | ||||||||
\(349\) | −19.1678 | −1.02603 | −0.513015 | − | 0.858379i | \(-0.671472\pi\) | ||||
−0.513015 | + | 0.858379i | \(0.671472\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.46120 | −0.184745 | ||||||||
\(352\) | 39.5705i | 2.10911i | ||||||||
\(353\) | − 7.61950i | − 0.405545i | −0.979226 | − | 0.202773i | \(-0.935005\pi\) | ||||
0.979226 | − | 0.202773i | \(-0.0649952\pi\) | |||||||
\(354\) | −20.0747 | −1.06696 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −42.7172 | −2.26401 | ||||||||
\(357\) | − 17.8906i | − 0.946869i | ||||||||
\(358\) | − 4.05606i | − 0.214369i | ||||||||
\(359\) | −31.2943 | −1.65165 | −0.825826 | − | 0.563925i | \(-0.809291\pi\) | ||||
−0.825826 | + | 0.563925i | \(0.809291\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 39.2821 | 2.06748 | ||||||||
\(362\) | 4.03279i | 0.211959i | ||||||||
\(363\) | − 7.56181i | − 0.396892i | ||||||||
\(364\) | 53.9395 | 2.82720 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −7.67880 | −0.401377 | ||||||||
\(367\) | − 6.35079i | − 0.331508i | −0.986167 | − | 0.165754i | \(-0.946994\pi\) | ||||
0.986167 | − | 0.165754i | \(-0.0530058\pi\) | |||||||
\(368\) | 45.5846i | 2.37626i | ||||||||
\(369\) | −3.89896 | −0.202972 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.25894 | −0.428783 | ||||||||
\(372\) | − 9.80645i | − 0.508441i | ||||||||
\(373\) | − 11.1710i | − 0.578410i | −0.957267 | − | 0.289205i | \(-0.906609\pi\) | ||||
0.957267 | − | 0.289205i | \(-0.0933909\pi\) | |||||||
\(374\) | 60.9554 | 3.15193 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 44.8167 | 2.31124 | ||||||||
\(377\) | 10.8103i | 0.556761i | ||||||||
\(378\) | − 8.52943i | − 0.438707i | ||||||||
\(379\) | 20.7113 | 1.06387 | 0.531933 | − | 0.846787i | \(-0.321466\pi\) | ||||
0.531933 | + | 0.846787i | \(0.321466\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10.2112 | 0.523135 | ||||||||
\(382\) | 68.9911i | 3.52989i | ||||||||
\(383\) | 12.5869i | 0.643158i | 0.946883 | + | 0.321579i | \(0.104214\pi\) | ||||
−0.946883 | + | 0.321579i | \(0.895786\pi\) | |||||||
\(384\) | 3.30537 | 0.168676 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −35.7480 | −1.81952 | ||||||||
\(387\) | − 3.20815i | − 0.163079i | ||||||||
\(388\) | − 12.2085i | − 0.619792i | ||||||||
\(389\) | −10.8301 | −0.549110 | −0.274555 | − | 0.961571i | \(-0.588531\pi\) | ||||
−0.274555 | + | 0.961571i | \(0.588531\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 27.5095 | 1.39121 | ||||||||
\(392\) | 26.9905i | 1.36322i | ||||||||
\(393\) | 4.91686i | 0.248023i | ||||||||
\(394\) | −16.2544 | −0.818884 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 20.4442 | 1.02736 | ||||||||
\(397\) | − 4.90704i | − 0.246277i | −0.992389 | − | 0.123139i | \(-0.960704\pi\) | ||||
0.992389 | − | 0.123139i | \(-0.0392960\pi\) | |||||||
\(398\) | − 8.70072i | − 0.436128i | ||||||||
\(399\) | 25.0720 | 1.25517 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −27.5223 | −1.37440 | −0.687198 | − | 0.726470i | \(-0.741160\pi\) | ||||
−0.687198 | + | 0.726470i | \(0.741160\pi\) | |||||||
\(402\) | 33.7508i | 1.68333i | ||||||||
\(403\) | − 7.15285i | − 0.356309i | ||||||||
\(404\) | −37.3861 | −1.86003 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −26.6399 | −1.32212 | ||||||||
\(407\) | − 8.14888i | − 0.403925i | ||||||||
\(408\) | 38.8404i | 1.92289i | ||||||||
\(409\) | −19.7665 | −0.977390 | −0.488695 | − | 0.872455i | \(-0.662527\pi\) | ||||
−0.488695 | + | 0.872455i | \(0.662527\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −12.3817 | −0.610743 | ||||||||
\(412\) | 58.8630i | 2.89997i | ||||||||
\(413\) | − 25.3847i | − 1.24910i | ||||||||
\(414\) | 13.1153 | 0.644582 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −31.7898 | −1.55862 | ||||||||
\(417\) | 13.2420i | 0.648461i | ||||||||
\(418\) | 85.4234i | 4.17820i | ||||||||
\(419\) | 6.67948 | 0.326314 | 0.163157 | − | 0.986600i | \(-0.447832\pi\) | ||||
0.163157 | + | 0.986600i | \(0.447832\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.65996 | 0.275849 | 0.137925 | − | 0.990443i | \(-0.455957\pi\) | ||||
0.137925 | + | 0.990443i | \(0.455957\pi\) | |||||||
\(422\) | 62.5875i | 3.04671i | ||||||||
\(423\) | − 6.28577i | − 0.305625i | ||||||||
\(424\) | 17.9302 | 0.870766 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −12.2759 | −0.594768 | ||||||||
\(427\) | − 9.70991i | − 0.469896i | ||||||||
\(428\) | − 40.4340i | − 1.95445i | ||||||||
\(429\) | 14.9120 | 0.719959 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.41717 | 0.309104 | 0.154552 | − | 0.987985i | \(-0.450607\pi\) | ||||
0.154552 | + | 0.987985i | \(0.450607\pi\) | |||||||
\(432\) | 9.02691i | 0.434307i | ||||||||
\(433\) | 1.10506i | 0.0531059i | 0.999647 | + | 0.0265530i | \(0.00845307\pi\) | ||||
−0.999647 | + | 0.0265530i | \(0.991547\pi\) | |||||||
\(434\) | 17.6268 | 0.846112 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 83.1077 | 3.98014 | ||||||||
\(437\) | 38.5520i | 1.84419i | ||||||||
\(438\) | 4.28358i | 0.204677i | ||||||||
\(439\) | 5.11313 | 0.244036 | 0.122018 | − | 0.992528i | \(-0.461063\pi\) | ||||
0.122018 | + | 0.992528i | \(0.461063\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.78555 | 0.180264 | ||||||||
\(442\) | 48.9698i | 2.32926i | ||||||||
\(443\) | 17.9079i | 0.850829i | 0.904999 | + | 0.425414i | \(0.139872\pi\) | ||||
−0.904999 | + | 0.425414i | \(0.860128\pi\) | |||||||
\(444\) | 8.97526 | 0.425947 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −47.4493 | −2.24679 | ||||||||
\(447\) | 5.20686i | 0.246276i | ||||||||
\(448\) | − 19.0484i | − 0.899953i | ||||||||
\(449\) | −27.3710 | −1.29172 | −0.645859 | − | 0.763457i | \(-0.723501\pi\) | ||||
−0.645859 | + | 0.763457i | \(0.723501\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.7980 | 0.790989 | ||||||||
\(452\) | 19.8214i | 0.932322i | ||||||||
\(453\) | − 7.78162i | − 0.365612i | ||||||||
\(454\) | 46.6456 | 2.18919 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −54.4313 | −2.54898 | ||||||||
\(457\) | 8.92806i | 0.417637i | 0.977954 | + | 0.208819i | \(0.0669618\pi\) | ||||
−0.977954 | + | 0.208819i | \(0.933038\pi\) | |||||||
\(458\) | − 15.6001i | − 0.728943i | ||||||||
\(459\) | 5.44757 | 0.254271 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.81204 | 0.0843952 | 0.0421976 | − | 0.999109i | \(-0.486564\pi\) | ||||
0.0421976 | + | 0.999109i | \(0.486564\pi\) | |||||||
\(462\) | 36.7477i | 1.70966i | ||||||||
\(463\) | − 2.72192i | − 0.126498i | −0.997998 | − | 0.0632492i | \(-0.979854\pi\) | ||||
0.997998 | − | 0.0632492i | \(-0.0201463\pi\) | |||||||
\(464\) | 28.1937 | 1.30886 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −54.1575 | −2.50880 | ||||||||
\(467\) | − 40.2261i | − 1.86144i | −0.365729 | − | 0.930721i | \(-0.619180\pi\) | ||||
0.365729 | − | 0.930721i | \(-0.380820\pi\) | |||||||
\(468\) | 16.4243i | 0.759211i | ||||||||
\(469\) | −42.6781 | −1.97069 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −16.4474 | −0.757855 | ||||||||
\(472\) | 55.1101i | 2.53665i | ||||||||
\(473\) | 13.8218i | 0.635527i | ||||||||
\(474\) | −35.6717 | −1.63846 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −84.8953 | −3.89117 | ||||||||
\(477\) | − 2.51480i | − 0.115145i | ||||||||
\(478\) | 72.3886i | 3.31098i | ||||||||
\(479\) | 27.9457 | 1.27687 | 0.638435 | − | 0.769676i | \(-0.279582\pi\) | ||||
0.638435 | + | 0.769676i | \(0.279582\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.54657 | 0.298498 | ||||||||
\(482\) | − 48.6082i | − 2.21404i | ||||||||
\(483\) | 16.5844i | 0.754617i | ||||||||
\(484\) | −35.8827 | −1.63103 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 2.59716 | 0.117810 | ||||||||
\(487\) | − 25.8089i | − 1.16951i | −0.811209 | − | 0.584756i | \(-0.801190\pi\) | ||||
0.811209 | − | 0.584756i | \(-0.198810\pi\) | |||||||
\(488\) | 21.0802i | 0.954257i | ||||||||
\(489\) | −7.81342 | −0.353335 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 23.7044 | 1.06976 | 0.534882 | − | 0.844927i | \(-0.320356\pi\) | ||||
0.534882 | + | 0.844927i | \(0.320356\pi\) | |||||||
\(492\) | 18.5015i | 0.834113i | ||||||||
\(493\) | − 17.0144i | − 0.766288i | ||||||||
\(494\) | −68.6267 | −3.08766 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −18.6548 | −0.837627 | ||||||||
\(497\) | − 15.5230i | − 0.696300i | ||||||||
\(498\) | 13.0296i | 0.583871i | ||||||||
\(499\) | −8.95752 | −0.400994 | −0.200497 | − | 0.979694i | \(-0.564256\pi\) | ||||
−0.200497 | + | 0.979694i | \(0.564256\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.77030 | −0.123768 | ||||||||
\(502\) | 28.8272i | 1.28662i | ||||||||
\(503\) | − 10.1655i | − 0.453256i | −0.973981 | − | 0.226628i | \(-0.927230\pi\) | ||||
0.973981 | − | 0.226628i | \(-0.0727701\pi\) | |||||||
\(504\) | −23.4154 | −1.04301 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −56.5052 | −2.51196 | ||||||||
\(507\) | − 1.02011i | − 0.0453047i | ||||||||
\(508\) | − 48.4547i | − 2.14983i | ||||||||
\(509\) | 6.54473 | 0.290090 | 0.145045 | − | 0.989425i | \(-0.453667\pi\) | ||||
0.145045 | + | 0.989425i | \(0.453667\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.41663 | −0.239618 | ||||||||
\(512\) | − 45.8125i | − 2.02465i | ||||||||
\(513\) | 7.63427i | 0.337061i | ||||||||
\(514\) | 46.4488 | 2.04877 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −15.2235 | −0.670176 | ||||||||
\(517\) | 27.0813i | 1.19103i | ||||||||
\(518\) | 16.1327i | 0.708832i | ||||||||
\(519\) | 16.9573 | 0.744343 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −25.6022 | −1.12165 | −0.560827 | − | 0.827933i | \(-0.689517\pi\) | ||||
−0.560827 | + | 0.827933i | \(0.689517\pi\) | |||||||
\(522\) | − 8.11170i | − 0.355039i | ||||||||
\(523\) | − 5.02210i | − 0.219601i | −0.993954 | − | 0.109801i | \(-0.964979\pi\) | ||||
0.993954 | − | 0.109801i | \(-0.0350212\pi\) | |||||||
\(524\) | 23.3318 | 1.01925 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −47.0971 | −2.05353 | ||||||||
\(527\) | 11.2579i | 0.490400i | ||||||||
\(528\) | − 38.8910i | − 1.69251i | ||||||||
\(529\) | −2.50105 | −0.108741 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.72948 | 0.335431 | ||||||||
\(532\) | − 118.973i | − 5.15813i | ||||||||
\(533\) | 13.4951i | 0.584536i | ||||||||
\(534\) | 23.3799 | 1.01175 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 92.6543 | 4.00206 | ||||||||
\(537\) | 1.56173i | 0.0673935i | ||||||||
\(538\) | 57.9071i | 2.49655i | ||||||||
\(539\) | −16.3094 | −0.702498 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.99099 | −0.343560 | −0.171780 | − | 0.985135i | \(-0.554952\pi\) | ||||
−0.171780 | + | 0.985135i | \(0.554952\pi\) | |||||||
\(542\) | 43.7936i | 1.88109i | ||||||||
\(543\) | − 1.55277i | − 0.0666356i | ||||||||
\(544\) | 50.0339 | 2.14518 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −29.5221 | −1.26343 | ||||||||
\(547\) | − 21.9399i | − 0.938084i | −0.883176 | − | 0.469042i | \(-0.844599\pi\) | ||||
0.883176 | − | 0.469042i | \(-0.155401\pi\) | |||||||
\(548\) | 58.7542i | 2.50986i | ||||||||
\(549\) | 2.95661 | 0.126185 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 23.8441 | 1.01579 | ||||||||
\(552\) | − 36.0048i | − 1.53247i | ||||||||
\(553\) | − 45.1072i | − 1.91815i | ||||||||
\(554\) | 48.5486 | 2.06263 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 62.8364 | 2.66486 | ||||||||
\(557\) | 32.6366i | 1.38286i | 0.722444 | + | 0.691429i | \(0.243019\pi\) | ||||
−0.722444 | + | 0.691429i | \(0.756981\pi\) | |||||||
\(558\) | 5.36725i | 0.227214i | ||||||||
\(559\) | −11.1040 | −0.469651 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −23.4700 | −0.990905 | ||||||||
\(562\) | 67.4879i | 2.84680i | ||||||||
\(563\) | 5.25771i | 0.221586i | 0.993843 | + | 0.110793i | \(0.0353391\pi\) | ||||
−0.993843 | + | 0.110793i | \(0.964661\pi\) | |||||||
\(564\) | −29.8276 | −1.25597 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 43.9490 | 1.84732 | ||||||||
\(567\) | 3.28414i | 0.137921i | ||||||||
\(568\) | 33.7004i | 1.41404i | ||||||||
\(569\) | −15.1931 | −0.636926 | −0.318463 | − | 0.947935i | \(-0.603167\pi\) | ||||
−0.318463 | + | 0.947935i | \(0.603167\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.29434 | −0.347107 | −0.173554 | − | 0.984824i | \(-0.555525\pi\) | ||||
−0.173554 | + | 0.984824i | \(0.555525\pi\) | |||||||
\(572\) | − 70.7613i | − 2.95868i | ||||||||
\(573\) | − 26.5640i | − 1.10973i | ||||||||
\(574\) | −33.2559 | −1.38807 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 5.80013 | 0.241672 | ||||||||
\(577\) | 2.69155i | 0.112051i | 0.998429 | + | 0.0560253i | \(0.0178427\pi\) | ||||
−0.998429 | + | 0.0560253i | \(0.982157\pi\) | |||||||
\(578\) | − 32.9218i | − 1.36936i | ||||||||
\(579\) | 13.7642 | 0.572022 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −16.4761 | −0.683543 | ||||||||
\(582\) | 6.68192i | 0.276975i | ||||||||
\(583\) | 10.8346i | 0.448724i | ||||||||
\(584\) | 11.7595 | 0.486612 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.75244 | 0.113702 | ||||||||
\(587\) | 27.2841i | 1.12613i | 0.826411 | + | 0.563067i | \(0.190379\pi\) | ||||
−0.826411 | + | 0.563067i | \(0.809621\pi\) | |||||||
\(588\) | − 17.9634i | − 0.740798i | ||||||||
\(589\) | −15.7768 | −0.650074 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.25851 | 0.257441 | ||||||||
\(592\) | − 17.0737i | − 0.701723i | ||||||||
\(593\) | 3.04738i | 0.125141i | 0.998041 | + | 0.0625704i | \(0.0199298\pi\) | ||||
−0.998041 | + | 0.0625704i | \(0.980070\pi\) | |||||||
\(594\) | −11.1895 | −0.459109 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 24.7079 | 1.01207 | ||||||||
\(597\) | 3.35009i | 0.137110i | ||||||||
\(598\) | − 45.3946i | − 1.85632i | ||||||||
\(599\) | 21.1104 | 0.862549 | 0.431274 | − | 0.902221i | \(-0.358064\pi\) | ||||
0.431274 | + | 0.902221i | \(0.358064\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.78443 | 0.0727884 | 0.0363942 | − | 0.999338i | \(-0.488413\pi\) | ||||
0.0363942 | + | 0.999338i | \(0.488413\pi\) | |||||||
\(602\) | − 27.3637i | − 1.11526i | ||||||||
\(603\) | − 12.9952i | − 0.529207i | ||||||||
\(604\) | −36.9258 | −1.50249 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 20.4621 | 0.831215 | ||||||||
\(607\) | 43.9927i | 1.78561i | 0.450444 | + | 0.892805i | \(0.351266\pi\) | ||||
−0.450444 | + | 0.892805i | \(0.648734\pi\) | |||||||
\(608\) | 70.1179i | 2.84366i | ||||||||
\(609\) | 10.2573 | 0.415648 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −21.7563 | −0.880166 | ||||||||
\(612\) | − 25.8501i | − 1.04493i | ||||||||
\(613\) | 37.9419i | 1.53246i | 0.642567 | + | 0.766230i | \(0.277870\pi\) | ||||
−0.642567 | + | 0.766230i | \(0.722130\pi\) | |||||||
\(614\) | −77.1977 | −3.11544 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 100.882 | 4.06464 | ||||||||
\(617\) | − 7.92668i | − 0.319116i | −0.987189 | − | 0.159558i | \(-0.948993\pi\) | ||||
0.987189 | − | 0.159558i | \(-0.0510069\pi\) | |||||||
\(618\) | − 32.2168i | − 1.29595i | ||||||||
\(619\) | 7.83411 | 0.314880 | 0.157440 | − | 0.987529i | \(-0.449676\pi\) | ||||
0.157440 | + | 0.987529i | \(0.449676\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.04986 | −0.202644 | ||||||||
\(622\) | 13.2069i | 0.529548i | ||||||||
\(623\) | 29.5641i | 1.18446i | ||||||||
\(624\) | 31.2439 | 1.25076 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 67.3673 | 2.69254 | ||||||||
\(627\) | − 32.8911i | − 1.31354i | ||||||||
\(628\) | 78.0469i | 3.11441i | ||||||||
\(629\) | −10.3036 | −0.410833 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.0248 | 0.757366 | 0.378683 | − | 0.925526i | \(-0.376377\pi\) | ||||
0.378683 | + | 0.925526i | \(0.376377\pi\) | |||||||
\(632\) | 97.9279i | 3.89536i | ||||||||
\(633\) | − 24.0984i | − 0.957826i | ||||||||
\(634\) | −51.3528 | −2.03948 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −11.9333 | −0.473188 | ||||||||
\(637\) | − 13.1025i | − 0.519141i | ||||||||
\(638\) | 34.9480i | 1.38360i | ||||||||
\(639\) | 4.72665 | 0.186983 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −32.5783 | −1.28677 | −0.643383 | − | 0.765545i | \(-0.722470\pi\) | ||||
−0.643383 | + | 0.765545i | \(0.722470\pi\) | |||||||
\(642\) | 22.1303i | 0.873411i | ||||||||
\(643\) | − 40.0025i | − 1.57755i | −0.614684 | − | 0.788773i | \(-0.710717\pi\) | ||||
0.614684 | − | 0.788773i | \(-0.289283\pi\) | |||||||
\(644\) | 78.6972 | 3.10111 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 108.011 | 4.24965 | ||||||||
\(647\) | − 20.0199i | − 0.787063i | −0.919311 | − | 0.393532i | \(-0.871253\pi\) | ||||
0.919311 | − | 0.393532i | \(-0.128747\pi\) | |||||||
\(648\) | − 7.12986i | − 0.280087i | ||||||||
\(649\) | −33.3012 | −1.30719 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.78693 | −0.266001 | ||||||||
\(652\) | 37.0766i | 1.45203i | ||||||||
\(653\) | 10.3332i | 0.404369i | 0.979347 | + | 0.202185i | \(0.0648041\pi\) | ||||
−0.979347 | + | 0.202185i | \(0.935196\pi\) | |||||||
\(654\) | −45.4863 | −1.77866 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 35.1955 | 1.37415 | ||||||||
\(657\) | − 1.64933i | − 0.0643466i | ||||||||
\(658\) | − 53.6141i | − 2.09009i | ||||||||
\(659\) | 47.2403 | 1.84022 | 0.920111 | − | 0.391657i | \(-0.128098\pi\) | ||||
0.920111 | + | 0.391657i | \(0.128098\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 51.3528 | 1.99739 | 0.998696 | − | 0.0510604i | \(-0.0162601\pi\) | ||||
0.998696 | + | 0.0510604i | \(0.0162601\pi\) | |||||||
\(662\) | − 62.2250i | − 2.41844i | ||||||||
\(663\) | − 18.8551i | − 0.732272i | ||||||||
\(664\) | 35.7696 | 1.38813 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.91232 | −0.190349 | ||||||||
\(667\) | 15.7722i | 0.610701i | ||||||||
\(668\) | 13.1458i | 0.508625i | ||||||||
\(669\) | 18.2697 | 0.706346 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12.7381 | −0.491749 | ||||||||
\(672\) | 30.1635i | 1.16358i | ||||||||
\(673\) | − 40.5790i | − 1.56420i | −0.623150 | − | 0.782102i | \(-0.714147\pi\) | ||||
0.623150 | − | 0.782102i | \(-0.285853\pi\) | |||||||
\(674\) | 71.8841 | 2.76887 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.84068 | −0.186180 | ||||||||
\(677\) | 9.21482i | 0.354154i | 0.984197 | + | 0.177077i | \(0.0566642\pi\) | ||||
−0.984197 | + | 0.177077i | \(0.943336\pi\) | |||||||
\(678\) | − 10.8486i | − 0.416639i | ||||||||
\(679\) | −8.44935 | −0.324256 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −17.9602 | −0.688237 | ||||||||
\(682\) | − 23.1239i | − 0.885461i | ||||||||
\(683\) | − 13.3281i | − 0.509987i | −0.966943 | − | 0.254994i | \(-0.917927\pi\) | ||||
0.966943 | − | 0.254994i | \(-0.0820734\pi\) | |||||||
\(684\) | 36.2265 | 1.38516 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −27.4174 | −1.04680 | ||||||||
\(687\) | 6.00658i | 0.229165i | ||||||||
\(688\) | 28.9597i | 1.10408i | ||||||||
\(689\) | −8.70421 | −0.331604 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −32.5862 | −1.23964 | −0.619819 | − | 0.784745i | \(-0.712794\pi\) | ||||
−0.619819 | + | 0.784745i | \(0.712794\pi\) | |||||||
\(692\) | − 80.4667i | − 3.05889i | ||||||||
\(693\) | − 14.1492i | − 0.537483i | ||||||||
\(694\) | 35.0306 | 1.32974 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −22.2687 | −0.844091 | ||||||||
\(697\) | − 21.2398i | − 0.804516i | ||||||||
\(698\) | − 49.7820i | − 1.88428i | ||||||||
\(699\) | 20.8526 | 0.788717 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −33.5547 | −1.26734 | −0.633672 | − | 0.773602i | \(-0.718453\pi\) | ||||
−0.633672 | + | 0.773602i | \(0.718453\pi\) | |||||||
\(702\) | − 8.98929i | − 0.339279i | ||||||||
\(703\) | − 14.4396i | − 0.544600i | ||||||||
\(704\) | −24.9889 | −0.941806 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 19.7891 | 0.744772 | ||||||||
\(707\) | 25.8745i | 0.973110i | ||||||||
\(708\) | − 36.6783i | − 1.37846i | ||||||||
\(709\) | −12.4731 | −0.468436 | −0.234218 | − | 0.972184i | \(-0.575253\pi\) | ||||
−0.234218 | + | 0.972184i | \(0.575253\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13.7349 | 0.515098 | ||||||||
\(712\) | − 64.1837i | − 2.40539i | ||||||||
\(713\) | − 10.4359i | − 0.390829i | ||||||||
\(714\) | 46.4647 | 1.73890 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 7.41079 | 0.276954 | ||||||||
\(717\) | − 27.8722i | − 1.04091i | ||||||||
\(718\) | − 81.2765i | − 3.03321i | ||||||||
\(719\) | 7.53586 | 0.281040 | 0.140520 | − | 0.990078i | \(-0.455123\pi\) | ||||
0.140520 | + | 0.990078i | \(0.455123\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 40.7384 | 1.51718 | ||||||||
\(722\) | 102.022i | 3.79687i | ||||||||
\(723\) | 18.7159i | 0.696051i | ||||||||
\(724\) | −7.36827 | −0.273839 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 19.6393 | 0.728881 | ||||||||
\(727\) | − 42.8265i | − 1.58835i | −0.607691 | − | 0.794173i | \(-0.707904\pi\) | ||||
0.607691 | − | 0.794173i | \(-0.292096\pi\) | |||||||
\(728\) | 81.0455i | 3.00375i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 17.4766 | 0.646396 | ||||||||
\(732\) | − 14.0299i | − 0.518559i | ||||||||
\(733\) | − 48.4170i | − 1.78832i | −0.447745 | − | 0.894161i | \(-0.647773\pi\) | ||||
0.447745 | − | 0.894161i | \(-0.352227\pi\) | |||||||
\(734\) | 16.4940 | 0.608806 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −46.3810 | −1.70963 | ||||||||
\(737\) | 55.9880i | 2.06234i | ||||||||
\(738\) | − 10.1262i | − 0.372751i | ||||||||
\(739\) | −31.1926 | −1.14744 | −0.573720 | − | 0.819052i | \(-0.694500\pi\) | ||||
−0.573720 | + | 0.819052i | \(0.694500\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 26.4237 | 0.970700 | ||||||||
\(742\) | − 21.4498i | − 0.787447i | ||||||||
\(743\) | − 45.9840i | − 1.68699i | −0.537137 | − | 0.843495i | \(-0.680494\pi\) | ||||
0.537137 | − | 0.843495i | \(-0.319506\pi\) | |||||||
\(744\) | 14.7344 | 0.540191 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 29.0128 | 1.06223 | ||||||||
\(747\) | − 5.01687i | − 0.183558i | ||||||||
\(748\) | 111.371i | 4.07213i | ||||||||
\(749\) | −27.9839 | −1.02251 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.51488 | 0.0917695 | 0.0458847 | − | 0.998947i | \(-0.485389\pi\) | ||||
0.0458847 | + | 0.998947i | \(0.485389\pi\) | |||||||
\(752\) | 56.7411i | 2.06913i | ||||||||
\(753\) | − 11.0995i | − 0.404488i | ||||||||
\(754\) | −28.0762 | −1.02247 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 15.5841 | 0.566786 | ||||||||
\(757\) | − 39.6597i | − 1.44146i | −0.693218 | − | 0.720728i | \(-0.743808\pi\) | ||||
0.693218 | − | 0.720728i | \(-0.256192\pi\) | |||||||
\(758\) | 53.7905i | 1.95376i | ||||||||
\(759\) | 21.7565 | 0.789711 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 17.2752 | 0.626225 | 0.313113 | − | 0.949716i | \(-0.398628\pi\) | ||||
0.313113 | + | 0.949716i | \(0.398628\pi\) | |||||||
\(762\) | 26.5201i | 0.960723i | ||||||||
\(763\) | − 57.5179i | − 2.08229i | ||||||||
\(764\) | −126.053 | −4.56044 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −32.6901 | −1.18114 | ||||||||
\(767\) | − 26.7533i | − 0.966004i | ||||||||
\(768\) | 20.1848i | 0.728357i | ||||||||
\(769\) | 4.50943 | 0.162614 | 0.0813071 | − | 0.996689i | \(-0.474091\pi\) | ||||
0.0813071 | + | 0.996689i | \(0.474091\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −17.8844 | −0.644092 | ||||||||
\(772\) | − 65.3148i | − 2.35073i | ||||||||
\(773\) | 33.6503i | 1.21032i | 0.796105 | + | 0.605159i | \(0.206890\pi\) | ||||
−0.796105 | + | 0.605159i | \(0.793110\pi\) | |||||||
\(774\) | 8.33208 | 0.299491 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 18.3436 | 0.658495 | ||||||||
\(777\) | − 6.21168i | − 0.222843i | ||||||||
\(778\) | − 28.1276i | − 1.00842i | ||||||||
\(779\) | 29.7657 | 1.06647 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −20.3640 | −0.728682 | ||||||||
\(782\) | 71.4465i | 2.55492i | ||||||||
\(783\) | 3.12329i | 0.111617i | ||||||||
\(784\) | −34.1718 | −1.22042 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −12.7699 | −0.455487 | ||||||||
\(787\) | 36.8366i | 1.31308i | 0.754289 | + | 0.656542i | \(0.227982\pi\) | ||||
−0.754289 | + | 0.656542i | \(0.772018\pi\) | |||||||
\(788\) | − 29.6982i | − 1.05796i | ||||||||
\(789\) | 18.1341 | 0.645589 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13.7182 | 0.487763 | ||||||||
\(792\) | 30.7179i | 1.09151i | ||||||||
\(793\) | − 10.2334i | − 0.363399i | ||||||||
\(794\) | 12.7444 | 0.452281 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 15.8970 | 0.563455 | ||||||||
\(797\) | − 40.4962i | − 1.43445i | −0.696843 | − | 0.717224i | \(-0.745412\pi\) | ||||
0.696843 | − | 0.717224i | \(-0.254588\pi\) | |||||||
\(798\) | 65.1160i | 2.30508i | ||||||||
\(799\) | 34.2422 | 1.21140 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.00209 | −0.318073 | ||||||||
\(802\) | − 71.4798i | − 2.52404i | ||||||||
\(803\) | 7.10589i | 0.250761i | ||||||||
\(804\) | −61.6657 | −2.17478 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 18.5771 | 0.654350 | ||||||||
\(807\) | − 22.2963i | − 0.784866i | ||||||||
\(808\) | − 56.1735i | − 1.97618i | ||||||||
\(809\) | 11.9110 | 0.418767 | 0.209384 | − | 0.977834i | \(-0.432854\pi\) | ||||
0.209384 | + | 0.977834i | \(0.432854\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −42.2433 | −1.48336 | −0.741681 | − | 0.670752i | \(-0.765971\pi\) | ||||
−0.741681 | + | 0.670752i | \(0.765971\pi\) | |||||||
\(812\) | − 48.6736i | − 1.70811i | ||||||||
\(813\) | − 16.8621i | − 0.591379i | ||||||||
\(814\) | 21.1640 | 0.741796 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −49.1747 | −1.72146 | ||||||||
\(817\) | 24.4919i | 0.856863i | ||||||||
\(818\) | − 51.3368i | − 1.79495i | ||||||||
\(819\) | 11.3670 | 0.397197 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 44.5710 | 1.55554 | 0.777769 | − | 0.628551i | \(-0.216352\pi\) | ||||
0.777769 | + | 0.628551i | \(0.216352\pi\) | |||||||
\(822\) | − 32.1572i | − 1.12161i | ||||||||
\(823\) | − 12.3125i | − 0.429186i | −0.976704 | − | 0.214593i | \(-0.931157\pi\) | ||||
0.976704 | − | 0.214593i | \(-0.0688425\pi\) | |||||||
\(824\) | −88.4431 | −3.08106 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 65.9281 | 2.29393 | ||||||||
\(827\) | − 24.7421i | − 0.860367i | −0.902742 | − | 0.430183i | \(-0.858449\pi\) | ||||
0.902742 | − | 0.430183i | \(-0.141551\pi\) | |||||||
\(828\) | 23.9628i | 0.832766i | ||||||||
\(829\) | 53.7221 | 1.86584 | 0.932922 | − | 0.360077i | \(-0.117250\pi\) | ||||
0.932922 | + | 0.360077i | \(0.117250\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −18.6929 | −0.648451 | ||||||||
\(832\) | − 20.0754i | − 0.695989i | ||||||||
\(833\) | 20.6221i | 0.714512i | ||||||||
\(834\) | −34.3915 | −1.19088 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −156.076 | −5.39801 | ||||||||
\(837\) | − 2.06658i | − 0.0714315i | ||||||||
\(838\) | 17.3477i | 0.599266i | ||||||||
\(839\) | 45.7865 | 1.58073 | 0.790363 | − | 0.612639i | \(-0.209892\pi\) | ||||
0.790363 | + | 0.612639i | \(0.209892\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.2450 | −0.663622 | ||||||||
\(842\) | 14.6998i | 0.506589i | ||||||||
\(843\) | − 25.9852i | − 0.894979i | ||||||||
\(844\) | −114.353 | −3.93620 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 16.3252 | 0.561271 | ||||||||
\(847\) | 24.8340i | 0.853307i | ||||||||
\(848\) | 22.7009i | 0.779550i | ||||||||
\(849\) | −16.9219 | −0.580760 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.55139 | 0.327418 | ||||||||
\(852\) | − 22.4291i | − 0.768410i | ||||||||
\(853\) | 20.3074i | 0.695311i | 0.937622 | + | 0.347655i | \(0.113022\pi\) | ||||
−0.937622 | + | 0.347655i | \(0.886978\pi\) | |||||||
\(854\) | 25.2182 | 0.862950 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 60.7531 | 2.07650 | ||||||||
\(857\) | − 47.4031i | − 1.61926i | −0.586941 | − | 0.809630i | \(-0.699668\pi\) | ||||
0.586941 | − | 0.809630i | \(-0.300332\pi\) | |||||||
\(858\) | 38.7289i | 1.32218i | ||||||||
\(859\) | 5.37538 | 0.183406 | 0.0917028 | − | 0.995786i | \(-0.470769\pi\) | ||||
0.0917028 | + | 0.995786i | \(0.470769\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 12.8047 | 0.436383 | ||||||||
\(862\) | 16.6664i | 0.567661i | ||||||||
\(863\) | 15.0679i | 0.512916i | 0.966555 | + | 0.256458i | \(0.0825556\pi\) | ||||
−0.966555 | + | 0.256458i | \(0.917444\pi\) | |||||||
\(864\) | −9.18462 | −0.312467 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −2.87003 | −0.0975275 | ||||||||
\(867\) | 12.6760i | 0.430501i | ||||||||
\(868\) | 32.2057i | 1.09313i | ||||||||
\(869\) | −59.1746 | −2.00736 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −44.9791 | −1.52406 | ||||||||
\(872\) | 124.871i | 4.22868i | ||||||||
\(873\) | − 2.57278i | − 0.0870753i | ||||||||
\(874\) | −100.126 | −3.38680 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −7.82649 | −0.264433 | ||||||||
\(877\) | 6.43572i | 0.217319i | 0.994079 | + | 0.108659i | \(0.0346558\pi\) | ||||
−0.994079 | + | 0.108659i | \(0.965344\pi\) | |||||||
\(878\) | 13.2796i | 0.448165i | ||||||||
\(879\) | −1.05979 | −0.0357457 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 46.2411 | 1.55790 | 0.778950 | − | 0.627085i | \(-0.215752\pi\) | ||||
0.778950 | + | 0.627085i | \(0.215752\pi\) | |||||||
\(882\) | 9.83169i | 0.331050i | ||||||||
\(883\) | 12.8545i | 0.432590i | 0.976328 | + | 0.216295i | \(0.0693972\pi\) | ||||
−0.976328 | + | 0.216295i | \(0.930603\pi\) | |||||||
\(884\) | −89.4723 | −3.00928 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −46.5097 | −1.56252 | ||||||||
\(887\) | − 33.5617i | − 1.12689i | −0.826153 | − | 0.563446i | \(-0.809475\pi\) | ||||
0.826153 | − | 0.563446i | \(-0.190525\pi\) | |||||||
\(888\) | 13.4856i | 0.452546i | ||||||||
\(889\) | −33.5350 | −1.12473 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.30834 | 0.144335 | ||||||||
\(892\) | − 86.6942i | − 2.90274i | ||||||||
\(893\) | 47.9873i | 1.60583i | ||||||||
\(894\) | −13.5231 | −0.452279 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −10.8553 | −0.362649 | ||||||||
\(897\) | 17.4786i | 0.583592i | ||||||||
\(898\) | − 71.0870i | − 2.37220i | ||||||||
\(899\) | −6.45454 | −0.215271 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.6995 | 0.456398 | ||||||||
\(902\) | 43.6272i | 1.45263i | ||||||||
\(903\) | 10.5360i | 0.350616i | ||||||||
\(904\) | −29.7822 | −0.990542 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 20.2101 | 0.671437 | ||||||||
\(907\) | 5.73678i | 0.190487i | 0.995454 | + | 0.0952433i | \(0.0303629\pi\) | ||||
−0.995454 | + | 0.0952433i | \(0.969637\pi\) | |||||||
\(908\) | 85.2257i | 2.82831i | ||||||||
\(909\) | −7.87863 | −0.261318 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.08321 | 0.135283 | 0.0676413 | − | 0.997710i | \(-0.478453\pi\) | ||||
0.0676413 | + | 0.997710i | \(0.478453\pi\) | |||||||
\(912\) | − 68.9139i | − 2.28197i | ||||||||
\(913\) | 21.6144i | 0.715332i | ||||||||
\(914\) | −23.1876 | −0.766978 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 28.5027 | 0.941757 | ||||||||
\(917\) | − 16.1476i | − 0.533242i | ||||||||
\(918\) | 14.1482i | 0.466961i | ||||||||
\(919\) | −34.1894 | −1.12780 | −0.563902 | − | 0.825842i | \(-0.690700\pi\) | ||||
−0.563902 | + | 0.825842i | \(0.690700\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 29.7239 | 0.979434 | ||||||||
\(922\) | 4.70617i | 0.154989i | ||||||||
\(923\) | − 16.3599i | − 0.538492i | ||||||||
\(924\) | −67.1414 | −2.20879 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 7.06927 | 0.232311 | ||||||||
\(927\) | 12.4046i | 0.407421i | ||||||||
\(928\) | 28.6863i | 0.941672i | ||||||||
\(929\) | 23.9398 | 0.785438 | 0.392719 | − | 0.919659i | \(-0.371535\pi\) | ||||
0.392719 | + | 0.919659i | \(0.371535\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −28.8999 | −0.947157 | ||||||||
\(932\) | − 98.9507i | − 3.24124i | ||||||||
\(933\) | − 5.08513i | − 0.166480i | ||||||||
\(934\) | 104.474 | 3.41849 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −24.6779 | −0.806621 | ||||||||
\(937\) | 21.4640i | 0.701199i | 0.936525 | + | 0.350600i | \(0.114022\pi\) | ||||
−0.936525 | + | 0.350600i | \(0.885978\pi\) | |||||||
\(938\) | − 110.842i | − 3.61912i | ||||||||
\(939\) | −25.9388 | −0.846481 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.78646 | −0.0582371 | −0.0291185 | − | 0.999576i | \(-0.509270\pi\) | ||||
−0.0291185 | + | 0.999576i | \(0.509270\pi\) | |||||||
\(942\) | − 42.7165i | − 1.39178i | ||||||||
\(943\) | 19.6892i | 0.641167i | ||||||||
\(944\) | −69.7733 | −2.27093 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −35.8975 | −1.16713 | ||||||||
\(947\) | − 45.4097i | − 1.47562i | −0.675009 | − | 0.737809i | \(-0.735860\pi\) | ||||
0.675009 | − | 0.737809i | \(-0.264140\pi\) | |||||||
\(948\) | − 65.1755i | − 2.11680i | ||||||||
\(949\) | −5.70866 | −0.185311 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 19.7727 | 0.641172 | ||||||||
\(952\) | − 127.557i | − 4.13416i | ||||||||
\(953\) | − 1.00850i | − 0.0326686i | −0.999867 | − | 0.0163343i | \(-0.994800\pi\) | ||||
0.999867 | − | 0.0163343i | \(-0.00519960\pi\) | |||||||
\(954\) | 6.53134 | 0.211460 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −132.261 | −4.27761 | ||||||||
\(957\) | − 13.4562i | − 0.434978i | ||||||||
\(958\) | 72.5794i | 2.34493i | ||||||||
\(959\) | 40.6631 | 1.31308 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.7292 | −0.862234 | ||||||||
\(962\) | 17.0025i | 0.548183i | ||||||||
\(963\) | − 8.52094i | − 0.274583i | ||||||||
\(964\) | 88.8115 | 2.86043 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −43.0724 | −1.38583 | ||||||||
\(967\) | 21.4625i | 0.690188i | 0.938568 | + | 0.345094i | \(0.112153\pi\) | ||||
−0.938568 | + | 0.345094i | \(0.887847\pi\) | |||||||
\(968\) | − 53.9147i | − 1.73288i | ||||||||
\(969\) | −41.5883 | −1.33601 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 47.3619 | 1.51992 | 0.759958 | − | 0.649972i | \(-0.225219\pi\) | ||||
0.759958 | + | 0.649972i | \(0.225219\pi\) | |||||||
\(972\) | 4.74525i | 0.152204i | ||||||||
\(973\) | − 43.4884i | − 1.39417i | ||||||||
\(974\) | 67.0298 | 2.14777 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −26.6891 | −0.854296 | ||||||||
\(977\) | 6.29459i | 0.201382i | 0.994918 | + | 0.100691i | \(0.0321053\pi\) | ||||
−0.994918 | + | 0.100691i | \(0.967895\pi\) | |||||||
\(978\) | − 20.2927i | − 0.648889i | ||||||||
\(979\) | 38.7841 | 1.23955 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 17.5139 | 0.559174 | ||||||||
\(982\) | 61.5641i | 1.96459i | ||||||||
\(983\) | 7.80790i | 0.249033i | 0.992218 | + | 0.124517i | \(0.0397381\pi\) | ||||
−0.992218 | + | 0.124517i | \(0.960262\pi\) | |||||||
\(984\) | −27.7990 | −0.886200 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 44.1891 | 1.40727 | ||||||||
\(987\) | 20.6433i | 0.657084i | ||||||||
\(988\) | − 125.387i | − 3.98910i | ||||||||
\(989\) | −16.2007 | −0.515152 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21.0569 | −0.668896 | −0.334448 | − | 0.942414i | \(-0.608550\pi\) | ||||
−0.334448 | + | 0.942414i | \(0.608550\pi\) | |||||||
\(992\) | − 18.9808i | − 0.602640i | ||||||||
\(993\) | 23.9589i | 0.760311i | ||||||||
\(994\) | 40.3156 | 1.27873 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −23.8063 | −0.754332 | ||||||||
\(997\) | 29.3042i | 0.928072i | 0.885816 | + | 0.464036i | \(0.153599\pi\) | ||||
−0.885816 | + | 0.464036i | \(0.846401\pi\) | |||||||
\(998\) | − 23.2641i | − 0.736413i | ||||||||
\(999\) | 1.89142 | 0.0598418 |
(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 | 1875.2.b.g.1249.15 | 16 | ||
5.2 | odd | 4 | 1875.2.a.n.1.1 | ✓ | 8 | ||
5.3 | odd | 4 | 1875.2.a.o.1.8 | yes | 8 | ||
5.4 | even | 2 | inner | 1875.2.b.g.1249.2 | 16 | ||
15.2 | even | 4 | 5625.2.a.bc.1.8 | 8 | |||
15.8 | even | 4 | 5625.2.a.u.1.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1875.2.a.n.1.1 | ✓ | 8 | 5.2 | odd | 4 | ||
1875.2.a.o.1.8 | yes | 8 | 5.3 | odd | 4 | ||
1875.2.b.g.1249.2 | 16 | 5.4 | even | 2 | inner | ||
1875.2.b.g.1249.15 | 16 | 1.1 | even | 1 | trivial | ||
5625.2.a.u.1.1 | 8 | 15.8 | even | 4 | |||
5625.2.a.bc.1.8 | 8 | 15.2 | even | 4 |