Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [896,2,Mod(113,896)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(896, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("896.113");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 896 = 2^{7} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 896.u (of order \(8\), degree \(4\), 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: | \(7.15459602111\) |
Analytic rank: | \(0\) |
Dimension: | \(52\) |
Relative dimension: | \(13\) over \(\Q(\zeta_{8})\) |
Twist minimal: | no (minimal twist has level 224) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 113.7 | ||
Character | \(\chi\) | \(=\) | 896.113 |
Dual form | 896.2.u.c.785.7 |
$q$-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 \(\left(\mathbb{Z}/896\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(645\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{8}\right)\) |
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 | ||||||||
\(3\) | −0.0427122 | − | 0.103116i | −0.0246599 | − | 0.0595343i | 0.911070 | − | 0.412252i | \(-0.135258\pi\) |
−0.935730 | + | 0.352718i | \(0.885258\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.38883 | + | 0.989485i | 1.06832 | + | 0.442511i | 0.846396 | − | 0.532554i | \(-0.178768\pi\) |
0.221920 | + | 0.975065i | \(0.428768\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.707107 | + | 0.707107i | 0.267261 | + | 0.267261i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.11251 | − | 2.11251i | 0.704171 | − | 0.704171i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.21011 | + | 5.33568i | −0.666373 | + | 1.60877i | 0.121258 | + | 0.992621i | \(0.461307\pi\) |
−0.787632 | + | 0.616146i | \(0.788693\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.786702 | + | 0.325863i | −0.218192 | + | 0.0903780i | −0.489102 | − | 0.872227i | \(-0.662675\pi\) |
0.270910 | + | 0.962605i | \(0.412675\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 0.288590i | − | 0.0745137i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.93074i | 1.19588i | 0.801541 | + | 0.597940i | \(0.204014\pi\) | ||||
−0.801541 | + | 0.597940i | \(0.795986\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.25079 | − | 1.76074i | 0.975198 | − | 0.403940i | 0.162554 | − | 0.986700i | \(-0.448027\pi\) |
0.812645 | + | 0.582759i | \(0.198027\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.0427122 | − | 0.103116i | 0.00932056 | − | 0.0225018i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.84321 | − | 1.84321i | 0.384336 | − | 0.384336i | −0.488326 | − | 0.872661i | \(-0.662392\pi\) |
0.872661 | + | 0.488326i | \(0.162392\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.19188 | + | 1.19188i | 0.238376 | + | 0.238376i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.617414 | − | 0.255741i | −0.118821 | − | 0.0492174i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.76117 | + | 4.25184i | 0.327041 | + | 0.789546i | 0.998809 | + | 0.0487850i | \(0.0155349\pi\) |
−0.671769 | + | 0.740761i | \(0.734465\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.41557 | −1.15227 | −0.576135 | − | 0.817354i | \(-0.695440\pi\) | ||||
−0.576135 | + | 0.817354i | \(0.695440\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.644594 | 0.112209 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.989485 | + | 2.38883i | 0.167253 | + | 0.403785i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.10729 | − | 1.70130i | −0.675235 | − | 0.279691i | 0.0185985 | − | 0.999827i | \(-0.494080\pi\) |
−0.693833 | + | 0.720136i | \(0.744080\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.0672035 | + | 0.0672035i | 0.0107612 | + | 0.0107612i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.92263 | − | 1.92263i | 0.300264 | − | 0.300264i | −0.540853 | − | 0.841117i | \(-0.681899\pi\) |
0.841117 | + | 0.540853i | \(0.181899\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.47055 | − | 8.37866i | 0.529255 | − | 1.27773i | −0.402758 | − | 0.915307i | \(-0.631948\pi\) |
0.932012 | − | 0.362427i | \(-0.118052\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 7.13672 | − | 2.95613i | 1.06388 | − | 0.440673i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 2.58511i | − | 0.377076i | −0.982066 | − | 0.188538i | \(-0.939625\pi\) | ||
0.982066 | − | 0.188538i | \(-0.0603749\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000i | 0.142857i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.508440 | − | 0.210603i | 0.0711958 | − | 0.0294903i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.99079 | + | 7.22041i | −0.410817 | + | 0.991799i | 0.574102 | + | 0.818783i | \(0.305351\pi\) |
−0.984919 | + | 0.173016i | \(0.944649\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −10.5591 | + | 10.5591i | −1.42379 | + | 1.42379i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.363121 | − | 0.363121i | −0.0480966 | − | 0.0480966i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.67423 | + | 3.17877i | 0.999100 | + | 0.413841i | 0.821467 | − | 0.570256i | \(-0.193156\pi\) |
0.177633 | + | 0.984097i | \(0.443156\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.77294 | + | 13.9371i | 0.739149 | + | 1.78446i | 0.609314 | + | 0.792929i | \(0.291445\pi\) |
0.129836 | + | 0.991536i | \(0.458555\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.98754 | 0.376395 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.20173 | −0.273091 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.75199 | + | 9.05810i | 0.458378 | + | 1.10662i | 0.969054 | + | 0.246850i | \(0.0793954\pi\) |
−0.510675 | + | 0.859774i | \(0.670605\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.268792 | − | 0.111337i | −0.0323588 | − | 0.0134035i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.24880 | + | 3.24880i | 0.385562 | + | 0.385562i | 0.873101 | − | 0.487539i | \(-0.162105\pi\) |
−0.487539 | + | 0.873101i | \(0.662105\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.07125 | − | 9.07125i | 1.06171 | − | 1.06171i | 0.0637427 | − | 0.997966i | \(-0.479696\pi\) |
0.997966 | − | 0.0637427i | \(-0.0203037\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.0719946 | − | 0.173810i | 0.00831322 | − | 0.0200699i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.33568 | + | 2.21011i | −0.608057 | + | 0.251865i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 8.45254i | − | 0.950985i | −0.879720 | − | 0.475492i | \(-0.842270\pi\) | ||
0.879720 | − | 0.475492i | \(-0.157730\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | − | 8.88804i | − | 0.987560i | ||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.24766 | − | 3.83051i | 1.01506 | − | 0.420453i | 0.187763 | − | 0.982214i | \(-0.439876\pi\) |
0.827299 | + | 0.561762i | \(0.189876\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.87889 | + | 11.7787i | −0.529190 | + | 1.27758i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.363210 | − | 0.363210i | 0.0389402 | − | 0.0389402i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.81906 | − | 7.81906i | −0.828819 | − | 0.828819i | 0.158534 | − | 0.987353i | \(-0.449323\pi\) |
−0.987353 | + | 0.158534i | \(0.949323\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.786702 | − | 0.325863i | −0.0824688 | − | 0.0341597i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.274023 | + | 0.661550i | 0.0284149 | + | 0.0685996i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 11.8966 | 1.22057 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.58236 | 0.871407 | 0.435704 | − | 0.900090i | \(-0.356500\pi\) | ||||
0.435704 | + | 0.900090i | \(0.356500\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.60280 | + | 15.9406i | 0.663606 | + | 1.60209i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −16.7673 | − | 6.94523i | −1.66841 | − | 0.691076i | −0.669734 | − | 0.742601i | \(-0.733592\pi\) |
−0.998672 | + | 0.0515244i | \(0.983592\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.88000 | − | 7.88000i | −0.776439 | − | 0.776439i | 0.202784 | − | 0.979223i | \(-0.435001\pi\) |
−0.979223 | + | 0.202784i | \(0.935001\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.204064 | − | 0.204064i | 0.0199146 | − | 0.0199146i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.15732 | + | 2.79402i | −0.111882 | + | 0.270108i | −0.969896 | − | 0.243519i | \(-0.921698\pi\) |
0.858014 | + | 0.513627i | \(0.171698\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.12306 | − | 3.77890i | 0.873831 | − | 0.361953i | 0.0997298 | − | 0.995015i | \(-0.468202\pi\) |
0.774101 | + | 0.633062i | \(0.218202\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.496195i | 0.0470968i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1.15922i | − | 0.109050i | −0.998512 | − | 0.0545252i | \(-0.982635\pi\) | ||
0.998512 | − | 0.0545252i | \(-0.0173645\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.22693 | − | 2.57928i | 0.580664 | − | 0.240519i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.973528 | + | 2.35031i | −0.0900027 | + | 0.217286i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.48656 | + | 3.48656i | −0.319612 | + | 0.319612i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −15.8067 | − | 15.8067i | −1.43697 | − | 1.43697i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.280374 | − | 0.116135i | −0.0252805 | − | 0.0104715i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.27957 | − | 7.91759i | −0.293334 | − | 0.708171i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.07162 | −0.627505 | −0.313752 | − | 0.949505i | \(-0.601586\pi\) | ||||
−0.313752 | + | 0.949505i | \(0.601586\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.01221 | −0.0891203 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.643982 | − | 1.55471i | −0.0562650 | − | 0.135836i | 0.893247 | − | 0.449566i | \(-0.148421\pi\) |
−0.949512 | + | 0.313730i | \(0.898421\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.25079 | + | 1.76074i | 0.368590 | + | 0.152675i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.22184 | − | 1.22184i | −0.105159 | − | 0.105159i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.58507 | − | 1.58507i | 0.135422 | − | 0.135422i | −0.636147 | − | 0.771568i | \(-0.719473\pi\) |
0.771568 | + | 0.636147i | \(0.219473\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.854676 | − | 2.06337i | 0.0724927 | − | 0.175013i | −0.883480 | − | 0.468469i | \(-0.844806\pi\) |
0.955972 | + | 0.293457i | \(0.0948056\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.266567 | + | 0.110416i | −0.0224490 | + | 0.00929867i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 4.91778i | − | 0.411245i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.8995i | 0.988204i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.103116 | − | 0.0427122i | 0.00850489 | − | 0.00352284i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.40745 | − | 3.39788i | 0.115303 | − | 0.278366i | −0.855684 | − | 0.517499i | \(-0.826863\pi\) |
0.970987 | + | 0.239133i | \(0.0768632\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.8351 | + | 15.8351i | −1.28864 | + | 1.28864i | −0.353026 | + | 0.935614i | \(0.614847\pi\) |
−0.935614 | + | 0.353026i | \(0.885153\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 10.4162 | + | 10.4162i | 0.842103 | + | 0.842103i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −15.3257 | − | 6.34811i | −1.23099 | − | 0.509893i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.08115 | − | 17.0954i | −0.565137 | − | 1.36436i | −0.905612 | − | 0.424108i | \(-0.860588\pi\) |
0.340475 | − | 0.940254i | \(-0.389412\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.872285 | 0.0691767 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.60669 | 0.205436 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.587312 | + | 1.41790i | 0.0460018 | + | 0.111058i | 0.945210 | − | 0.326462i | \(-0.105857\pi\) |
−0.899208 | + | 0.437521i | \(0.855857\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.53982 | + | 0.637816i | 0.119875 | + | 0.0496539i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −11.3464 | − | 11.3464i | −0.878009 | − | 0.878009i | 0.115320 | − | 0.993328i | \(-0.463211\pi\) |
−0.993328 | + | 0.115320i | \(0.963211\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.67967 | + | 8.67967i | −0.667667 | + | 0.667667i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.26027 | − | 12.6994i | 0.402263 | − | 0.971149i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.98159 | + | 1.64923i | −0.302715 | + | 0.125388i | −0.528870 | − | 0.848703i | \(-0.677384\pi\) |
0.226156 | + | 0.974091i | \(0.427384\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.68557i | 0.127417i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 0.927111i | − | 0.0696860i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.06700 | + | 0.856179i | −0.154495 | + | 0.0639938i | −0.458591 | − | 0.888648i | \(-0.651646\pi\) |
0.304096 | + | 0.952641i | \(0.401646\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.180356 | + | 0.435418i | −0.0134058 | + | 0.0323643i | −0.930441 | − | 0.366443i | \(-0.880576\pi\) |
0.917035 | + | 0.398807i | \(0.130576\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.19057 | − | 1.19057i | 0.0880094 | − | 0.0880094i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.12821 | − | 8.12821i | −0.597598 | − | 0.597598i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −26.3088 | − | 10.8975i | −1.92389 | − | 0.796902i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.255741 | − | 0.617414i | −0.0186024 | − | 0.0449102i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.8891 | 0.860267 | 0.430133 | − | 0.902765i | \(-0.358466\pi\) | ||||
0.430133 | + | 0.902765i | \(0.358466\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15.1747 | −1.09230 | −0.546148 | − | 0.837689i | \(-0.683906\pi\) | ||||
−0.546148 | + | 0.837689i | \(0.683906\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.0940407 | + | 0.227034i | 0.00673440 | + | 0.0162583i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.00227 | − | 0.415154i | −0.0714088 | − | 0.0295785i | 0.346693 | − | 0.937979i | \(-0.387305\pi\) |
−0.418102 | + | 0.908400i | \(0.637305\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.912005 | − | 0.912005i | −0.0646504 | − | 0.0646504i | 0.674042 | − | 0.738693i | \(-0.264557\pi\) |
−0.738693 | + | 0.674042i | \(0.764557\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.773783 | − | 0.773783i | 0.0545784 | − | 0.0545784i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.76117 | + | 4.25184i | −0.123610 | + | 0.298420i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.49523 | − | 2.69041i | 0.453647 | − | 0.187907i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 7.78760i | − | 0.541276i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 26.5723i | 1.83804i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.6330 | + | 5.23275i | −0.869689 | + | 0.360237i | −0.772489 | − | 0.635028i | \(-0.780989\pi\) |
−0.0972000 | + | 0.995265i | \(0.530989\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.196241 | − | 0.473768i | 0.0134462 | − | 0.0324621i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 16.5811 | − | 16.5811i | 1.13082 | − | 1.13082i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.53650 | − | 4.53650i | −0.307957 | − | 0.307957i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.32285 | − | 0.547941i | −0.0893897 | − | 0.0370264i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.60674 | − | 3.87902i | −0.108081 | − | 0.260931i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.27134 | 0.0851354 | 0.0425677 | − | 0.999094i | \(-0.486446\pi\) | ||||
0.0425677 | + | 0.999094i | \(0.486446\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.03573 | 0.335715 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.45381 | − | 17.9951i | −0.494727 | − | 1.19438i | −0.952289 | − | 0.305199i | \(-0.901277\pi\) |
0.457562 | − | 0.889178i | \(-0.348723\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.50872 | − | 2.69600i | −0.430109 | − | 0.178157i | 0.157117 | − | 0.987580i | \(-0.449780\pi\) |
−0.587226 | + | 0.809423i | \(0.699780\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.455797 | + | 0.455797i | 0.0299892 | + | 0.0299892i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.6132 | − | 13.6132i | 0.891831 | − | 0.891831i | −0.102864 | − | 0.994695i | \(-0.532801\pi\) |
0.994695 | + | 0.102864i | \(0.0328008\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.55792 | − | 6.17537i | 0.166860 | − | 0.402837i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.871595 | + | 0.361026i | −0.0566162 | + | 0.0234512i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 11.2693i | − | 0.728950i | −0.931213 | − | 0.364475i | \(-0.881248\pi\) | ||
0.931213 | − | 0.364475i | \(-0.118752\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 26.1689i | − | 1.68568i | −0.538161 | − | 0.842842i | \(-0.680881\pi\) | ||
0.538161 | − | 0.842842i | \(-0.319119\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2.76874 | + | 1.14685i | −0.177615 | + | 0.0735705i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.989485 | + | 2.38883i | −0.0632159 | + | 0.152617i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.77035 | + | 2.77035i | −0.176273 | + | 0.176273i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.789976 | − | 0.789976i | −0.0500627 | − | 0.0500627i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.49612 | + | 3.51921i | 0.536270 | + | 0.222130i | 0.634347 | − | 0.773048i | \(-0.281269\pi\) |
−0.0980767 | + | 0.995179i | \(0.531269\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.76107 | + | 13.9085i | 0.362196 | + | 0.874417i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.42296 | 0.0891094 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 25.6035 | 1.59710 | 0.798552 | − | 0.601925i | \(-0.205599\pi\) | ||||
0.798552 | + | 0.601925i | \(0.205599\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.70130 | − | 4.10729i | −0.105713 | − | 0.255215i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 12.7025 | + | 5.26156i | 0.786267 | + | 0.325683i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.13840 | + | 7.13840i | 0.440173 | + | 0.440173i | 0.892070 | − | 0.451897i | \(-0.149253\pi\) |
−0.451897 | + | 0.892070i | \(0.649253\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −14.2890 | + | 14.2890i | −0.877764 | + | 0.877764i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.472304 | + | 1.14024i | −0.0289045 | + | 0.0697817i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 15.1259 | − | 6.26534i | 0.922241 | − | 0.382005i | 0.129511 | − | 0.991578i | \(-0.458659\pi\) |
0.792730 | + | 0.609573i | \(0.208659\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 10.5616i | − | 0.641573i | −0.947151 | − | 0.320787i | \(-0.896053\pi\) | ||
0.947151 | − | 0.320787i | \(-0.103947\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.0950401i | 0.00575209i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −8.99368 | + | 3.72531i | −0.542340 | + | 0.224644i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.539748 | + | 1.30307i | −0.0324303 | + | 0.0782937i | −0.939265 | − | 0.343193i | \(-0.888492\pi\) |
0.906835 | + | 0.421487i | \(0.138492\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −13.5530 | + | 13.5530i | −0.811395 | + | 0.811395i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.4433 | + | 17.4433i | 1.04058 | + | 1.04058i | 0.999141 | + | 0.0414418i | \(0.0131951\pi\) |
0.0414418 | + | 0.999141i | \(0.486805\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −20.5289 | − | 8.50335i | −1.22032 | − | 0.505472i | −0.322806 | − | 0.946465i | \(-0.604626\pi\) |
−0.897510 | + | 0.440993i | \(0.854626\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.508131 | − | 1.22674i | −0.0300991 | − | 0.0726656i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.71900 | 0.160498 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.31217 | −0.430127 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.366572 | − | 0.884982i | −0.0214888 | − | 0.0518786i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −25.7260 | − | 10.6561i | −1.50293 | − | 0.622534i | −0.528845 | − | 0.848719i | \(-0.677375\pi\) |
−0.974084 | + | 0.226185i | \(0.927375\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 15.1871 | + | 15.1871i | 0.884226 | + | 0.884226i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.72910 | − | 2.72910i | 0.158359 | − | 0.158359i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.849423 | + | 2.05069i | −0.0491234 | + | 0.118594i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.37866 | − | 3.47055i | 0.482938 | − | 0.200039i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.02563i | 0.116369i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 39.0056i | 2.23345i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.8674 | − | 6.98671i | 0.962673 | − | 0.398752i | 0.154693 | − | 0.987963i | \(-0.450561\pi\) |
0.807980 | + | 0.589210i | \(0.200561\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.475985 | + | 1.14913i | −0.0270778 | + | 0.0653717i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.94765 | + | 2.94765i | −0.167146 | + | 0.167146i | −0.785724 | − | 0.618578i | \(-0.787709\pi\) |
0.618578 | + | 0.785724i | \(0.287709\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.8460 | − | 16.8460i | −0.952190 | − | 0.952190i | 0.0467182 | − | 0.998908i | \(-0.485124\pi\) |
−0.998908 | + | 0.0467182i | \(0.985124\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 7.13672 | + | 2.95613i | 0.402109 | + | 0.166559i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.90426 | + | 4.59730i | 0.106954 | + | 0.258210i | 0.968291 | − | 0.249823i | \(-0.0803726\pi\) |
−0.861337 | + | 0.508034i | \(0.830373\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −26.5788 | −1.48813 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.337541 | 0.0188397 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.68172 | + | 20.9595i | 0.483064 | + | 1.16622i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.32604 | − | 0.549266i | −0.0735557 | − | 0.0304678i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.779332 | − | 0.779332i | −0.0430972 | − | 0.0430972i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.82795 | − | 1.82795i | 0.100778 | − | 0.100778i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.83420 | + | 11.6708i | −0.265711 | + | 0.641484i | −0.999272 | − | 0.0381394i | \(-0.987857\pi\) |
0.733561 | + | 0.679624i | \(0.237857\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −12.2707 | + | 5.08270i | −0.672431 | + | 0.278530i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 25.3508i | 1.38506i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 7.15072i | − | 0.389524i | −0.980850 | − | 0.194762i | \(-0.937606\pi\) | ||
0.980850 | − | 0.194762i | \(-0.0623935\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.119535 | + | 0.0495129i | −0.00649224 | + | 0.00268917i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 14.1791 | − | 34.2314i | 0.767843 | − | 1.85374i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.707107 | + | 0.707107i | −0.0381802 | + | 0.0381802i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.531932 | − | 0.531932i | −0.0286382 | − | 0.0286382i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 26.2900 | + | 10.8897i | 1.41132 | + | 0.584589i | 0.952664 | − | 0.304024i | \(-0.0983303\pi\) |
0.458658 | + | 0.888613i | \(0.348330\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.908593 | + | 2.19354i | 0.0486359 | + | 0.117417i | 0.946330 | − | 0.323201i | \(-0.104759\pi\) |
−0.897694 | + | 0.440619i | \(0.854759\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.569057 | 0.0303740 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −21.1802 | −1.12731 | −0.563655 | − | 0.826010i | \(-0.690605\pi\) | ||||
−0.563655 | + | 0.826010i | \(0.690605\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.54619 | + | 10.9755i | 0.241287 | + | 0.582518i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.508440 | + | 0.210603i | 0.0269095 | + | 0.0111463i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 14.7991 | + | 14.7991i | 0.781068 | + | 0.781068i | 0.980011 | − | 0.198943i | \(-0.0637508\pi\) |
−0.198943 | + | 0.980011i | \(0.563751\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.53400 | − | 1.53400i | 0.0807371 | − | 0.0807371i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.954790 | + | 2.30507i | −0.0501135 | + | 0.120985i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 30.6455 | − | 12.6938i | 1.60406 | − | 0.664423i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 30.1594i | − | 1.57431i | −0.616757 | − | 0.787153i | \(-0.711554\pi\) | ||
0.616757 | − | 0.787153i | \(-0.288446\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 8.12314i | − | 0.422874i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.22041 | + | 2.99079i | −0.374865 | + | 0.155274i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.61011 | + | 15.9582i | −0.342259 | + | 0.826286i | 0.655228 | + | 0.755431i | \(0.272573\pi\) |
−0.997487 | + | 0.0708544i | \(0.977427\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.676355 | + | 0.676355i | −0.0349268 | + | 0.0349268i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.77103 | − | 2.77103i | −0.142715 | − | 0.142715i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.5376 | − | 4.77902i | −0.592646 | − | 0.245482i | 0.0661427 | − | 0.997810i | \(-0.478931\pi\) |
−0.658788 | + | 0.752328i | \(0.728931\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.302044 | + | 0.729199i | 0.0154742 | + | 0.0373580i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11.4990 | 0.587569 | 0.293785 | − | 0.955872i | \(-0.405085\pi\) | ||||
0.293785 | + | 0.955872i | \(0.405085\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −14.9329 | −0.761050 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −10.3684 | − | 25.0316i | −0.527057 | − | 1.27243i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −11.8548 | − | 4.91043i | −0.601063 | − | 0.248968i | 0.0613390 | − | 0.998117i | \(-0.480463\pi\) |
−0.662402 | + | 0.749149i | \(0.730463\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.08838 | + | 9.08838i | 0.459619 | + | 0.459619i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.132810 | + | 0.132810i | −0.00669939 | + | 0.00669939i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.36366 | − | 20.1917i | 0.420821 | − | 1.01595i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.31721 | + | 1.37403i | −0.166486 | + | 0.0689607i | −0.464370 | − | 0.885641i | \(-0.653719\pi\) |
0.297884 | + | 0.954602i | \(0.403719\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 0.513531i | − | 0.0257087i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 6.54378i | − | 0.326781i | −0.986561 | − | 0.163390i | \(-0.947757\pi\) | ||
0.986561 | − | 0.163390i | \(-0.0522430\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.04714 | − | 2.09060i | 0.251416 | − | 0.104140i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 8.79458 | − | 21.2320i | 0.437006 | − | 1.05503i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 18.1551 | − | 18.1551i | 0.899917 | − | 0.899917i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 20.4982 | + | 20.4982i | 1.01357 | + | 1.01357i | 0.999907 | + | 0.0136658i | \(0.00435009\pi\) |
0.0136658 | + | 0.999907i | \(0.495650\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.231149 | − | 0.0957449i | −0.0114017 | − | 0.00472275i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.17877 | + | 7.67423i | 0.156417 | + | 0.377624i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 25.8813 | 1.27046 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.249272 | −0.0122069 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.78532 | − | 4.31013i | −0.0872184 | − | 0.210564i | 0.874252 | − | 0.485472i | \(-0.161352\pi\) |
−0.961470 | + | 0.274909i | \(0.911352\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.34745 | − | 2.21499i | −0.260619 | − | 0.107952i | 0.248548 | − | 0.968620i | \(-0.420047\pi\) |
−0.509167 | + | 0.860668i | \(0.670047\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.46107 | − | 5.46107i | −0.265526 | − | 0.265526i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.87685 | + | 5.87685i | −0.285069 | + | 0.285069i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.77294 | + | 13.9371i | −0.279372 | + | 0.674464i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.507104 | + | 0.210049i | −0.0244832 | + | 0.0101413i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.4021i | 0.790063i | 0.918668 | + | 0.395031i | \(0.129266\pi\) | ||||
−0.918668 | + | 0.395031i | \(0.870734\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 35.7323i | 1.71719i | 0.512659 | + | 0.858593i | \(0.328661\pi\) | ||||
−0.512659 | + | 0.858593i | \(0.671339\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.22704 | − | 0.508256i | 0.0588320 | − | 0.0243690i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.58969 | − | 11.0805i | 0.219555 | − | 0.530052i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.67257 | − | 4.67257i | 0.223010 | − | 0.223010i | −0.586755 | − | 0.809765i | \(-0.699595\pi\) |
0.809765 | + | 0.586755i | \(0.199595\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.11251 | + | 2.11251i | 0.100596 | + | 0.100596i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.6836 | − | 5.25371i | −0.602615 | − | 0.249611i | 0.0604524 | − | 0.998171i | \(-0.480746\pi\) |
−0.663067 | + | 0.748560i | \(0.730746\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.9415 | − | 26.4152i | −0.518679 | − | 1.25220i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.410493 | −0.0194156 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −23.9736 | −1.13139 | −0.565693 | − | 0.824616i | \(-0.691391\pi\) | ||||
−0.565693 | + | 0.824616i | \(0.691391\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.00930 | + | 14.5077i | 0.282967 | + | 0.683143i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.30920 | + | 0.956504i | 0.108496 | + | 0.0449405i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.55686 | − | 1.55686i | −0.0729867 | − | 0.0729867i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.390350 | − | 0.390350i | 0.0182598 | − | 0.0182598i | −0.697918 | − | 0.716178i | \(-0.745890\pi\) |
0.716178 | + | 0.697918i | \(0.245890\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.26099 | − | 3.04430i | 0.0588581 | − | 0.142096i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.71309 | + | 4.02330i | −0.452384 | + | 0.187384i | −0.597229 | − | 0.802071i | \(-0.703732\pi\) |
0.144845 | + | 0.989454i | \(0.453732\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 40.7995i | 1.89612i | 0.318099 | + | 0.948058i | \(0.396956\pi\) | ||||
−0.318099 | + | 0.948058i | \(0.603044\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.85147i | 0.0858599i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.10562 | − | 2.52903i | 0.282535 | − | 0.117030i | −0.236916 | − | 0.971530i | \(-0.576137\pi\) |
0.519451 | + | 0.854500i | \(0.326137\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.75199 | + | 9.05810i | −0.173251 | + | 0.418264i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.46036 | + | 1.46036i | −0.0672900 | + | 0.0672900i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 37.0355 | + | 37.0355i | 1.70290 | + | 1.70290i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.16503 | + | 2.96785i | 0.328754 | + | 0.136174i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.93511 | + | 21.5713i | 0.409111 | + | 0.987681i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 30.0314 | 1.37217 | 0.686086 | − | 0.727521i | \(-0.259327\pi\) | ||||
0.686086 | + | 0.727521i | \(0.259327\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.78560 | 0.172609 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.111337 | − | 0.268792i | −0.00506603 | − | 0.0122305i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 20.5018 | + | 8.49212i | 0.930938 | + | 0.385607i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.4987 | + | 14.4987i | 0.657001 | + | 0.657001i | 0.954669 | − | 0.297668i | \(-0.0962090\pi\) |
−0.297668 | + | 0.954669i | \(0.596209\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.121123 | − | 0.121123i | 0.00547737 | − | 0.00547737i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.6643 | + | 37.8170i | −0.706921 | + | 1.70666i | 0.000632562 | 1.00000i | \(0.499799\pi\) | |
−0.707554 | + | 0.706659i | \(0.750201\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −20.9647 | + | 8.68385i | −0.944202 | + | 0.391101i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 44.6126i | 2.00519i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.59450i | 0.206092i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20.1154 | + | 8.33206i | −0.900488 | + | 0.372994i | −0.784408 | − | 0.620246i | \(-0.787033\pi\) |
−0.116080 | + | 0.993240i | \(0.537033\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.685368 | + | 1.65463i | −0.0306200 | + | 0.0739232i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 29.0379 | − | 29.0379i | 1.29474 | − | 1.29474i | 0.362914 | − | 0.931823i | \(-0.381782\pi\) |
0.931823 | − | 0.362914i | \(-0.118218\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −33.1819 | − | 33.1819i | −1.47658 | − | 1.47658i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.26574 | + | 0.524288i | 0.0562137 | + | 0.0232845i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.2966 | + | 29.6866i | 0.545036 | + | 1.31583i | 0.921131 | + | 0.389253i | \(0.127267\pi\) |
−0.376095 | + | 0.926581i | \(0.622733\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.8287 | 0.567507 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.07479 | −0.135755 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11.0268 | − | 26.6211i | −0.485900 | − | 1.17307i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.7933 | + | 5.71337i | 0.606628 | + | 0.251274i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.340125 | + | 0.340125i | 0.0149298 | + | 0.0149298i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17.0565 | + | 17.0565i | −0.747257 | + | 0.747257i | −0.973963 | − | 0.226706i | \(-0.927204\pi\) |
0.226706 | + | 0.973963i | \(0.427204\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.03979 | + | 7.33869i | −0.132921 | + | 0.320899i | −0.976301 | − | 0.216419i | \(-0.930562\pi\) |
0.843380 | + | 0.537318i | \(0.180562\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.173810 | − | 0.0719946i | 0.00758570 | − | 0.00314210i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 31.6335i | − | 1.37798i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 16.2052i | 0.704572i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 22.9271 | − | 9.49672i | 0.994952 | − | 0.412122i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.886022 | + | 2.13905i | −0.0383779 | + | 0.0926524i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.52928 | + | 5.52928i | −0.239051 | + | 0.239051i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.176572 | + | 0.176572i | 0.00761965 | + | 0.00761965i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.33568 | − | 2.21011i | −0.229824 | − | 0.0951962i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.3582 | − | 39.4922i | −0.703293 | − | 1.69790i | −0.716115 | − | 0.697983i | \(-0.754081\pi\) |
0.0128211 | − | 0.999918i | \(-0.495919\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.0526021 | 0.00225737 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 25.5326 | 1.09370 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.91004 | − | 23.9250i | −0.423723 | − | 1.02296i | −0.981240 | − | 0.192792i | \(-0.938246\pi\) |
0.557517 | − | 0.830166i | \(-0.311754\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 41.6377 | + | 17.2469i | 1.77705 | + | 0.736080i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 14.9727 | + | 14.9727i | 0.637859 | + | 0.637859i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.97685 | − | 5.97685i | 0.254161 | − | 0.254161i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.490978 | + | 1.18532i | −0.0208408 | + | 0.0503142i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 16.6979 | − | 6.91650i | 0.707513 | − | 0.293061i | 0.000237874 | − | 1.00000i | \(-0.499924\pi\) |
0.707275 | + | 0.706939i | \(0.249924\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.72243i | 0.326624i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.17832i | 0.134189i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −14.5187 | + | 6.01384i | −0.611890 | + | 0.253453i | −0.667037 | − | 0.745025i | \(-0.732438\pi\) |
0.0551461 | + | 0.998478i | \(0.482438\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.14703 | − | 2.76918i | 0.0482560 | − | 0.116500i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 6.28479 | − | 6.28479i | 0.263936 | − | 0.263936i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 29.2630 | + | 29.2630i | 1.22677 | + | 1.22677i | 0.965179 | + | 0.261589i | \(0.0842464\pi\) |
0.261589 | + | 0.965179i | \(0.415754\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.0802 | + | 5.83222i | 0.589239 | + | 0.244071i | 0.657323 | − | 0.753609i | \(-0.271689\pi\) |
−0.0680840 | + | 0.997680i | \(0.521689\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.507811 | − | 1.22596i | −0.0212141 | − | 0.0512154i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.39377 | 0.183233 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 33.0545 | 1.37608 | 0.688039 | − | 0.725674i | \(-0.258472\pi\) | ||||
0.688039 | + | 0.725674i | \(0.258472\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.648143 | + | 1.56476i | 0.0269359 | + | 0.0650290i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.24766 | + | 3.83051i | 0.383658 | + | 0.158916i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −31.9158 | − | 31.9158i | −1.32182 | − | 1.32182i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.65118 | + | 4.65118i | −0.192303 | + | 0.192303i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 10.1001 | − | 24.3838i | 0.416876 | − | 1.00643i | −0.566371 | − | 0.824150i | \(-0.691653\pi\) |
0.983247 | − | 0.182277i | \(-0.0583469\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −27.2713 | + | 11.2961i | −1.12369 | + | 0.465449i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.121083i | 0.00498067i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 34.2521i | − | 1.40656i | −0.710911 | − | 0.703282i | \(-0.751717\pi\) | ||
0.710911 | − | 0.703282i | \(-0.248283\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −11.7787 | + | 4.87889i | −0.482879 | + | 0.200015i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.0550889 | + | 0.132996i | −0.00225464 | + | 0.00544318i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.01007 | + | 6.01007i | −0.245565 | + | 0.245565i | −0.819148 | − | 0.573583i | \(-0.805553\pi\) |
0.573583 | + | 0.819148i | \(0.305553\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.40420 | + | 1.40420i | 0.0572784 | + | 0.0572784i | 0.735166 | − | 0.677887i | \(-0.237104\pi\) |
−0.677887 | + | 0.735166i | \(0.737104\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 27.0615 | + | 11.2092i | 1.10203 | + | 0.456475i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −22.1190 | − | 53.4000i | −0.899265 | − | 2.17102i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −28.6512 | −1.16292 | −0.581458 | − | 0.813576i | \(-0.697518\pi\) | ||||
−0.581458 | + | 0.813576i | \(0.697518\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.513657 | 0.0208144 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.842389 | + | 2.03371i | 0.0340794 | + | 0.0822750i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.128901 | − | 0.0533925i | −0.00520625 | − | 0.00215650i | 0.380079 | − | 0.924954i | \(-0.375897\pi\) |
−0.385285 | + | 0.922798i | \(0.625897\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.554851 | − | 0.554851i | −0.0223738 | − | 0.0223738i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.70245 | + | 1.70245i | −0.0685380 | + | 0.0685380i | −0.740545 | − | 0.672007i | \(-0.765433\pi\) |
0.672007 | + | 0.740545i | \(0.265433\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.85543 | + | 14.1363i | −0.235349 | + | 0.568184i | −0.996791 | − | 0.0800499i | \(-0.974492\pi\) |
0.761441 | + | 0.648234i | \(0.224492\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.60941 | + | 0.666638i | −0.0645832 | + | 0.0267513i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 11.0578i | − | 0.443023i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | − | 30.5867i | − | 1.22347i | ||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.74004 | − | 1.13496i | 0.109426 | − | 0.0453259i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.38865 | − | 20.2520i | 0.334477 | − | 0.807499i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.4333 | − | 12.4333i | 0.494962 | − | 0.494962i | −0.414903 | − | 0.909865i | \(-0.636185\pi\) |
0.909865 | + | 0.414903i | \(0.136185\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.07916 | + | 1.07916i | 0.0428929 | + | 0.0428929i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −16.8929 | − | 6.99726i | −0.670373 | − | 0.277678i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.325863 | − | 0.786702i | −0.0129111 | − | 0.0311703i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 13.7263 | 0.543003 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 21.9009 | 0.865033 | 0.432517 | − | 0.901626i | \(-0.357626\pi\) | ||||
0.432517 | + | 0.901626i | \(0.357626\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.7001 | + | 28.2465i | 0.461406 | + | 1.11393i | 0.967820 | + | 0.251642i | \(0.0809705\pi\) |
−0.506415 | + | 0.862290i | \(0.669030\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.41800 | − | 1.00157i | −0.0952086 | − | 0.0394367i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.24919 | − | 1.24919i | −0.0491107 | − | 0.0491107i | 0.682125 | − | 0.731236i | \(-0.261056\pi\) |
−0.731236 | + | 0.682125i | \(0.761056\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −33.9218 | + | 33.9218i | −1.33155 | + | 1.33155i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.274023 | + | 0.661550i | −0.0107398 | + | 0.0259282i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −15.0420 | + | 6.23061i | −0.588640 | + | 0.243823i | −0.657065 | − | 0.753834i | \(-0.728202\pi\) |
0.0684256 | + | 0.997656i | \(0.478202\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 4.35115i | − | 0.170013i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 38.3262i | − | 1.49525i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −36.1878 | + | 14.9895i | −1.40968 | + | 0.583908i | −0.952245 | − | 0.305336i | \(-0.901231\pi\) |
−0.457433 | + | 0.889244i | \(0.651231\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.17095 | + | 10.0696i | −0.162231 | + | 0.391660i | −0.984002 | − | 0.178158i | \(-0.942986\pi\) |
0.821771 | + | 0.569818i | \(0.192986\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.331363 | + | 0.331363i | −0.0128691 | + | 0.0128691i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.41218 | + | 8.41218i | 0.326210 | + | 0.326210i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.0832 | + | 4.59082i | 0.429144 | + | 0.177757i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.0543018 | − | 0.131096i | −0.00209943 | − | 0.00506847i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −87.1228 | −3.36334 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 25.4507 | 0.981052 | 0.490526 | − | 0.871426i | \(-0.336805\pi\) | ||||
0.490526 | + | 0.871426i | \(0.336805\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.431071 | − | 1.04070i | −0.0165919 | − | 0.0400564i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.08597 | − | 0.864037i | −0.0801703 | − | 0.0332076i | 0.342238 | − | 0.939613i | \(-0.388815\pi\) |
−0.422408 | + | 0.906406i | \(0.638815\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.06865 | + | 6.06865i | 0.232893 | + | 0.232893i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.53722 | + | 1.53722i | −0.0589064 | + | 0.0589064i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.34610 | − | 10.4924i | 0.166299 | − | 0.401481i | −0.818658 | − | 0.574282i | \(-0.805281\pi\) |
0.984957 | + | 0.172800i | \(0.0552815\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.35486 | − | 2.21806i | 0.204599 | − | 0.0847476i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.786308i | 0.0299995i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 6.65489i | − | 0.253531i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21.2685 | − | 8.80972i | 0.809093 | − | 0.335137i | 0.0605011 | − | 0.998168i | \(-0.480730\pi\) |
0.748592 | + | 0.663031i | \(0.230730\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6.60280 | + | 15.9406i | −0.250820 | + | 0.605532i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.08335 | − | 4.08335i | 0.154890 | − | 0.154890i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.47997 | + | 9.47997i | 0.359079 | + | 0.359079i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.98519 | − | 0.822294i | −0.0750869 | − | 0.0311020i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.21862 | + | 12.5989i | 0.197105 | + | 0.475853i | 0.991270 | − | 0.131849i | \(-0.0420915\pi\) |
−0.794165 | + | 0.607702i | \(0.792091\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −20.4548 | −0.771467 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.746036 | −0.0280973 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.94523 | − | 16.7673i | −0.261202 | − | 0.630598i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.46044 | + | 3.09021i | 0.280183 | + | 0.116055i | 0.518350 | − | 0.855169i | \(-0.326547\pi\) |
−0.238167 | + | 0.971224i | \(0.576547\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −17.8561 | − | 17.8561i | −0.669656 | − | 0.669656i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −11.8252 | + | 11.8252i | −0.442859 | + | 0.442859i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.86607 | − | 11.7477i | 0.181981 | − | 0.439340i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.16205 | + | 0.481336i | −0.0433975 | + | 0.0179758i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 40.3483i | 1.50474i | 0.658742 | + | 0.752369i | \(0.271089\pi\) | ||||
−0.658742 | + | 0.752369i | \(0.728911\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 11.1440i | − | 0.415024i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.69844 | + | 1.11773i | −0.100356 | + | 0.0415688i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.96858 | + | 7.16679i | −0.110250 | + | 0.266168i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20.1134 | + | 20.1134i | −0.745965 | + | 0.745965i | −0.973719 | − | 0.227754i | \(-0.926862\pi\) |
0.227754 | + | 0.973719i | \(0.426862\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −18.6179 | − | 18.6179i | −0.689550 | − | 0.689550i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 41.3130 | + | 17.1124i | 1.52802 | + | 0.632925i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.98757 | + | 4.79842i | 0.0734126 | + | 0.177234i | 0.956326 | − | 0.292302i | \(-0.0944213\pi\) |
−0.882913 | + | 0.469536i | \(0.844421\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.288590 | 0.0106448 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −56.6234 | −2.08575 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.2543 | − | 39.2413i | −0.597923 | − | 1.44351i | −0.875694 | − | 0.482867i | \(-0.839596\pi\) |
0.277771 | − | 0.960647i | \(-0.410404\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.403996 | + | 0.167340i | 0.0148412 | + | 0.00614741i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −19.2443 | − | 19.2443i | −0.706005 | − | 0.706005i | 0.259687 | − | 0.965693i | \(-0.416380\pi\) |
−0.965693 | + | 0.259687i | \(0.916380\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.72431 | − | 6.72431i | 0.246360 | − | 0.246360i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 11.4438 | − | 27.6278i | 0.418707 | − | 1.01085i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.79402 | + | 1.15732i | −0.102091 | + | 0.0422876i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 24.7356i | − | 0.902617i | −0.892368 | − | 0.451308i | \(-0.850957\pi\) | ||
0.892368 | − | 0.451308i | \(-0.149043\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 1.02640i | − | 0.0374042i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −53.4958 | + | 22.1587i | −1.94691 | + | 0.806437i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.956469 | − | 2.30912i | 0.0347634 | − | 0.0839264i | −0.905544 | − | 0.424252i | \(-0.860537\pi\) |
0.940308 | + | 0.340325i | \(0.110537\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.18812 | − | 1.18812i | 0.0431261 | − | 0.0431261i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8.17156 | − | 8.17156i | −0.296219 | − | 0.296219i | 0.543312 | − | 0.839531i | \(-0.317170\pi\) |
−0.839531 | + | 0.543312i | \(0.817170\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.12306 | + | 3.77890i | 0.330277 | + | 0.136805i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 14.5759 | + | 35.1893i | 0.526992 | + | 1.27227i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −7.07318 | −0.255398 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.39428 | 0.230584 | 0.115292 | − | 0.993332i | \(-0.463220\pi\) | ||||
0.115292 | + | 0.993332i | \(0.463220\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.09358 | − | 2.64014i | −0.0393844 | − | 0.0950824i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.86511 | + | 0.772553i | 0.0670833 | + | 0.0277868i | 0.415973 | − | 0.909377i | \(-0.363441\pi\) |
−0.348890 | + | 0.937164i | \(0.613441\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.64660 | − | 7.64660i | −0.274674 | − | 0.274674i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.350863 | + | 0.350863i | −0.0125871 | + | 0.0125871i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.78745 | − | 11.5579i | 0.171528 | − | 0.414105i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −24.5148 | + | 10.1544i | −0.877208 | + | 0.363351i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 3.07554i | − | 0.109911i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 47.8446i | − | 1.70765i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.33063 | − | 2.62223i | 0.225663 | − | 0.0934725i | −0.266988 | − | 0.963700i | \(-0.586028\pi\) |
0.492650 | + | 0.870227i | \(0.336028\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.431189 | − | 1.04098i | 0.0153507 | − | 0.0370600i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.819694 | − | 0.819694i | 0.0291450 | − | 0.0291450i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.08317 | − | 9.08317i | −0.322553 | − | 0.322553i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.08374 | + | 0.863113i | 0.0739026 | + | 0.0306115i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −11.7831 | − | 28.4469i | −0.417379 | − | 1.00764i | −0.983104 | − | 0.183048i | \(-0.941404\pi\) |
0.565725 | − | 0.824594i | \(-0.308596\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.7465 | 0.450938 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −33.0357 | −1.16726 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 28.3528 | + | 68.4497i | 1.00055 | + | 2.41554i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.22693 | + | 2.57928i | 0.219471 | + | 0.0909077i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.29212 | − | 1.29212i | −0.0454847 | − | 0.0454847i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 26.8872 | − | 26.8872i | 0.945302 | − | 0.945302i | −0.0532776 | − | 0.998580i | \(-0.516967\pi\) |
0.998580 | + | 0.0532776i | \(0.0169668\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.13213 | − | 9.97584i | 0.145099 | − | 0.350299i | −0.834576 | − | 0.550893i | \(-0.814287\pi\) |
0.979674 | + | 0.200594i | \(0.0642872\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.08908 | + | 0.451110i | −0.0381956 | + | 0.0158211i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.96824i | 0.139002i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 41.7267i | − | 1.45983i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.35031 | + | 0.973528i | −0.0821263 | + | 0.0340178i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10.2842 | + | 24.8283i | −0.358922 | + | 0.866514i | 0.636530 | + | 0.771252i | \(0.280369\pi\) |
−0.995452 | + | 0.0952624i | \(0.969631\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −22.7571 | + | 22.7571i | −0.793263 | + | 0.793263i | −0.982023 | − | 0.188761i | \(-0.939553\pi\) |
0.188761 | + | 0.982023i | \(0.439553\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.768280 | + | 0.768280i | 0.0267481 | + | 0.0267481i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −18.0804 | − | 7.48915i | −0.628718 | − | 0.260423i | 0.0454904 | − | 0.998965i | \(-0.485515\pi\) |
−0.674208 | + | 0.738541i | \(0.735515\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.0301 | + | 43.5285i | 0.626211 | + | 1.51181i | 0.844296 | + | 0.535878i | \(0.180019\pi\) |
−0.218084 | + | 0.975930i | \(0.569981\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.157421 | 0.00546088 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.93074 | −0.170840 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −15.8775 | − | 38.3316i | −0.549462 | − | 1.32652i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.96106 | + | 1.64073i | 0.136914 | + | 0.0567118i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0.265001 | + | 0.265001i | 0.00914885 | + | 0.00914885i | 0.711666 | − | 0.702518i | \(-0.247941\pi\) |
−0.702518 | + | 0.711666i | \(0.747941\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.52971 | − | 5.52971i | 0.190680 | − | 0.190680i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.05365 | − | 2.54374i | 0.0362897 | − | 0.0876110i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −29.3226 | + | 12.1458i | −1.00873 | + | 0.417830i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 22.3540i | − | 0.768094i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.48006i | 0.0851155i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.7064 | + | 4.43475i | −0.367012 | + | 0.152021i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.71394 | − | 23.4515i | 0.332599 | − | 0.802965i | −0.665785 | − | 0.746143i | \(-0.731903\pi\) |
0.998384 | − | 0.0568218i | \(-0.0180967\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 25.1318 | − | 25.1318i | 0.859488 | − | 0.859488i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.89081 | + | 1.89081i | 0.0645887 | + | 0.0645887i | 0.738663 | − | 0.674075i | \(-0.235457\pi\) |
−0.674075 | + | 0.738663i | \(0.735457\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.9540 | − | 4.95152i | −0.407866 | − | 0.168944i | 0.169311 | − | 0.985563i | \(-0.445846\pi\) |
−0.577177 | + | 0.816619i | \(0.695846\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.116135 | − | 0.280374i | −0.00395786 | − | 0.00955512i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −4.09524 | −0.139404 | −0.0697018 | − | 0.997568i | \(-0.522205\pi\) | ||||
−0.0697018 | + | 0.997568i | \(0.522205\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.1432 | −0.378881 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.312319 | + | 0.754004i | 0.0106069 | + | 0.0256073i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 45.1000 | + | 18.6810i | 1.52991 | + | 0.633711i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.90339 | − | 5.90339i | −0.200029 | − | 0.200029i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 18.1303 | − | 18.1303i | 0.613619 | − | 0.613619i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.27957 | − | 7.91759i | 0.110870 | − | 0.267663i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 24.3419 | − | 10.0827i | 0.821967 | − | 0.340470i | 0.0682495 | − | 0.997668i | \(-0.478259\pi\) |
0.753718 | + | 0.657198i | \(0.228259\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.10792i | 0.104827i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 7.47198i | − | 0.251737i | −0.992047 | − | 0.125869i | \(-0.959828\pi\) | ||
0.992047 | − | 0.125869i | \(-0.0401718\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 50.0643 | − | 20.7373i | 1.68480 | − | 0.697866i | 0.685260 | − | 0.728298i | \(-0.259688\pi\) |
0.999537 | + | 0.0304324i | \(0.00968844\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.917362 | − | 2.21471i | 0.0308368 | − | 0.0744466i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 34.8539 | − | 34.8539i | 1.17028 | − | 1.17028i | 0.188137 | − | 0.982143i | \(-0.439755\pi\) |
0.982143 | − | 0.188137i | \(-0.0602447\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.00039 | − | 5.00039i | −0.167708 | − | 0.167708i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 47.4237 | + | 19.6435i | 1.58875 | + | 0.658084i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.55169 | − | 10.9887i | −0.152316 | − | 0.367724i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.78488 | −0.193367 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.247740 | 0.00827180 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −11.2989 | − | 27.2780i | −0.376839 | − | 0.909771i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −35.6019 | − | 14.7468i | −1.18607 | − | 0.491287i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.715742 | − | 0.715742i | −0.0238184 | − | 0.0238184i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.861678 | + | 0.861678i | −0.0286432 | + | 0.0286432i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.83871 | + | 18.9243i | −0.260280 | + | 0.628372i | −0.998956 | − | 0.0456892i | \(-0.985452\pi\) |
0.738676 | + | 0.674061i | \(0.235452\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −50.0929 | + | 20.7492i | −1.66148 | + | 0.688207i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.83115i | 0.226326i | 0.993576 | + | 0.113163i | \(0.0360982\pi\) | ||||
−0.993576 | + | 0.113163i | \(0.963902\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 57.8084i | 1.91318i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.02211 | − | 1.66601i | 0.132967 | − | 0.0550767i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.643982 | − | 1.55471i | 0.0212662 | − | 0.0513411i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.10525 | − | 2.10525i | 0.0694458 | − | 0.0694458i | −0.671531 | − | 0.740977i | \(-0.734363\pi\) |
0.740977 | + | 0.671531i | \(0.234363\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.44089 | − | 1.44089i | −0.0474788 | − | 0.0474788i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.61450 | − | 1.49718i | −0.118973 | − | 0.0492802i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.86766 | − | 6.92315i | −0.0942882 | − | 0.227632i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −33.2932 | −1.09349 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 17.0256 | 0.558591 | 0.279295 | − | 0.960205i | \(-0.409899\pi\) | ||||
0.279295 | + | 0.960205i | \(0.409899\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.76074 | + | 4.25079i | 0.0577058 | + | 0.139314i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0.429852 | + | 0.178050i | 0.0140727 | + | 0.00582911i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −52.0644 | − | 52.0644i | −1.70269 | − | 1.70269i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.75833 | − | 8.75833i | 0.286122 | − | 0.286122i | −0.549423 | − | 0.835545i | \(-0.685152\pi\) |
0.835545 | + | 0.549423i | \(0.185152\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.01757 | + | 2.45662i | −0.0332070 | + | 0.0801688i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −37.1950 | + | 15.4067i | −1.21252 | + | 0.502243i | −0.895025 | − | 0.446016i | \(-0.852842\pi\) |
−0.317497 | + | 0.948259i | \(0.602842\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 7.08760i | − | 0.230804i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 1.72795i | − | 0.0562101i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8.71240 | − | 3.60880i | 0.283115 | − | 0.117270i | −0.236607 | − | 0.971605i | \(-0.576035\pi\) |
0.519722 | + | 0.854335i | \(0.326035\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.18039 | + | 10.0923i | −0.135701 | + | 0.327611i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.392722 | − | 0.392722i | 0.0127349 | − | 0.0127349i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.07561 | − | 5.07561i | −0.164415 | − | 0.164415i | 0.620104 | − | 0.784519i | \(-0.287090\pi\) |
−0.784519 | + | 0.620104i | \(0.787090\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 28.4011 | + | 11.7641i | 0.919037 | + | 0.380678i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.13524 | + | 2.74071i | 0.0366971 | + | 0.0885945i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.24163 | 0.0723860 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.1596 | 0.327728 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.45754 | + | 8.34725i | 0.111418 | + | 0.268986i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −36.2496 | − | 15.0151i | −1.16692 | − | 0.483353i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.43070 | − | 9.43070i | −0.303271 | − | 0.303271i | 0.539021 | − | 0.842292i | \(-0.318794\pi\) |
−0.842292 | + | 0.539021i | \(0.818794\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.79045 | − | 1.79045i | 0.0575177 | − | 0.0575177i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −16.7488 | + | 40.4351i | −0.537493 | + | 1.29762i | 0.388974 | + | 0.921249i | \(0.372829\pi\) |
−0.926468 | + | 0.376375i | \(0.877171\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.06337 | − | 0.854676i | 0.0661486 | − | 0.0273997i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.160197i | 0.00513042i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 26.5281i | − | 0.848708i | −0.905496 | − | 0.424354i | \(-0.860501\pi\) | ||
0.905496 | − | 0.424354i | \(-0.139499\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 59.0010 | − | 24.4390i | 1.88568 | − | 0.781074i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11.2896 | − | 27.2555i | 0.360450 | − | 0.870202i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −17.3494 | + | 17.3494i | −0.553360 | + | 0.553360i | −0.927409 | − | 0.374049i | \(-0.877969\pi\) |
0.374049 | + | 0.927409i | \(0.377969\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.98346 | − | 1.98346i | −0.0631983 | − | 0.0631983i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.266567 | − | 0.110416i | −0.00848491 | − | 0.00351457i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.04666 | − | 21.8406i | −0.287667 | − | 0.694490i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28.9954 | 0.921069 | 0.460535 | − | 0.887642i | \(-0.347658\pi\) | ||||
0.460535 | + | 0.887642i | \(0.347658\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.40993 | 0.0447427 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.27621 | − | 3.08104i | −0.0404585 | − | 0.0976755i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6.34404 | − | 2.62779i | −0.200918 | − | 0.0832228i | 0.279956 | − | 0.960013i | \(-0.409680\pi\) |
−0.480873 | + | 0.876790i | \(0.659680\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.10081 | + | 2.10081i | 0.0664666 | + | 0.0664666i |
(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 | 896.2.u.c.113.7 | 52 | ||
4.3 | odd | 2 | 224.2.u.c.197.8 | yes | 52 | ||
32.13 | even | 8 | inner | 896.2.u.c.785.7 | 52 | ||
32.19 | odd | 8 | 224.2.u.c.141.8 | ✓ | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.2.u.c.141.8 | ✓ | 52 | 32.19 | odd | 8 | ||
224.2.u.c.197.8 | yes | 52 | 4.3 | odd | 2 | ||
896.2.u.c.113.7 | 52 | 1.1 | even | 1 | trivial | ||
896.2.u.c.785.7 | 52 | 32.13 | even | 8 | inner |