Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [975,2,Mod(307,975)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(975, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("975.307");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 975 = 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 975.k (of order \(4\), degree \(2\), 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: | \(7.78541419707\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(14\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 195) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 343.3 | ||
Character | \(\chi\) | \(=\) | 975.343 |
Dual form | 975.2.k.d.307.12 |
$q$-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 \(\left(\mathbb{Z}/975\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(326\) | \(352\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.94332i | − | 1.37413i | −0.726595 | − | 0.687066i | \(-0.758898\pi\) | ||
0.726595 | − | 0.687066i | \(-0.241102\pi\) | |||||||
\(3\) | 0.707107 | + | 0.707107i | 0.408248 | + | 0.408248i | ||||
\(4\) | −1.77647 | −0.888237 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.37413 | − | 1.37413i | 0.560987 | − | 0.560987i | ||||
\(7\) | −2.33552 | −0.882743 | −0.441372 | − | 0.897324i | \(-0.645508\pi\) | ||||
−0.441372 | + | 0.897324i | \(0.645508\pi\) | |||||||
\(8\) | − | 0.434380i | − | 0.153577i | ||||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.233447 | − | 0.233447i | −0.0703869 | − | 0.0703869i | 0.671037 | − | 0.741424i | \(-0.265849\pi\) |
−0.741424 | + | 0.671037i | \(0.765849\pi\) | |||||||
\(12\) | −1.25616 | − | 1.25616i | −0.362621 | − | 0.362621i | ||||
\(13\) | 3.58770 | + | 0.358340i | 0.995049 | + | 0.0993858i | ||||
\(14\) | 4.53865i | 1.21301i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.39709 | −1.09927 | ||||||||
\(17\) | −5.71657 | − | 5.71657i | −1.38647 | − | 1.38647i | −0.832608 | − | 0.553863i | \(-0.813153\pi\) |
−0.553863 | − | 0.832608i | \(-0.686847\pi\) | |||||||
\(18\) | 1.94332 | 0.458044 | ||||||||
\(19\) | −3.63852 | − | 3.63852i | −0.834733 | − | 0.834733i | 0.153427 | − | 0.988160i | \(-0.450969\pi\) |
−0.988160 | + | 0.153427i | \(0.950969\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.65146 | − | 1.65146i | −0.360378 | − | 0.360378i | ||||
\(22\) | −0.453661 | + | 0.453661i | −0.0967208 | + | 0.0967208i | ||||
\(23\) | 0.974048 | − | 0.974048i | 0.203103 | − | 0.203103i | −0.598225 | − | 0.801328i | \(-0.704127\pi\) |
0.801328 | + | 0.598225i | \(0.204127\pi\) | |||||||
\(24\) | 0.307153 | − | 0.307153i | 0.0626974 | − | 0.0626974i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.696369 | − | 6.97203i | 0.136569 | − | 1.36733i | ||||
\(27\) | −0.707107 | + | 0.707107i | −0.136083 | + | 0.136083i | ||||
\(28\) | 4.14899 | 0.784086 | ||||||||
\(29\) | − | 9.59085i | − | 1.78098i | −0.455007 | − | 0.890488i | \(-0.650363\pi\) | ||
0.455007 | − | 0.890488i | \(-0.349637\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.43455 | − | 3.43455i | 0.616863 | − | 0.616863i | −0.327862 | − | 0.944725i | \(-0.606328\pi\) |
0.944725 | + | 0.327862i | \(0.106328\pi\) | |||||||
\(32\) | 7.67617i | 1.35697i | ||||||||
\(33\) | − | 0.330144i | − | 0.0574706i | ||||||
\(34\) | −11.1091 | + | 11.1091i | −1.90519 | + | 1.90519i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | − | 1.77647i | − | 0.296079i | ||||||
\(37\) | 1.32880 | 0.218454 | 0.109227 | − | 0.994017i | \(-0.465163\pi\) | ||||
0.109227 | + | 0.994017i | \(0.465163\pi\) | |||||||
\(38\) | −7.07079 | + | 7.07079i | −1.14703 | + | 1.14703i | ||||
\(39\) | 2.28350 | + | 2.79027i | 0.365653 | + | 0.446801i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.14586 | + | 1.14586i | −0.178953 | + | 0.178953i | −0.790899 | − | 0.611946i | \(-0.790387\pi\) |
0.611946 | + | 0.790899i | \(0.290387\pi\) | |||||||
\(42\) | −3.20931 | + | 3.20931i | −0.495207 | + | 0.495207i | ||||
\(43\) | −3.06448 | + | 3.06448i | −0.467328 | + | 0.467328i | −0.901048 | − | 0.433720i | \(-0.857201\pi\) |
0.433720 | + | 0.901048i | \(0.357201\pi\) | |||||||
\(44\) | 0.414712 | + | 0.414712i | 0.0625202 | + | 0.0625202i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.89288 | − | 1.89288i | −0.279090 | − | 0.279090i | ||||
\(47\) | 6.39859 | 0.933330 | 0.466665 | − | 0.884434i | \(-0.345455\pi\) | ||||
0.466665 | + | 0.884434i | \(0.345455\pi\) | |||||||
\(48\) | −3.10921 | − | 3.10921i | −0.448776 | − | 0.448776i | ||||
\(49\) | −1.54535 | −0.220764 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 8.08444i | − | 1.13205i | ||||||
\(52\) | −6.37346 | − | 0.636583i | −0.883840 | − | 0.0882781i | ||||
\(53\) | −2.64422 | − | 2.64422i | −0.363211 | − | 0.363211i | 0.501783 | − | 0.864994i | \(-0.332678\pi\) |
−0.864994 | + | 0.501783i | \(0.832678\pi\) | |||||||
\(54\) | 1.37413 | + | 1.37413i | 0.186996 | + | 0.186996i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.01450i | 0.135569i | ||||||||
\(57\) | − | 5.14564i | − | 0.681557i | ||||||
\(58\) | −18.6380 | −2.44729 | ||||||||
\(59\) | 5.84154 | − | 5.84154i | 0.760503 | − | 0.760503i | −0.215910 | − | 0.976413i | \(-0.569272\pi\) |
0.976413 | + | 0.215910i | \(0.0692718\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.24856 | −0.800047 | −0.400023 | − | 0.916505i | \(-0.630998\pi\) | ||||
−0.400023 | + | 0.916505i | \(0.630998\pi\) | |||||||
\(62\) | −6.67441 | − | 6.67441i | −0.847651 | − | 0.847651i | ||||
\(63\) | − | 2.33552i | − | 0.294248i | ||||||
\(64\) | 6.12304 | 0.765380 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.641573 | −0.0789722 | ||||||||
\(67\) | 12.6687i | 1.54773i | 0.633349 | + | 0.773867i | \(0.281680\pi\) | ||||
−0.633349 | + | 0.773867i | \(0.718320\pi\) | |||||||
\(68\) | 10.1553 | + | 10.1553i | 1.23152 | + | 1.23152i | ||||
\(69\) | 1.37751 | 0.165833 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.562923 | + | 0.562923i | −0.0668066 | + | 0.0668066i | −0.739721 | − | 0.672914i | \(-0.765042\pi\) |
0.672914 | + | 0.739721i | \(0.265042\pi\) | |||||||
\(72\) | 0.434380 | 0.0511922 | ||||||||
\(73\) | 3.65149i | 0.427375i | 0.976902 | + | 0.213688i | \(0.0685474\pi\) | ||||
−0.976902 | + | 0.213688i | \(0.931453\pi\) | |||||||
\(74\) | − | 2.58228i | − | 0.300184i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.46373 | + | 6.46373i | 0.741441 | + | 0.741441i | ||||
\(77\) | 0.545220 | + | 0.545220i | 0.0621335 | + | 0.0621335i | ||||
\(78\) | 5.42238 | − | 4.43756i | 0.613963 | − | 0.502455i | ||||
\(79\) | − | 7.38140i | − | 0.830472i | −0.909714 | − | 0.415236i | \(-0.863699\pi\) | ||
0.909714 | − | 0.415236i | \(-0.136301\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 2.22677 | + | 2.22677i | 0.245905 | + | 0.245905i | ||||
\(83\) | 11.3338 | 1.24405 | 0.622025 | − | 0.782997i | \(-0.286310\pi\) | ||||
0.622025 | + | 0.782997i | \(0.286310\pi\) | |||||||
\(84\) | 2.93378 | + | 2.93378i | 0.320102 | + | 0.320102i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 5.95524 | + | 5.95524i | 0.642171 | + | 0.642171i | ||||
\(87\) | 6.78175 | − | 6.78175i | 0.727080 | − | 0.727080i | ||||
\(88\) | −0.101405 | + | 0.101405i | −0.0108098 | + | 0.0108098i | ||||
\(89\) | −7.56761 | + | 7.56761i | −0.802165 | + | 0.802165i | −0.983434 | − | 0.181269i | \(-0.941980\pi\) |
0.181269 | + | 0.983434i | \(0.441980\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.37914 | − | 0.836911i | −0.878373 | − | 0.0877321i | ||||
\(92\) | −1.73037 | + | 1.73037i | −0.180404 | + | 0.180404i | ||||
\(93\) | 4.85718 | 0.503667 | ||||||||
\(94\) | − | 12.4345i | − | 1.28252i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −5.42787 | + | 5.42787i | −0.553980 | + | 0.553980i | ||||
\(97\) | − | 9.27392i | − | 0.941624i | −0.882234 | − | 0.470812i | \(-0.843961\pi\) | ||
0.882234 | − | 0.470812i | \(-0.156039\pi\) | |||||||
\(98\) | 3.00310i | 0.303359i | ||||||||
\(99\) | 0.233447 | − | 0.233447i | 0.0234623 | − | 0.0234623i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.3141i | 1.22530i | 0.790354 | + | 0.612651i | \(0.209897\pi\) | ||||
−0.790354 | + | 0.612651i | \(0.790103\pi\) | |||||||
\(102\) | −15.7106 | −1.55558 | ||||||||
\(103\) | −6.85102 | + | 6.85102i | −0.675051 | + | 0.675051i | −0.958876 | − | 0.283825i | \(-0.908397\pi\) |
0.283825 | + | 0.958876i | \(0.408397\pi\) | |||||||
\(104\) | 0.155656 | − | 1.55843i | 0.0152633 | − | 0.152816i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.13854 | + | 5.13854i | −0.499100 | + | 0.499100i | ||||
\(107\) | 7.44452 | − | 7.44452i | 0.719689 | − | 0.719689i | −0.248853 | − | 0.968541i | \(-0.580053\pi\) |
0.968541 | + | 0.248853i | \(0.0800535\pi\) | |||||||
\(108\) | 1.25616 | − | 1.25616i | 0.120874 | − | 0.120874i | ||||
\(109\) | 7.05924 | + | 7.05924i | 0.676152 | + | 0.676152i | 0.959127 | − | 0.282975i | \(-0.0913213\pi\) |
−0.282975 | + | 0.959127i | \(0.591321\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.939604 | + | 0.939604i | 0.0891833 | + | 0.0891833i | ||||
\(112\) | 10.2695 | 0.970375 | ||||||||
\(113\) | −2.50383 | − | 2.50383i | −0.235541 | − | 0.235541i | 0.579460 | − | 0.815001i | \(-0.303264\pi\) |
−0.815001 | + | 0.579460i | \(0.803264\pi\) | |||||||
\(114\) | −9.99960 | −0.936548 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 17.0379i | 1.58193i | ||||||||
\(117\) | −0.358340 | + | 3.58770i | −0.0331286 | + | 0.331683i | ||||
\(118\) | −11.3519 | − | 11.3519i | −1.04503 | − | 1.04503i | ||||
\(119\) | 13.3511 | + | 13.3511i | 1.22390 | + | 1.22390i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 10.8910i | − | 0.990091i | ||||||
\(122\) | 12.1429i | 1.09937i | ||||||||
\(123\) | −1.62049 | −0.146115 | ||||||||
\(124\) | −6.10139 | + | 6.10139i | −0.547921 | + | 0.547921i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −4.53865 | −0.404335 | ||||||||
\(127\) | −3.70439 | − | 3.70439i | −0.328712 | − | 0.328712i | 0.523385 | − | 0.852096i | \(-0.324669\pi\) |
−0.852096 | + | 0.523385i | \(0.824669\pi\) | |||||||
\(128\) | 3.45334i | 0.305235i | ||||||||
\(129\) | −4.33382 | −0.381572 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.33540 | 0.728267 | 0.364134 | − | 0.931347i | \(-0.381365\pi\) | ||||
0.364134 | + | 0.931347i | \(0.381365\pi\) | |||||||
\(132\) | 0.586492i | 0.0510476i | ||||||||
\(133\) | 8.49783 | + | 8.49783i | 0.736855 | + | 0.736855i | ||||
\(134\) | 24.6194 | 2.12679 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.48316 | + | 2.48316i | −0.212929 | + | 0.212929i | ||||
\(137\) | 6.36241 | 0.543577 | 0.271789 | − | 0.962357i | \(-0.412385\pi\) | ||||
0.271789 | + | 0.962357i | \(0.412385\pi\) | |||||||
\(138\) | − | 2.67694i | − | 0.227876i | ||||||
\(139\) | 9.32196i | 0.790679i | 0.918535 | + | 0.395339i | \(0.129373\pi\) | ||||
−0.918535 | + | 0.395339i | \(0.870627\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.52448 | + | 4.52448i | 0.381030 | + | 0.381030i | ||||
\(142\) | 1.09394 | + | 1.09394i | 0.0918011 | + | 0.0918011i | ||||
\(143\) | −0.753884 | − | 0.921191i | −0.0630429 | − | 0.0770338i | ||||
\(144\) | − | 4.39709i | − | 0.366424i | ||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 7.09600 | 0.587270 | ||||||||
\(147\) | −1.09273 | − | 1.09273i | −0.0901266 | − | 0.0901266i | ||||
\(148\) | −2.36058 | −0.194039 | ||||||||
\(149\) | 1.23267 | + | 1.23267i | 0.100984 | + | 0.100984i | 0.755794 | − | 0.654810i | \(-0.227251\pi\) |
−0.654810 | + | 0.755794i | \(0.727251\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.97344 | + | 8.97344i | 0.730248 | + | 0.730248i | 0.970669 | − | 0.240421i | \(-0.0772854\pi\) |
−0.240421 | + | 0.970669i | \(0.577285\pi\) | |||||||
\(152\) | −1.58050 | + | 1.58050i | −0.128195 | + | 0.128195i | ||||
\(153\) | 5.71657 | − | 5.71657i | 0.462157 | − | 0.462157i | ||||
\(154\) | 1.05953 | − | 1.05953i | 0.0853796 | − | 0.0853796i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −4.05658 | − | 4.95685i | −0.324787 | − | 0.396865i | ||||
\(157\) | −9.19439 | + | 9.19439i | −0.733792 | + | 0.733792i | −0.971369 | − | 0.237576i | \(-0.923647\pi\) |
0.237576 | + | 0.971369i | \(0.423647\pi\) | |||||||
\(158\) | −14.3444 | −1.14118 | ||||||||
\(159\) | − | 3.73949i | − | 0.296560i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.27491 | + | 2.27491i | −0.179288 | + | 0.179288i | ||||
\(162\) | 1.94332i | 0.152681i | ||||||||
\(163\) | − | 12.4311i | − | 0.973682i | −0.873491 | − | 0.486841i | \(-0.838149\pi\) | ||
0.873491 | − | 0.486841i | \(-0.161851\pi\) | |||||||
\(164\) | 2.03559 | − | 2.03559i | 0.158953 | − | 0.158953i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 22.0252i | − | 1.70949i | ||||||
\(167\) | 23.9518 | 1.85345 | 0.926724 | − | 0.375744i | \(-0.122613\pi\) | ||||
0.926724 | + | 0.375744i | \(0.122613\pi\) | |||||||
\(168\) | −0.717362 | + | 0.717362i | −0.0553457 | + | 0.0553457i | ||||
\(169\) | 12.7432 | + | 2.57124i | 0.980245 | + | 0.197787i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.63852 | − | 3.63852i | 0.278244 | − | 0.278244i | ||||
\(172\) | 5.44397 | − | 5.44397i | 0.415098 | − | 0.415098i | ||||
\(173\) | 9.25151 | − | 9.25151i | 0.703380 | − | 0.703380i | −0.261755 | − | 0.965134i | \(-0.584301\pi\) |
0.965134 | + | 0.261755i | \(0.0843012\pi\) | |||||||
\(174\) | −13.1791 | − | 13.1791i | −0.999104 | − | 0.999104i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.02649 | + | 1.02649i | 0.0773743 | + | 0.0773743i | ||||
\(177\) | 8.26118 | 0.620948 | ||||||||
\(178\) | 14.7063 | + | 14.7063i | 1.10228 | + | 1.10228i | ||||
\(179\) | 5.00257 | 0.373910 | 0.186955 | − | 0.982368i | \(-0.440138\pi\) | ||||
0.186955 | + | 0.982368i | \(0.440138\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.69556i | 0.423348i | 0.977340 | + | 0.211674i | \(0.0678914\pi\) | ||||
−0.977340 | + | 0.211674i | \(0.932109\pi\) | |||||||
\(182\) | −1.62638 | + | 16.2833i | −0.120555 | + | 1.20700i | ||||
\(183\) | −4.41840 | − | 4.41840i | −0.326618 | − | 0.326618i | ||||
\(184\) | −0.423107 | − | 0.423107i | −0.0311919 | − | 0.0311919i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | − | 9.43904i | − | 0.692104i | ||||||
\(187\) | 2.66903i | 0.195179i | ||||||||
\(188\) | −11.3669 | −0.829018 | ||||||||
\(189\) | 1.65146 | − | 1.65146i | 0.120126 | − | 0.120126i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.2034 | 1.17244 | 0.586218 | − | 0.810153i | \(-0.300616\pi\) | ||||
0.586218 | + | 0.810153i | \(0.300616\pi\) | |||||||
\(192\) | 4.32964 | + | 4.32964i | 0.312465 | + | 0.312465i | ||||
\(193\) | − | 6.54564i | − | 0.471165i | −0.971854 | − | 0.235583i | \(-0.924300\pi\) | ||
0.971854 | − | 0.235583i | \(-0.0756998\pi\) | |||||||
\(194\) | −18.0221 | −1.29391 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.74527 | 0.196091 | ||||||||
\(197\) | − | 15.5862i | − | 1.11047i | −0.831694 | − | 0.555234i | \(-0.812629\pi\) | ||
0.831694 | − | 0.555234i | \(-0.187371\pi\) | |||||||
\(198\) | −0.453661 | − | 0.453661i | −0.0322403 | − | 0.0322403i | ||||
\(199\) | −19.6618 | −1.39379 | −0.696893 | − | 0.717175i | \(-0.745435\pi\) | ||||
−0.696893 | + | 0.717175i | \(0.745435\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.95815 | + | 8.95815i | −0.631859 | + | 0.631859i | ||||
\(202\) | 23.9302 | 1.68372 | ||||||||
\(203\) | 22.3996i | 1.57214i | ||||||||
\(204\) | 14.3618i | 1.00553i | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 13.3137 | + | 13.3137i | 0.927609 | + | 0.927609i | ||||
\(207\) | 0.974048 | + | 0.974048i | 0.0677010 | + | 0.0677010i | ||||
\(208\) | −15.7754 | − | 1.57565i | −1.09383 | − | 0.109252i | ||||
\(209\) | 1.69880i | 0.117508i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.07359 | 0.555809 | 0.277904 | − | 0.960609i | \(-0.410360\pi\) | ||||
0.277904 | + | 0.960609i | \(0.410360\pi\) | |||||||
\(212\) | 4.69738 | + | 4.69738i | 0.322618 | + | 0.322618i | ||||
\(213\) | −0.796093 | −0.0545474 | ||||||||
\(214\) | −14.4670 | − | 14.4670i | −0.988947 | − | 0.988947i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0.307153 | + | 0.307153i | 0.0208991 | + | 0.0208991i | ||||
\(217\) | −8.02145 | + | 8.02145i | −0.544532 | + | 0.544532i | ||||
\(218\) | 13.7183 | − | 13.7183i | 0.929122 | − | 0.929122i | ||||
\(219\) | −2.58200 | + | 2.58200i | −0.174475 | + | 0.174475i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −18.4608 | − | 22.5578i | −1.24181 | − | 1.51740i | ||||
\(222\) | 1.82595 | − | 1.82595i | 0.122550 | − | 0.122550i | ||||
\(223\) | 14.8348 | 0.993413 | 0.496706 | − | 0.867919i | \(-0.334543\pi\) | ||||
0.496706 | + | 0.867919i | \(0.334543\pi\) | |||||||
\(224\) | − | 17.9278i | − | 1.19785i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.86574 | + | 4.86574i | −0.323664 | + | 0.323664i | ||||
\(227\) | 0.417274i | 0.0276954i | 0.999904 | + | 0.0138477i | \(0.00440800\pi\) | ||||
−0.999904 | + | 0.0138477i | \(0.995592\pi\) | |||||||
\(228\) | 9.14110i | 0.605384i | ||||||||
\(229\) | 12.8346 | − | 12.8346i | 0.848135 | − | 0.848135i | −0.141765 | − | 0.989900i | \(-0.545278\pi\) |
0.989900 | + | 0.141765i | \(0.0452778\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.771057i | 0.0507318i | ||||||||
\(232\) | −4.16607 | −0.273516 | ||||||||
\(233\) | −8.13574 | + | 8.13574i | −0.532990 | + | 0.532990i | −0.921461 | − | 0.388471i | \(-0.873003\pi\) |
0.388471 | + | 0.921461i | \(0.373003\pi\) | |||||||
\(234\) | 6.97203 | + | 0.696369i | 0.455776 | + | 0.0455230i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −10.3773 | + | 10.3773i | −0.675507 | + | 0.675507i | ||||
\(237\) | 5.21944 | − | 5.21944i | 0.339039 | − | 0.339039i | ||||
\(238\) | 25.9455 | − | 25.9455i | 1.68180 | − | 1.68180i | ||||
\(239\) | −14.5707 | − | 14.5707i | −0.942501 | − | 0.942501i | 0.0559333 | − | 0.998435i | \(-0.482187\pi\) |
−0.998435 | + | 0.0559333i | \(0.982187\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.02552 | − | 9.02552i | −0.581385 | − | 0.581385i | 0.353899 | − | 0.935284i | \(-0.384856\pi\) |
−0.935284 | + | 0.353899i | \(0.884856\pi\) | |||||||
\(242\) | −21.1647 | −1.36052 | ||||||||
\(243\) | −0.707107 | − | 0.707107i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | 11.1004 | 0.710631 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 3.14912i | 0.200781i | ||||||||
\(247\) | −11.7501 | − | 14.3577i | −0.747640 | − | 0.913561i | ||||
\(248\) | −1.49190 | − | 1.49190i | −0.0947357 | − | 0.0947357i | ||||
\(249\) | 8.01423 | + | 8.01423i | 0.507881 | + | 0.507881i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 6.58691i | − | 0.415762i | −0.978154 | − | 0.207881i | \(-0.933343\pi\) | ||
0.978154 | − | 0.207881i | \(-0.0666567\pi\) | |||||||
\(252\) | 4.14899i | 0.261362i | ||||||||
\(253\) | −0.454777 | −0.0285916 | ||||||||
\(254\) | −7.19881 | + | 7.19881i | −0.451693 | + | 0.451693i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 18.9570 | 1.18481 | ||||||||
\(257\) | −12.4943 | − | 12.4943i | −0.779371 | − | 0.779371i | 0.200353 | − | 0.979724i | \(-0.435791\pi\) |
−0.979724 | + | 0.200353i | \(0.935791\pi\) | |||||||
\(258\) | 8.42199i | 0.524330i | ||||||||
\(259\) | −3.10344 | −0.192838 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.59085 | 0.593659 | ||||||||
\(262\) | − | 16.1983i | − | 1.00073i | ||||||
\(263\) | −17.8119 | − | 17.8119i | −1.09833 | − | 1.09833i | −0.994607 | − | 0.103720i | \(-0.966925\pi\) |
−0.103720 | − | 0.994607i | \(-0.533075\pi\) | |||||||
\(264\) | −0.143408 | −0.00882614 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 16.5140 | − | 16.5140i | 1.01254 | − | 1.01254i | ||||
\(267\) | −10.7022 | −0.654965 | ||||||||
\(268\) | − | 22.5057i | − | 1.37475i | ||||||
\(269\) | − | 24.0742i | − | 1.46783i | −0.679241 | − | 0.733916i | \(-0.737691\pi\) | ||
0.679241 | − | 0.733916i | \(-0.262309\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.18975 | − | 4.18975i | −0.254509 | − | 0.254509i | 0.568307 | − | 0.822816i | \(-0.307599\pi\) |
−0.822816 | + | 0.568307i | \(0.807599\pi\) | |||||||
\(272\) | 25.1362 | + | 25.1362i | 1.52411 | + | 1.52411i | ||||
\(273\) | −5.33316 | − | 6.51673i | −0.322778 | − | 0.394411i | ||||
\(274\) | − | 12.3642i | − | 0.746947i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2.44711 | −0.147299 | ||||||||
\(277\) | −10.8816 | − | 10.8816i | −0.653810 | − | 0.653810i | 0.300098 | − | 0.953908i | \(-0.402980\pi\) |
−0.953908 | + | 0.300098i | \(0.902980\pi\) | |||||||
\(278\) | 18.1155 | 1.08650 | ||||||||
\(279\) | 3.43455 | + | 3.43455i | 0.205621 | + | 0.205621i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.342678 | − | 0.342678i | −0.0204424 | − | 0.0204424i | 0.696812 | − | 0.717254i | \(-0.254601\pi\) |
−0.717254 | + | 0.696812i | \(0.754601\pi\) | |||||||
\(282\) | 8.79250 | − | 8.79250i | 0.523586 | − | 0.523586i | ||||
\(283\) | 18.2779 | − | 18.2779i | 1.08651 | − | 1.08651i | 0.0906253 | − | 0.995885i | \(-0.471113\pi\) |
0.995885 | − | 0.0906253i | \(-0.0288866\pi\) | |||||||
\(284\) | 1.00002 | − | 1.00002i | 0.0593402 | − | 0.0593402i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.79016 | + | 1.46503i | −0.105855 | + | 0.0866293i | ||||
\(287\) | 2.67618 | − | 2.67618i | 0.157970 | − | 0.157970i | ||||
\(288\) | −7.67617 | −0.452322 | ||||||||
\(289\) | 48.3582i | 2.84460i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.55765 | − | 6.55765i | 0.384416 | − | 0.384416i | ||||
\(292\) | − | 6.48679i | − | 0.379610i | ||||||
\(293\) | − | 13.8013i | − | 0.806282i | −0.915138 | − | 0.403141i | \(-0.867918\pi\) | ||
0.915138 | − | 0.403141i | \(-0.132082\pi\) | |||||||
\(294\) | −2.12351 | + | 2.12351i | −0.123846 | + | 0.123846i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 0.577205i | − | 0.0335493i | ||||||
\(297\) | 0.330144 | 0.0191569 | ||||||||
\(298\) | 2.39547 | − | 2.39547i | 0.138766 | − | 0.138766i | ||||
\(299\) | 3.84363 | − | 3.14555i | 0.222283 | − | 0.181912i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.15714 | − | 7.15714i | 0.412531 | − | 0.412531i | ||||
\(302\) | 17.4382 | − | 17.4382i | 1.00346 | − | 1.00346i | ||||
\(303\) | −8.70740 | + | 8.70740i | −0.500227 | + | 0.500227i | ||||
\(304\) | 15.9989 | + | 15.9989i | 0.917598 | + | 0.917598i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −11.1091 | − | 11.1091i | −0.635064 | − | 0.635064i | ||||
\(307\) | 23.3385 | 1.33200 | 0.666000 | − | 0.745952i | \(-0.268005\pi\) | ||||
0.666000 | + | 0.745952i | \(0.268005\pi\) | |||||||
\(308\) | −0.968569 | − | 0.968569i | −0.0551893 | − | 0.0551893i | ||||
\(309\) | −9.68881 | −0.551177 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 27.6379i | 1.56720i | 0.621265 | + | 0.783601i | \(0.286619\pi\) | ||||
−0.621265 | + | 0.783601i | \(0.713381\pi\) | |||||||
\(312\) | 1.21204 | − | 0.991908i | 0.0686182 | − | 0.0561557i | ||||
\(313\) | −2.26616 | − | 2.26616i | −0.128091 | − | 0.128091i | 0.640155 | − | 0.768246i | \(-0.278870\pi\) |
−0.768246 | + | 0.640155i | \(0.778870\pi\) | |||||||
\(314\) | 17.8676 | + | 17.8676i | 1.00833 | + | 1.00833i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 13.1129i | 0.737656i | ||||||||
\(317\) | 33.4912i | 1.88105i | 0.339722 | + | 0.940526i | \(0.389667\pi\) | ||||
−0.339722 | + | 0.940526i | \(0.610333\pi\) | |||||||
\(318\) | −7.26700 | −0.407513 | ||||||||
\(319\) | −2.23895 | + | 2.23895i | −0.125357 | + | 0.125357i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.5281 | 0.587623 | ||||||||
\(322\) | 4.42086 | + | 4.42086i | 0.246365 | + | 0.246365i | ||||
\(323\) | 41.5996i | 2.31467i | ||||||||
\(324\) | 1.77647 | 0.0986930 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −24.1576 | −1.33797 | ||||||||
\(327\) | 9.98327i | 0.552076i | ||||||||
\(328\) | 0.497738 | + | 0.497738i | 0.0274830 | + | 0.0274830i | ||||
\(329\) | −14.9440 | −0.823891 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.7870 | + | 12.7870i | −0.702838 | + | 0.702838i | −0.965019 | − | 0.262181i | \(-0.915558\pi\) |
0.262181 | + | 0.965019i | \(0.415558\pi\) | |||||||
\(332\) | −20.1343 | −1.10501 | ||||||||
\(333\) | 1.32880i | 0.0728178i | ||||||||
\(334\) | − | 46.5459i | − | 2.54688i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 7.26162 | + | 7.26162i | 0.396154 | + | 0.396154i | ||||
\(337\) | 0.301897 | + | 0.301897i | 0.0164454 | + | 0.0164454i | 0.715282 | − | 0.698836i | \(-0.246298\pi\) |
−0.698836 | + | 0.715282i | \(0.746298\pi\) | |||||||
\(338\) | 4.99672 | − | 24.7640i | 0.271786 | − | 1.34699i | ||||
\(339\) | − | 3.54096i | − | 0.192318i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.60357 | −0.0868381 | ||||||||
\(342\) | −7.07079 | − | 7.07079i | −0.382344 | − | 0.382344i | ||||
\(343\) | 19.9578 | 1.07762 | ||||||||
\(344\) | 1.33115 | + | 1.33115i | 0.0717707 | + | 0.0717707i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −17.9786 | − | 17.9786i | −0.966536 | − | 0.966536i | ||||
\(347\) | −0.152124 | + | 0.152124i | −0.00816647 | + | 0.00816647i | −0.711178 | − | 0.703012i | \(-0.751838\pi\) |
0.703012 | + | 0.711178i | \(0.251838\pi\) | |||||||
\(348\) | −12.0476 | + | 12.0476i | −0.645820 | + | 0.645820i | ||||
\(349\) | 3.10267 | − | 3.10267i | 0.166082 | − | 0.166082i | −0.619173 | − | 0.785255i | \(-0.712532\pi\) |
0.785255 | + | 0.619173i | \(0.212532\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.79027 | + | 2.28350i | −0.148934 | + | 0.121884i | ||||
\(352\) | 1.79198 | − | 1.79198i | 0.0955127 | − | 0.0955127i | ||||
\(353\) | 16.5017 | 0.878297 | 0.439149 | − | 0.898414i | \(-0.355280\pi\) | ||||
0.439149 | + | 0.898414i | \(0.355280\pi\) | |||||||
\(354\) | − | 16.0541i | − | 0.853265i | ||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 13.4437 | − | 13.4437i | 0.712513 | − | 0.712513i | ||||
\(357\) | 18.8814i | 0.999308i | ||||||||
\(358\) | − | 9.72158i | − | 0.513801i | ||||||
\(359\) | −19.9727 | + | 19.9727i | −1.05412 | + | 1.05412i | −0.0556708 | + | 0.998449i | \(0.517730\pi\) |
−0.998449 | + | 0.0556708i | \(0.982270\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.47761i | 0.393558i | ||||||||
\(362\) | 11.0683 | 0.581735 | ||||||||
\(363\) | 7.70110 | − | 7.70110i | 0.404203 | − | 0.404203i | ||||
\(364\) | 14.8853 | + | 1.48675i | 0.780204 | + | 0.0779269i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −8.58635 | + | 8.58635i | −0.448816 | + | 0.448816i | ||||
\(367\) | −26.1777 | + | 26.1777i | −1.36646 | + | 1.36646i | −0.501040 | + | 0.865424i | \(0.667049\pi\) |
−0.865424 | + | 0.501040i | \(0.832951\pi\) | |||||||
\(368\) | −4.28297 | + | 4.28297i | −0.223265 | + | 0.223265i | ||||
\(369\) | −1.14586 | − | 1.14586i | −0.0596510 | − | 0.0596510i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.17562 | + | 6.17562i | 0.320622 | + | 0.320622i | ||||
\(372\) | −8.62866 | −0.447375 | ||||||||
\(373\) | 22.7942 | + | 22.7942i | 1.18024 | + | 1.18024i | 0.979682 | + | 0.200556i | \(0.0642748\pi\) |
0.200556 | + | 0.979682i | \(0.435725\pi\) | |||||||
\(374\) | 5.18676 | 0.268201 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 2.77942i | − | 0.143338i | ||||||
\(377\) | 3.43679 | − | 34.4091i | 0.177004 | − | 1.77216i | ||||
\(378\) | −3.20931 | − | 3.20931i | −0.165069 | − | 0.165069i | ||||
\(379\) | 23.1221 | + | 23.1221i | 1.18770 | + | 1.18770i | 0.977700 | + | 0.210004i | \(0.0673477\pi\) |
0.210004 | + | 0.977700i | \(0.432652\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 5.23880i | − | 0.268392i | ||||||
\(382\) | − | 31.4883i | − | 1.61108i | ||||||
\(383\) | −16.7647 | −0.856636 | −0.428318 | − | 0.903628i | \(-0.640894\pi\) | ||||
−0.428318 | + | 0.903628i | \(0.640894\pi\) | |||||||
\(384\) | −2.44188 | + | 2.44188i | −0.124612 | + | 0.124612i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −12.7202 | −0.647443 | ||||||||
\(387\) | −3.06448 | − | 3.06448i | −0.155776 | − | 0.155776i | ||||
\(388\) | 16.4749i | 0.836385i | ||||||||
\(389\) | 0.398160 | 0.0201875 | 0.0100938 | − | 0.999949i | \(-0.496787\pi\) | ||||
0.0100938 | + | 0.999949i | \(0.496787\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.1364 | −0.563193 | ||||||||
\(392\) | 0.671269i | 0.0339042i | ||||||||
\(393\) | 5.89402 | + | 5.89402i | 0.297314 | + | 0.297314i | ||||
\(394\) | −30.2888 | −1.52593 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.414712 | + | 0.414712i | −0.0208401 | + | 0.0208401i | ||||
\(397\) | −6.56895 | −0.329686 | −0.164843 | − | 0.986320i | \(-0.552712\pi\) | ||||
−0.164843 | + | 0.986320i | \(0.552712\pi\) | |||||||
\(398\) | 38.2090i | 1.91525i | ||||||||
\(399\) | 12.0177i | 0.601640i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.58776 | − | 9.58776i | −0.478790 | − | 0.478790i | 0.425954 | − | 0.904745i | \(-0.359938\pi\) |
−0.904745 | + | 0.425954i | \(0.859938\pi\) | |||||||
\(402\) | 17.4085 | + | 17.4085i | 0.868258 | + | 0.868258i | ||||
\(403\) | 13.5529 | − | 11.0914i | 0.675116 | − | 0.552502i | ||||
\(404\) | − | 21.8757i | − | 1.08836i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 43.5295 | 2.16033 | ||||||||
\(407\) | −0.310204 | − | 0.310204i | −0.0153763 | − | 0.0153763i | ||||
\(408\) | −3.51172 | −0.173856 | ||||||||
\(409\) | 0.394438 | + | 0.394438i | 0.0195037 | + | 0.0195037i | 0.716791 | − | 0.697288i | \(-0.245610\pi\) |
−0.697288 | + | 0.716791i | \(0.745610\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.49890 | + | 4.49890i | 0.221915 | + | 0.221915i | ||||
\(412\) | 12.1707 | − | 12.1707i | 0.599606 | − | 0.599606i | ||||
\(413\) | −13.6430 | + | 13.6430i | −0.671329 | + | 0.671329i | ||||
\(414\) | 1.89288 | − | 1.89288i | 0.0930301 | − | 0.0930301i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.75068 | + | 27.5398i | −0.134863 | + | 1.35025i | ||||
\(417\) | −6.59162 | + | 6.59162i | −0.322793 | + | 0.322793i | ||||
\(418\) | 3.30130 | 0.161472 | ||||||||
\(419\) | − | 19.5115i | − | 0.953198i | −0.879121 | − | 0.476599i | \(-0.841869\pi\) | ||
0.879121 | − | 0.476599i | \(-0.158131\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.5178 | − | 17.5178i | 0.853764 | − | 0.853764i | −0.136830 | − | 0.990594i | \(-0.543692\pi\) |
0.990594 | + | 0.136830i | \(0.0436916\pi\) | |||||||
\(422\) | − | 15.6895i | − | 0.763754i | ||||||
\(423\) | 6.39859i | 0.311110i | ||||||||
\(424\) | −1.14859 | + | 1.14859i | −0.0557807 | + | 0.0557807i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.54706i | 0.0749553i | ||||||||
\(427\) | 14.5936 | 0.706236 | ||||||||
\(428\) | −13.2250 | + | 13.2250i | −0.639254 | + | 0.639254i | ||||
\(429\) | 0.118304 | − | 1.18446i | 0.00571176 | − | 0.0571861i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.07458 | − | 1.07458i | 0.0517608 | − | 0.0517608i | −0.680753 | − | 0.732513i | \(-0.738347\pi\) |
0.732513 | + | 0.680753i | \(0.238347\pi\) | |||||||
\(432\) | 3.10921 | − | 3.10921i | 0.149592 | − | 0.149592i | ||||
\(433\) | −1.79696 | + | 1.79696i | −0.0863564 | + | 0.0863564i | −0.748965 | − | 0.662609i | \(-0.769449\pi\) |
0.662609 | + | 0.748965i | \(0.269449\pi\) | |||||||
\(434\) | 15.5882 | + | 15.5882i | 0.748258 | + | 0.748258i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −12.5406 | − | 12.5406i | −0.600584 | − | 0.600584i | ||||
\(437\) | −7.08818 | −0.339074 | ||||||||
\(438\) | 5.01763 | + | 5.01763i | 0.239752 | + | 0.239752i | ||||
\(439\) | 22.7567 | 1.08612 | 0.543058 | − | 0.839695i | \(-0.317266\pi\) | ||||
0.543058 | + | 0.839695i | \(0.317266\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 1.54535i | − | 0.0735881i | ||||||
\(442\) | −43.8369 | + | 35.8752i | −2.08511 | + | 1.70641i | ||||
\(443\) | −24.0285 | − | 24.0285i | −1.14163 | − | 1.14163i | −0.988152 | − | 0.153476i | \(-0.950953\pi\) |
−0.153476 | − | 0.988152i | \(-0.549047\pi\) | |||||||
\(444\) | −1.66918 | − | 1.66918i | −0.0792159 | − | 0.0792159i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 28.8287i | − | 1.36508i | ||||||
\(447\) | 1.74326i | 0.0824533i | ||||||||
\(448\) | −14.3005 | −0.675634 | ||||||||
\(449\) | −9.30869 | + | 9.30869i | −0.439304 | + | 0.439304i | −0.891778 | − | 0.452473i | \(-0.850542\pi\) |
0.452473 | + | 0.891778i | \(0.350542\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.534994 | 0.0251919 | ||||||||
\(452\) | 4.44800 | + | 4.44800i | 0.209216 | + | 0.209216i | ||||
\(453\) | 12.6904i | 0.596245i | ||||||||
\(454\) | 0.810894 | 0.0380571 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.23516 | −0.104671 | ||||||||
\(457\) | 15.2997i | 0.715689i | 0.933781 | + | 0.357845i | \(0.116488\pi\) | ||||
−0.933781 | + | 0.357845i | \(0.883512\pi\) | |||||||
\(458\) | −24.9417 | − | 24.9417i | −1.16545 | − | 1.16545i | ||||
\(459\) | 8.08444 | 0.377350 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.62065 | + | 3.62065i | −0.168631 | + | 0.168631i | −0.786377 | − | 0.617747i | \(-0.788046\pi\) |
0.617747 | + | 0.786377i | \(0.288046\pi\) | |||||||
\(462\) | 1.49841 | 0.0697122 | ||||||||
\(463\) | − | 9.60651i | − | 0.446452i | −0.974767 | − | 0.223226i | \(-0.928341\pi\) | ||
0.974767 | − | 0.223226i | \(-0.0716588\pi\) | |||||||
\(464\) | 42.1718i | 1.95778i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 15.8103 | + | 15.8103i | 0.732399 | + | 0.732399i | ||||
\(467\) | −0.654055 | − | 0.654055i | −0.0302661 | − | 0.0302661i | 0.691812 | − | 0.722078i | \(-0.256813\pi\) |
−0.722078 | + | 0.691812i | \(0.756813\pi\) | |||||||
\(468\) | 0.636583 | − | 6.37346i | 0.0294260 | − | 0.294613i | ||||
\(469\) | − | 29.5881i | − | 1.36625i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −13.0028 | −0.599139 | ||||||||
\(472\) | −2.53745 | − | 2.53745i | −0.116796 | − | 0.116796i | ||||
\(473\) | 1.43078 | 0.0657876 | ||||||||
\(474\) | −10.1430 | − | 10.1430i | −0.465884 | − | 0.465884i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −23.7180 | − | 23.7180i | −1.08711 | − | 1.08711i | ||||
\(477\) | 2.64422 | − | 2.64422i | 0.121070 | − | 0.121070i | ||||
\(478\) | −28.3155 | + | 28.3155i | −1.29512 | + | 1.29512i | ||||
\(479\) | 5.52526 | − | 5.52526i | 0.252455 | − | 0.252455i | −0.569521 | − | 0.821977i | \(-0.692871\pi\) |
0.821977 | + | 0.569521i | \(0.192871\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.76734 | + | 0.476163i | 0.217372 | + | 0.0217112i | ||||
\(482\) | −17.5394 | + | 17.5394i | −0.798899 | + | 0.798899i | ||||
\(483\) | −3.21721 | −0.146388 | ||||||||
\(484\) | 19.3476i | 0.879436i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.37413 | + | 1.37413i | −0.0623319 | + | 0.0623319i | ||||
\(487\) | 22.6360i | 1.02574i | 0.858468 | + | 0.512868i | \(0.171417\pi\) | ||||
−0.858468 | + | 0.512868i | \(0.828583\pi\) | |||||||
\(488\) | 2.71425i | 0.122868i | ||||||||
\(489\) | 8.79014 | − | 8.79014i | 0.397504 | − | 0.397504i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 4.26897i | − | 0.192656i | −0.995350 | − | 0.0963280i | \(-0.969290\pi\) | ||
0.995350 | − | 0.0963280i | \(-0.0307098\pi\) | |||||||
\(492\) | 2.87876 | 0.129784 | ||||||||
\(493\) | −54.8267 | + | 54.8267i | −2.46927 | + | 2.46927i | ||||
\(494\) | −27.9016 | + | 22.8341i | −1.25535 | + | 1.02736i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −15.1020 | + | 15.1020i | −0.678100 | + | 0.678100i | ||||
\(497\) | 1.31472 | − | 1.31472i | 0.0589731 | − | 0.0589731i | ||||
\(498\) | 15.5742 | − | 15.5742i | 0.697896 | − | 0.697896i | ||||
\(499\) | −0.792199 | − | 0.792199i | −0.0354637 | − | 0.0354637i | 0.689153 | − | 0.724616i | \(-0.257983\pi\) |
−0.724616 | + | 0.689153i | \(0.757983\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 16.9365 | + | 16.9365i | 0.756667 | + | 0.756667i | ||||
\(502\) | −12.8004 | −0.571312 | ||||||||
\(503\) | 3.33985 | + | 3.33985i | 0.148916 | + | 0.148916i | 0.777634 | − | 0.628717i | \(-0.216420\pi\) |
−0.628717 | + | 0.777634i | \(0.716420\pi\) | |||||||
\(504\) | −1.01450 | −0.0451896 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.883775i | 0.0392886i | ||||||||
\(507\) | 7.19265 | + | 10.8289i | 0.319437 | + | 0.480930i | ||||
\(508\) | 6.58076 | + | 6.58076i | 0.291974 | + | 0.291974i | ||||
\(509\) | −7.90970 | − | 7.90970i | −0.350591 | − | 0.350591i | 0.509738 | − | 0.860330i | \(-0.329742\pi\) |
−0.860330 | + | 0.509738i | \(0.829742\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 8.52813i | − | 0.377262i | ||||||
\(512\) | − | 29.9328i | − | 1.32285i | ||||||
\(513\) | 5.14564 | 0.227186 | ||||||||
\(514\) | −24.2803 | + | 24.2803i | −1.07096 | + | 1.07096i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 7.69893 | 0.338926 | ||||||||
\(517\) | −1.49373 | − | 1.49373i | −0.0656942 | − | 0.0656942i | ||||
\(518\) | 6.03096i | 0.264985i | ||||||||
\(519\) | 13.0836 | 0.574307 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 30.1540 | 1.32107 | 0.660535 | − | 0.750796i | \(-0.270330\pi\) | ||||
0.660535 | + | 0.750796i | \(0.270330\pi\) | |||||||
\(522\) | − | 18.6380i | − | 0.815765i | ||||||
\(523\) | −1.32078 | − | 1.32078i | −0.0577535 | − | 0.0577535i | 0.677640 | − | 0.735394i | \(-0.263003\pi\) |
−0.735394 | + | 0.677640i | \(0.763003\pi\) | |||||||
\(524\) | −14.8076 | −0.646874 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −34.6141 | + | 34.6141i | −1.50925 | + | 1.50925i | ||||
\(527\) | −39.2676 | −1.71053 | ||||||||
\(528\) | 1.45167i | 0.0631758i | ||||||||
\(529\) | 21.1025i | 0.917498i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.84154 | + | 5.84154i | 0.253501 | + | 0.253501i | ||||
\(532\) | −15.0962 | − | 15.0962i | −0.654502 | − | 0.654502i | ||||
\(533\) | −4.52161 | + | 3.70039i | −0.195853 | + | 0.160282i | ||||
\(534\) | 20.7978i | 0.900008i | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 5.50305 | 0.237696 | ||||||||
\(537\) | 3.53735 | + | 3.53735i | 0.152648 | + | 0.152648i | ||||
\(538\) | −46.7838 | −2.01699 | ||||||||
\(539\) | 0.360757 | + | 0.360757i | 0.0155389 | + | 0.0155389i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.4734 | − | 11.4734i | −0.493281 | − | 0.493281i | 0.416058 | − | 0.909338i | \(-0.363411\pi\) |
−0.909338 | + | 0.416058i | \(0.863411\pi\) | |||||||
\(542\) | −8.14201 | + | 8.14201i | −0.349729 | + | 0.349729i | ||||
\(543\) | −4.02737 | + | 4.02737i | −0.172831 | + | 0.172831i | ||||
\(544\) | 43.8813 | − | 43.8813i | 1.88140 | − | 1.88140i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −12.6641 | + | 10.3640i | −0.541972 | + | 0.443539i | ||||
\(547\) | 13.9025 | − | 13.9025i | 0.594427 | − | 0.594427i | −0.344397 | − | 0.938824i | \(-0.611917\pi\) |
0.938824 | + | 0.344397i | \(0.111917\pi\) | |||||||
\(548\) | −11.3027 | −0.482826 | ||||||||
\(549\) | − | 6.24856i | − | 0.266682i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −34.8965 | + | 34.8965i | −1.48664 | + | 1.48664i | ||||
\(552\) | − | 0.598364i | − | 0.0254681i | ||||||
\(553\) | 17.2394i | 0.733094i | ||||||||
\(554\) | −21.1463 | + | 21.1463i | −0.898421 | + | 0.898421i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 16.5602i | − | 0.702310i | ||||||
\(557\) | −43.3035 | −1.83483 | −0.917414 | − | 0.397934i | \(-0.869727\pi\) | ||||
−0.917414 | + | 0.397934i | \(0.869727\pi\) | |||||||
\(558\) | 6.67441 | − | 6.67441i | 0.282550 | − | 0.282550i | ||||
\(559\) | −12.0925 | + | 9.89630i | −0.511460 | + | 0.418569i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.88729 | + | 1.88729i | −0.0796814 | + | 0.0796814i | ||||
\(562\) | −0.665931 | + | 0.665931i | −0.0280906 | + | 0.0280906i | ||||
\(563\) | 14.1035 | − | 14.1035i | 0.594390 | − | 0.594390i | −0.344424 | − | 0.938814i | \(-0.611926\pi\) |
0.938814 | + | 0.344424i | \(0.111926\pi\) | |||||||
\(564\) | −8.03763 | − | 8.03763i | −0.338445 | − | 0.338445i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −35.5198 | − | 35.5198i | −1.49301 | − | 1.49301i | ||||
\(567\) | 2.33552 | 0.0980826 | ||||||||
\(568\) | 0.244522 | + | 0.244522i | 0.0102599 | + | 0.0102599i | ||||
\(569\) | 6.15514 | 0.258037 | 0.129019 | − | 0.991642i | \(-0.458817\pi\) | ||||
0.129019 | + | 0.991642i | \(0.458817\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 29.0825i | 1.21706i | 0.793530 | + | 0.608532i | \(0.208241\pi\) | ||||
−0.793530 | + | 0.608532i | \(0.791759\pi\) | |||||||
\(572\) | 1.33926 | + | 1.63647i | 0.0559971 | + | 0.0684243i | ||||
\(573\) | 11.4575 | + | 11.4575i | 0.478645 | + | 0.478645i | ||||
\(574\) | −5.20065 | − | 5.20065i | −0.217071 | − | 0.217071i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 6.12304i | 0.255127i | ||||||||
\(577\) | 1.10695i | 0.0460829i | 0.999735 | + | 0.0230415i | \(0.00733498\pi\) | ||||
−0.999735 | + | 0.0230415i | \(0.992665\pi\) | |||||||
\(578\) | 93.9753 | 3.90886 | ||||||||
\(579\) | 4.62846 | − | 4.62846i | 0.192352 | − | 0.192352i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −26.4704 | −1.09818 | ||||||||
\(582\) | −12.7436 | − | 12.7436i | −0.528238 | − | 0.528238i | ||||
\(583\) | 1.23457i | 0.0511306i | ||||||||
\(584\) | 1.58614 | 0.0656348 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −26.8203 | −1.10794 | ||||||||
\(587\) | 7.65633i | 0.316010i | 0.987438 | + | 0.158005i | \(0.0505063\pi\) | ||||
−0.987438 | + | 0.158005i | \(0.949494\pi\) | |||||||
\(588\) | 1.94120 | + | 1.94120i | 0.0800538 | + | 0.0800538i | ||||
\(589\) | −24.9933 | −1.02983 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11.0211 | − | 11.0211i | 0.453347 | − | 0.453347i | ||||
\(592\) | −5.84285 | −0.240140 | ||||||||
\(593\) | − | 46.8058i | − | 1.92209i | −0.276400 | − | 0.961043i | \(-0.589141\pi\) | ||
0.276400 | − | 0.961043i | \(-0.410859\pi\) | |||||||
\(594\) | − | 0.641573i | − | 0.0263241i | ||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.18981 | − | 2.18981i | −0.0896979 | − | 0.0896979i | ||||
\(597\) | −13.9030 | − | 13.9030i | −0.569011 | − | 0.569011i | ||||
\(598\) | −6.11280 | − | 7.46939i | −0.249971 | − | 0.305446i | ||||
\(599\) | − | 20.0674i | − | 0.819933i | −0.912101 | − | 0.409967i | \(-0.865540\pi\) | ||
0.912101 | − | 0.409967i | \(-0.134460\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.8311 | 0.972092 | 0.486046 | − | 0.873933i | \(-0.338439\pi\) | ||||
0.486046 | + | 0.873933i | \(0.338439\pi\) | |||||||
\(602\) | −13.9086 | − | 13.9086i | −0.566872 | − | 0.566872i | ||||
\(603\) | −12.6687 | −0.515911 | ||||||||
\(604\) | −15.9411 | − | 15.9411i | −0.648633 | − | 0.648633i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 16.9212 | + | 16.9212i | 0.687378 | + | 0.687378i | ||||
\(607\) | 20.3443 | − | 20.3443i | 0.825748 | − | 0.825748i | −0.161177 | − | 0.986925i | \(-0.551529\pi\) |
0.986925 | + | 0.161177i | \(0.0515290\pi\) | |||||||
\(608\) | 27.9299 | − | 27.9299i | 1.13271 | − | 1.13271i | ||||
\(609\) | −15.8389 | + | 15.8389i | −0.641825 | + | 0.641825i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 22.9562 | + | 2.29287i | 0.928709 | + | 0.0927597i | ||||
\(612\) | −10.1553 | + | 10.1553i | −0.410505 | + | 0.410505i | ||||
\(613\) | −7.88256 | −0.318374 | −0.159187 | − | 0.987248i | \(-0.550887\pi\) | ||||
−0.159187 | + | 0.987248i | \(0.550887\pi\) | |||||||
\(614\) | − | 45.3541i | − | 1.83034i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.236833 | − | 0.236833i | 0.00954226 | − | 0.00954226i | ||||
\(617\) | 6.36174i | 0.256114i | 0.991767 | + | 0.128057i | \(0.0408740\pi\) | ||||
−0.991767 | + | 0.128057i | \(0.959126\pi\) | |||||||
\(618\) | 18.8284i | 0.757390i | ||||||||
\(619\) | −8.80252 | + | 8.80252i | −0.353803 | + | 0.353803i | −0.861523 | − | 0.507719i | \(-0.830489\pi\) |
0.507719 | + | 0.861523i | \(0.330489\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.37751i | 0.0552776i | ||||||||
\(622\) | 53.7091 | 2.15354 | ||||||||
\(623\) | 17.6743 | − | 17.6743i | 0.708106 | − | 0.708106i | ||||
\(624\) | −10.0408 | − | 12.2691i | −0.401952 | − | 0.491156i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −4.40387 | + | 4.40387i | −0.176014 | + | 0.176014i | ||||
\(627\) | −1.20123 | + | 1.20123i | −0.0479726 | + | 0.0479726i | ||||
\(628\) | 16.3336 | − | 16.3336i | 0.651782 | − | 0.651782i | ||||
\(629\) | −7.59618 | − | 7.59618i | −0.302879 | − | 0.302879i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.64324 | − | 1.64324i | −0.0654164 | − | 0.0654164i | 0.673642 | − | 0.739058i | \(-0.264729\pi\) |
−0.739058 | + | 0.673642i | \(0.764729\pi\) | |||||||
\(632\) | −3.20633 | −0.127541 | ||||||||
\(633\) | 5.70889 | + | 5.70889i | 0.226908 | + | 0.226908i | ||||
\(634\) | 65.0839 | 2.58481 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 6.64310i | 0.263416i | ||||||||
\(637\) | −5.54425 | − | 0.553761i | −0.219671 | − | 0.0219408i | ||||
\(638\) | 4.35099 | + | 4.35099i | 0.172257 | + | 0.172257i | ||||
\(639\) | −0.562923 | − | 0.562923i | −0.0222689 | − | 0.0222689i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 29.5982i | − | 1.16906i | −0.811373 | − | 0.584529i | \(-0.801279\pi\) | ||
0.811373 | − | 0.584529i | \(-0.198721\pi\) | |||||||
\(642\) | − | 20.4595i | − | 0.807472i | ||||||
\(643\) | 30.1991 | 1.19094 | 0.595468 | − | 0.803379i | \(-0.296967\pi\) | ||||
0.595468 | + | 0.803379i | \(0.296967\pi\) | |||||||
\(644\) | 4.04132 | − | 4.04132i | 0.159250 | − | 0.159250i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 80.8412 | 3.18066 | ||||||||
\(647\) | 19.9747 | + | 19.9747i | 0.785285 | + | 0.785285i | 0.980717 | − | 0.195432i | \(-0.0626110\pi\) |
−0.195432 | + | 0.980717i | \(0.562611\pi\) | |||||||
\(648\) | 0.434380i | 0.0170641i | ||||||||
\(649\) | −2.72738 | −0.107059 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −11.3440 | −0.444608 | ||||||||
\(652\) | 22.0836i | 0.864861i | ||||||||
\(653\) | 15.7632 | + | 15.7632i | 0.616863 | + | 0.616863i | 0.944726 | − | 0.327862i | \(-0.106328\pi\) |
−0.327862 | + | 0.944726i | \(0.606328\pi\) | |||||||
\(654\) | 19.4006 | 0.758625 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 5.03844 | − | 5.03844i | 0.196718 | − | 0.196718i | ||||
\(657\) | −3.65149 | −0.142458 | ||||||||
\(658\) | 29.0409i | 1.13213i | ||||||||
\(659\) | 18.4911i | 0.720311i | 0.932892 | + | 0.360156i | \(0.117276\pi\) | ||||
−0.932892 | + | 0.360156i | \(0.882724\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24.3251 | − | 24.3251i | −0.946138 | − | 0.946138i | 0.0524836 | − | 0.998622i | \(-0.483286\pi\) |
−0.998622 | + | 0.0524836i | \(0.983286\pi\) | |||||||
\(662\) | 24.8492 | + | 24.8492i | 0.965792 | + | 0.965792i | ||||
\(663\) | 2.89698 | − | 29.0046i | 0.112510 | − | 1.12644i | ||||
\(664\) | − | 4.92320i | − | 0.191057i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.58228 | 0.100061 | ||||||||
\(667\) | −9.34195 | − | 9.34195i | −0.361722 | − | 0.361722i | ||||
\(668\) | −42.5498 | −1.64630 | ||||||||
\(669\) | 10.4898 | + | 10.4898i | 0.405559 | + | 0.405559i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.45871 | + | 1.45871i | 0.0563128 | + | 0.0563128i | ||||
\(672\) | 12.6769 | − | 12.6769i | 0.489022 | − | 0.489022i | ||||
\(673\) | −12.4572 | + | 12.4572i | −0.480190 | + | 0.480190i | −0.905192 | − | 0.425002i | \(-0.860273\pi\) |
0.425002 | + | 0.905192i | \(0.360273\pi\) | |||||||
\(674\) | 0.586681 | − | 0.586681i | 0.0225981 | − | 0.0225981i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −22.6379 | − | 4.56774i | −0.870690 | − | 0.175682i | ||||
\(677\) | −11.5255 | + | 11.5255i | −0.442960 | + | 0.442960i | −0.893006 | − | 0.450045i | \(-0.851408\pi\) |
0.450045 | + | 0.893006i | \(0.351408\pi\) | |||||||
\(678\) | −6.88120 | −0.264271 | ||||||||
\(679\) | 21.6594i | 0.831212i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.295057 | + | 0.295057i | −0.0113066 | + | 0.0113066i | ||||
\(682\) | 3.11624i | 0.119327i | ||||||||
\(683\) | − | 4.24801i | − | 0.162546i | −0.996692 | − | 0.0812729i | \(-0.974101\pi\) | ||
0.996692 | − | 0.0812729i | \(-0.0258985\pi\) | |||||||
\(684\) | −6.46373 | + | 6.46373i | −0.247147 | + | 0.247147i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − | 38.7844i | − | 1.48079i | ||||||
\(687\) | 18.1509 | 0.692499 | ||||||||
\(688\) | 13.4748 | − | 13.4748i | 0.513721 | − | 0.513721i | ||||
\(689\) | −8.53912 | − | 10.4342i | −0.325315 | − | 0.397511i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.57211 | + | 4.57211i | −0.173931 | + | 0.173931i | −0.788704 | − | 0.614773i | \(-0.789248\pi\) |
0.614773 | + | 0.788704i | \(0.289248\pi\) | |||||||
\(692\) | −16.4351 | + | 16.4351i | −0.624768 | + | 0.624768i | ||||
\(693\) | −0.545220 | + | 0.545220i | −0.0207112 | + | 0.0207112i | ||||
\(694\) | 0.295626 | + | 0.295626i | 0.0112218 | + | 0.0112218i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −2.94586 | − | 2.94586i | −0.111663 | − | 0.111663i | ||||
\(697\) | 13.1008 | 0.496227 | ||||||||
\(698\) | −6.02946 | − | 6.02946i | −0.228218 | − | 0.228218i | ||||
\(699\) | −11.5057 | −0.435185 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 9.67189i | − | 0.365302i | −0.983178 | − | 0.182651i | \(-0.941532\pi\) | ||
0.983178 | − | 0.182651i | \(-0.0584679\pi\) | |||||||
\(702\) | 4.43756 | + | 5.42238i | 0.167485 | + | 0.204654i | ||||
\(703\) | −4.83486 | − | 4.83486i | −0.182350 | − | 0.182350i | ||||
\(704\) | −1.42940 | − | 1.42940i | −0.0538727 | − | 0.0538727i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 32.0680i | − | 1.20690i | ||||||
\(707\) | − | 28.7599i | − | 1.08163i | ||||||
\(708\) | −14.6758 | −0.551550 | ||||||||
\(709\) | 1.02427 | − | 1.02427i | 0.0384674 | − | 0.0384674i | −0.687611 | − | 0.726079i | \(-0.741341\pi\) |
0.726079 | + | 0.687611i | \(0.241341\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.38140 | 0.276824 | ||||||||
\(712\) | 3.28722 | + | 3.28722i | 0.123194 | + | 0.123194i | ||||
\(713\) | − | 6.69083i | − | 0.250574i | ||||||
\(714\) | 36.6925 | 1.37318 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −8.88695 | −0.332121 | ||||||||
\(717\) | − | 20.6061i | − | 0.769549i | ||||||
\(718\) | 38.8133 | + | 38.8133i | 1.44850 | + | 1.44850i | ||||
\(719\) | 14.1969 | 0.529457 | 0.264728 | − | 0.964323i | \(-0.414718\pi\) | ||||
0.264728 | + | 0.964323i | \(0.414718\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.0007 | − | 16.0007i | 0.595897 | − | 0.595897i | ||||
\(722\) | 14.5314 | 0.540801 | ||||||||
\(723\) | − | 12.7640i | − | 0.474699i | ||||||
\(724\) | − | 10.1180i | − | 0.376033i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −14.9657 | − | 14.9657i | −0.555428 | − | 0.555428i | ||||
\(727\) | −27.1036 | − | 27.1036i | −1.00522 | − | 1.00522i | −0.999986 | − | 0.00523224i | \(-0.998335\pi\) |
−0.00523224 | − | 0.999986i | \(-0.501665\pi\) | |||||||
\(728\) | −0.363538 | + | 3.63973i | −0.0134736 | + | 0.134898i | ||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 35.0366 | 1.29587 | ||||||||
\(732\) | 7.84918 | + | 7.84918i | 0.290114 | + | 0.290114i | ||||
\(733\) | −33.8532 | −1.25040 | −0.625198 | − | 0.780467i | \(-0.714982\pi\) | ||||
−0.625198 | + | 0.780467i | \(0.714982\pi\) | |||||||
\(734\) | 50.8715 | + | 50.8715i | 1.87770 | + | 1.87770i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.47695 | + | 7.47695i | 0.275604 | + | 0.275604i | ||||
\(737\) | 2.95748 | − | 2.95748i | 0.108940 | − | 0.108940i | ||||
\(738\) | −2.22677 | + | 2.22677i | −0.0819684 | + | 0.0819684i | ||||
\(739\) | −1.91247 | + | 1.91247i | −0.0703512 | + | 0.0703512i | −0.741407 | − | 0.671056i | \(-0.765841\pi\) |
0.671056 | + | 0.741407i | \(0.265841\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.84389 | − | 18.4610i | 0.0677370 | − | 0.678182i | ||||
\(742\) | 12.0012 | − | 12.0012i | 0.440577 | − | 0.440577i | ||||
\(743\) | −26.9709 | −0.989467 | −0.494734 | − | 0.869045i | \(-0.664734\pi\) | ||||
−0.494734 | + | 0.869045i | \(0.664734\pi\) | |||||||
\(744\) | − | 2.10986i | − | 0.0773514i | ||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 44.2963 | − | 44.2963i | 1.62180 | − | 1.62180i | ||||
\(747\) | 11.3338i | 0.414683i | ||||||||
\(748\) | − | 4.74146i | − | 0.173365i | ||||||
\(749\) | −17.3868 | + | 17.3868i | −0.635300 | + | 0.635300i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.2375i | 0.592516i | 0.955108 | + | 0.296258i | \(0.0957389\pi\) | ||||
−0.955108 | + | 0.296258i | \(0.904261\pi\) | |||||||
\(752\) | −28.1351 | −1.02598 | ||||||||
\(753\) | 4.65765 | − | 4.65765i | 0.169734 | − | 0.169734i | ||||
\(754\) | −66.8677 | − | 6.67876i | −2.43518 | − | 0.243226i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.93378 | + | 2.93378i | −0.106701 | + | 0.106701i | ||||
\(757\) | −11.0138 | + | 11.0138i | −0.400304 | + | 0.400304i | −0.878340 | − | 0.478036i | \(-0.841349\pi\) |
0.478036 | + | 0.878340i | \(0.341349\pi\) | |||||||
\(758\) | 44.9336 | − | 44.9336i | 1.63206 | − | 1.63206i | ||||
\(759\) | −0.321576 | − | 0.321576i | −0.0116725 | − | 0.0116725i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12.2514 | − | 12.2514i | −0.444114 | − | 0.444114i | 0.449278 | − | 0.893392i | \(-0.351681\pi\) |
−0.893392 | + | 0.449278i | \(0.851681\pi\) | |||||||
\(762\) | −10.1806 | −0.368806 | ||||||||
\(763\) | −16.4870 | − | 16.4870i | −0.596869 | − | 0.596869i | ||||
\(764\) | −28.7849 | −1.04140 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 32.5791i | 1.17713i | ||||||||
\(767\) | 23.0509 | − | 18.8644i | 0.832321 | − | 0.681155i | ||||
\(768\) | 13.4046 | + | 13.4046i | 0.483698 | + | 0.483698i | ||||
\(769\) | −15.7236 | − | 15.7236i | −0.567007 | − | 0.567007i | 0.364282 | − | 0.931289i | \(-0.381315\pi\) |
−0.931289 | + | 0.364282i | \(0.881315\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 17.6696i | − | 0.636354i | ||||||
\(772\) | 11.6282i | 0.418507i | ||||||||
\(773\) | 12.3241 | 0.443266 | 0.221633 | − | 0.975130i | \(-0.428861\pi\) | ||||
0.221633 | + | 0.975130i | \(0.428861\pi\) | |||||||
\(774\) | −5.95524 | + | 5.95524i | −0.214057 | + | 0.214057i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −4.02841 | −0.144611 | ||||||||
\(777\) | −2.19446 | − | 2.19446i | −0.0787259 | − | 0.0787259i | ||||
\(778\) | − | 0.773751i | − | 0.0277403i | ||||||
\(779\) | 8.33845 | 0.298756 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.262825 | 0.00940462 | ||||||||
\(782\) | 21.6416i | 0.773901i | ||||||||
\(783\) | 6.78175 | + | 6.78175i | 0.242360 | + | 0.242360i | ||||
\(784\) | 6.79504 | 0.242680 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 11.4539 | − | 11.4539i | 0.408548 | − | 0.408548i | ||||
\(787\) | 39.5841 | 1.41102 | 0.705511 | − | 0.708699i | \(-0.250717\pi\) | ||||
0.705511 | + | 0.708699i | \(0.250717\pi\) | |||||||
\(788\) | 27.6884i | 0.986359i | ||||||||
\(789\) | − | 25.1898i | − | 0.896780i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.84775 | + | 5.84775i | 0.207922 | + | 0.207922i | ||||
\(792\) | −0.101405 | − | 0.101405i | −0.00360326 | − | 0.00360326i | ||||
\(793\) | −22.4180 | − | 2.23911i | −0.796086 | − | 0.0795133i | ||||
\(794\) | 12.7655i | 0.453032i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 34.9287 | 1.23801 | ||||||||
\(797\) | 5.60381 | + | 5.60381i | 0.198497 | + | 0.198497i | 0.799355 | − | 0.600858i | \(-0.205174\pi\) |
−0.600858 | + | 0.799355i | \(0.705174\pi\) | |||||||
\(798\) | 23.3543 | 0.826732 | ||||||||
\(799\) | −36.5779 | − | 36.5779i | −1.29403 | − | 1.29403i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.56761 | − | 7.56761i | −0.267388 | − | 0.267388i | ||||
\(802\) | −18.6321 | + | 18.6321i | −0.657921 | + | 0.657921i | ||||
\(803\) | 0.852430 | − | 0.852430i | 0.0300816 | − | 0.0300816i | ||||
\(804\) | 15.9139 | − | 15.9139i | 0.561241 | − | 0.561241i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −21.5541 | − | 26.3375i | −0.759210 | − | 0.927699i | ||||
\(807\) | 17.0230 | − | 17.0230i | 0.599240 | − | 0.599240i | ||||
\(808\) | 5.34901 | 0.188178 | ||||||||
\(809\) | 29.3142i | 1.03063i | 0.857000 | + | 0.515316i | \(0.172325\pi\) | ||||
−0.857000 | + | 0.515316i | \(0.827675\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.3791 | − | 15.3791i | 0.540032 | − | 0.540032i | −0.383506 | − | 0.923538i | \(-0.625284\pi\) |
0.923538 | + | 0.383506i | \(0.125284\pi\) | |||||||
\(812\) | − | 39.7923i | − | 1.39644i | ||||||
\(813\) | − | 5.92521i | − | 0.207806i | ||||||
\(814\) | −0.602825 | + | 0.602825i | −0.0211290 | + | 0.0211290i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 35.5480i | 1.24443i | ||||||||
\(817\) | 22.3003 | 0.780189 | ||||||||
\(818\) | 0.766517 | − | 0.766517i | 0.0268006 | − | 0.0268006i | ||||
\(819\) | 0.836911 | − | 8.37914i | 0.0292440 | − | 0.292791i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.40447 | + | 2.40447i | −0.0839167 | + | 0.0839167i | −0.747819 | − | 0.663902i | \(-0.768899\pi\) |
0.663902 | + | 0.747819i | \(0.268899\pi\) | |||||||
\(822\) | 8.74279 | − | 8.74279i | 0.304940 | − | 0.304940i | ||||
\(823\) | −21.3112 | + | 21.3112i | −0.742861 | + | 0.742861i | −0.973128 | − | 0.230267i | \(-0.926040\pi\) |
0.230267 | + | 0.973128i | \(0.426040\pi\) | |||||||
\(824\) | 2.97595 | + | 2.97595i | 0.103672 | + | 0.103672i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 26.5127 | + | 26.5127i | 0.922495 | + | 0.922495i | ||||
\(827\) | 30.9701 | 1.07694 | 0.538468 | − | 0.842646i | \(-0.319003\pi\) | ||||
0.538468 | + | 0.842646i | \(0.319003\pi\) | |||||||
\(828\) | −1.73037 | − | 1.73037i | −0.0601346 | − | 0.0601346i | ||||
\(829\) | −18.1038 | −0.628771 | −0.314386 | − | 0.949295i | \(-0.601799\pi\) | ||||
−0.314386 | + | 0.949295i | \(0.601799\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 15.3889i | − | 0.533833i | ||||||
\(832\) | 21.9676 | + | 2.19413i | 0.761590 | + | 0.0760679i | ||||
\(833\) | 8.83409 | + | 8.83409i | 0.306083 | + | 0.306083i | ||||
\(834\) | 12.8096 | + | 12.8096i | 0.443560 | + | 0.443560i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 3.01788i | − | 0.104375i | ||||||
\(837\) | 4.85718i | 0.167889i | ||||||||
\(838\) | −37.9170 | −1.30982 | ||||||||
\(839\) | 24.5646 | − | 24.5646i | 0.848063 | − | 0.848063i | −0.141828 | − | 0.989891i | \(-0.545298\pi\) |
0.989891 | + | 0.141828i | \(0.0452981\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −62.9844 | −2.17187 | ||||||||
\(842\) | −34.0426 | − | 34.0426i | −1.17318 | − | 1.17318i | ||||
\(843\) | − | 0.484619i | − | 0.0166912i | ||||||
\(844\) | −14.3425 | −0.493690 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 12.4345 | 0.427506 | ||||||||
\(847\) | 25.4362i | 0.873997i | ||||||||
\(848\) | 11.6268 | + | 11.6268i | 0.399268 | + | 0.399268i | ||||
\(849\) | 25.8489 | 0.887132 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.29432 | − | 1.29432i | 0.0443686 | − | 0.0443686i | ||||
\(852\) | 1.41424 | 0.0484510 | ||||||||
\(853\) | − | 41.9606i | − | 1.43670i | −0.695680 | − | 0.718352i | \(-0.744897\pi\) | ||
0.695680 | − | 0.718352i | \(-0.255103\pi\) | |||||||
\(854\) | − | 28.3601i | − | 0.970461i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.23375 | − | 3.23375i | −0.110527 | − | 0.110527i | ||||
\(857\) | −2.33764 | − | 2.33764i | −0.0798523 | − | 0.0798523i | 0.666053 | − | 0.745905i | \(-0.267983\pi\) |
−0.745905 | + | 0.666053i | \(0.767983\pi\) | |||||||
\(858\) | −2.30177 | − | 0.229902i | −0.0785812 | − | 0.00784871i | ||||
\(859\) | − | 28.8875i | − | 0.985627i | −0.870135 | − | 0.492814i | \(-0.835968\pi\) | ||
0.870135 | − | 0.492814i | \(-0.164032\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.78468 | 0.128982 | ||||||||
\(862\) | −2.08825 | − | 2.08825i | −0.0711262 | − | 0.0711262i | ||||
\(863\) | 11.3214 | 0.385386 | 0.192693 | − | 0.981259i | \(-0.438278\pi\) | ||||
0.192693 | + | 0.981259i | \(0.438278\pi\) | |||||||
\(864\) | −5.42787 | − | 5.42787i | −0.184660 | − | 0.184660i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 3.49206 | + | 3.49206i | 0.118665 | + | 0.118665i | ||||
\(867\) | −34.1944 | + | 34.1944i | −1.16130 | + | 1.16130i | ||||
\(868\) | 14.2499 | − | 14.2499i | 0.483673 | − | 0.483673i | ||||
\(869\) | −1.72316 | + | 1.72316i | −0.0584543 | + | 0.0584543i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.53972 | + | 45.4516i | −0.153823 | + | 1.54007i | ||||
\(872\) | 3.06639 | − | 3.06639i | 0.103841 | − | 0.103841i | ||||
\(873\) | 9.27392 | 0.313875 | ||||||||
\(874\) | 13.7746i | 0.465932i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4.58685 | − | 4.58685i | 0.154975 | − | 0.154975i | ||||
\(877\) | 44.6698i | 1.50839i | 0.656649 | + | 0.754196i | \(0.271973\pi\) | ||||
−0.656649 | + | 0.754196i | \(0.728027\pi\) | |||||||
\(878\) | − | 44.2234i | − | 1.49247i | ||||||
\(879\) | 9.75901 | − | 9.75901i | 0.329163 | − | 0.329163i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 19.0340i | − | 0.641271i | −0.947203 | − | 0.320635i | \(-0.896104\pi\) | ||
0.947203 | − | 0.320635i | \(-0.103896\pi\) | |||||||
\(882\) | −3.00310 | −0.101120 | ||||||||
\(883\) | 32.7369 | − | 32.7369i | 1.10169 | − | 1.10169i | 0.107478 | − | 0.994208i | \(-0.465723\pi\) |
0.994208 | − | 0.107478i | \(-0.0342774\pi\) | |||||||
\(884\) | 32.7952 | + | 40.0734i | 1.10302 | + | 1.34781i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −46.6949 | + | 46.6949i | −1.56875 | + | 1.56875i | ||||
\(887\) | 31.0236 | − | 31.0236i | 1.04167 | − | 1.04167i | 0.0425761 | − | 0.999093i | \(-0.486444\pi\) |
0.999093 | − | 0.0425761i | \(-0.0135565\pi\) | |||||||
\(888\) | 0.408145 | − | 0.408145i | 0.0136965 | − | 0.0136965i | ||||
\(889\) | 8.65168 | + | 8.65168i | 0.290168 | + | 0.290168i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.233447 | + | 0.233447i | 0.00782076 | + | 0.00782076i | ||||
\(892\) | −26.3537 | −0.882386 | ||||||||
\(893\) | −23.2814 | − | 23.2814i | −0.779081 | − | 0.779081i | ||||
\(894\) | 3.38770 | 0.113302 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 8.06534i | − | 0.269444i | ||||||
\(897\) | 4.94210 | + | 0.493618i | 0.165012 | + | 0.0164814i | ||||
\(898\) | 18.0897 | + | 18.0897i | 0.603662 | + | 0.603662i | ||||
\(899\) | −32.9402 | − | 32.9402i | −1.09862 | − | 1.09862i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 30.2317i | 1.00716i | ||||||||
\(902\) | − | 1.03966i | − | 0.0346170i | ||||||
\(903\) | 10.1217 | 0.336830 | ||||||||
\(904\) | −1.08762 | + | 1.08762i | −0.0361736 | + | 0.0361736i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 24.6614 | 0.819319 | ||||||||
\(907\) | 28.8160 | + | 28.8160i | 0.956820 | + | 0.956820i | 0.999106 | − | 0.0422855i | \(-0.0134639\pi\) |
−0.0422855 | + | 0.999106i | \(0.513464\pi\) | |||||||
\(908\) | − | 0.741276i | − | 0.0246001i | ||||||
\(909\) | −12.3141 | −0.408434 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −27.9461 | −0.925895 | −0.462948 | − | 0.886386i | \(-0.653208\pi\) | ||||
−0.462948 | + | 0.886386i | \(0.653208\pi\) | |||||||
\(912\) | 22.6258i | 0.749216i | ||||||||
\(913\) | −2.64585 | − | 2.64585i | −0.0875648 | − | 0.0875648i | ||||
\(914\) | 29.7321 | 0.983451 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −22.8004 | + | 22.8004i | −0.753345 | + | 0.753345i | ||||
\(917\) | −19.4675 | −0.642873 | ||||||||
\(918\) | − | 15.7106i | − | 0.518528i | ||||||
\(919\) | − | 28.3713i | − | 0.935884i | −0.883759 | − | 0.467942i | \(-0.844996\pi\) | ||
0.883759 | − | 0.467942i | \(-0.155004\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 16.5028 | + | 16.5028i | 0.543786 | + | 0.543786i | ||||
\(922\) | 7.03607 | + | 7.03607i | 0.231721 | + | 0.231721i | ||||
\(923\) | −2.22132 | + | 1.81788i | −0.0731155 | + | 0.0598362i | ||||
\(924\) | − | 1.36976i | − | 0.0450619i | ||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −18.6685 | −0.613484 | ||||||||
\(927\) | −6.85102 | − | 6.85102i | −0.225017 | − | 0.225017i | ||||
\(928\) | 73.6209 | 2.41673 | ||||||||
\(929\) | 16.2725 | + | 16.2725i | 0.533885 | + | 0.533885i | 0.921726 | − | 0.387841i | \(-0.126779\pi\) |
−0.387841 | + | 0.921726i | \(0.626779\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.62278 | + | 5.62278i | 0.184279 | + | 0.184279i | ||||
\(932\) | 14.4529 | − | 14.4529i | 0.473422 | − | 0.473422i | ||||
\(933\) | −19.5429 | + | 19.5429i | −0.639807 | + | 0.639807i | ||||
\(934\) | −1.27104 | + | 1.27104i | −0.0415896 | + | 0.0415896i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.55843 | + | 0.155656i | 0.0509387 | + | 0.00508778i | ||||
\(937\) | 39.2274 | − | 39.2274i | 1.28150 | − | 1.28150i | 0.341693 | − | 0.939812i | \(-0.389000\pi\) |
0.939812 | − | 0.341693i | \(-0.111000\pi\) | |||||||
\(938\) | −57.4990 | −1.87741 | ||||||||
\(939\) | − | 3.20484i | − | 0.104586i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −28.9473 | + | 28.9473i | −0.943655 | + | 0.943655i | −0.998495 | − | 0.0548404i | \(-0.982535\pi\) |
0.0548404 | + | 0.998495i | \(0.482535\pi\) | |||||||
\(942\) | 25.2686i | 0.823296i | ||||||||
\(943\) | 2.23224i | 0.0726918i | ||||||||
\(944\) | −25.6857 | + | 25.6857i | −0.836000 | + | 0.836000i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | − | 2.78047i | − | 0.0904007i | ||||||
\(947\) | −10.0893 | −0.327859 | −0.163929 | − | 0.986472i | \(-0.552417\pi\) | ||||
−0.163929 | + | 0.986472i | \(0.552417\pi\) | |||||||
\(948\) | −9.27220 | + | 9.27220i | −0.301147 | + | 0.301147i | ||||
\(949\) | −1.30848 | + | 13.1005i | −0.0424750 | + | 0.425259i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −23.6818 | + | 23.6818i | −0.767936 | + | 0.767936i | ||||
\(952\) | 5.79947 | − | 5.79947i | 0.187962 | − | 0.187962i | ||||
\(953\) | −18.3680 | + | 18.3680i | −0.594996 | + | 0.594996i | −0.938977 | − | 0.343980i | \(-0.888225\pi\) |
0.343980 | + | 0.938977i | \(0.388225\pi\) | |||||||
\(954\) | −5.13854 | − | 5.13854i | −0.166367 | − | 0.166367i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 25.8845 | + | 25.8845i | 0.837165 | + | 0.837165i | ||||
\(957\) | −3.16636 | −0.102354 | ||||||||
\(958\) | −10.7373 | − | 10.7373i | −0.346907 | − | 0.346907i | ||||
\(959\) | −14.8595 | −0.479839 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.40776i | 0.238960i | ||||||||
\(962\) | 0.925335 | − | 9.26444i | 0.0298340 | − | 0.298698i | ||||
\(963\) | 7.44452 | + | 7.44452i | 0.239896 | + | 0.239896i | ||||
\(964\) | 16.0336 | + | 16.0336i | 0.516408 | + | 0.516408i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 6.25204i | 0.201156i | ||||||||
\(967\) | 30.3379i | 0.975600i | 0.872955 | + | 0.487800i | \(0.162200\pi\) | ||||
−0.872955 | + | 0.487800i | \(0.837800\pi\) | |||||||
\(968\) | −4.73084 | −0.152055 | ||||||||
\(969\) | −29.4154 | + | 29.4154i | −0.944958 | + | 0.944958i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −22.4552 | −0.720622 | −0.360311 | − | 0.932832i | \(-0.617329\pi\) | ||||
−0.360311 | + | 0.932832i | \(0.617329\pi\) | |||||||
\(972\) | 1.25616 | + | 1.25616i | 0.0402913 | + | 0.0402913i | ||||
\(973\) | − | 21.7716i | − | 0.697966i | ||||||
\(974\) | 43.9889 | 1.40950 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 27.4755 | 0.879469 | ||||||||
\(977\) | 15.8680i | 0.507664i | 0.967248 | + | 0.253832i | \(0.0816910\pi\) | ||||
−0.967248 | + | 0.253832i | \(0.918309\pi\) | |||||||
\(978\) | −17.0820 | − | 17.0820i | −0.546223 | − | 0.546223i | ||||
\(979\) | 3.53327 | 0.112924 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.05924 | + | 7.05924i | −0.225384 | + | 0.225384i | ||||
\(982\) | −8.29596 | −0.264735 | ||||||||
\(983\) | − | 6.22199i | − | 0.198451i | −0.995065 | − | 0.0992253i | \(-0.968364\pi\) | ||
0.995065 | − | 0.0992253i | \(-0.0316365\pi\) | |||||||
\(984\) | 0.703909i | 0.0224398i | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 106.546 | + | 106.546i | 3.39310 | + | 3.39310i | ||||
\(987\) | −10.5670 | − | 10.5670i | −0.336352 | − | 0.336352i | ||||
\(988\) | 20.8737 | + | 25.5062i | 0.664081 | + | 0.811459i | ||||
\(989\) | 5.96989i | 0.189832i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28.0780 | 0.891928 | 0.445964 | − | 0.895051i | \(-0.352861\pi\) | ||||
0.445964 | + | 0.895051i | \(0.352861\pi\) | |||||||
\(992\) | 26.3642 | + | 26.3642i | 0.837063 | + | 0.837063i | ||||
\(993\) | −18.0836 | −0.573865 | ||||||||
\(994\) | −2.55491 | − | 2.55491i | −0.0810368 | − | 0.0810368i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −14.2371 | − | 14.2371i | −0.451119 | − | 0.451119i | ||||
\(997\) | −25.9092 | + | 25.9092i | −0.820554 | + | 0.820554i | −0.986187 | − | 0.165634i | \(-0.947033\pi\) |
0.165634 | + | 0.986187i | \(0.447033\pi\) | |||||||
\(998\) | −1.53949 | + | 1.53949i | −0.0487318 | + | 0.0487318i | ||||
\(999\) | −0.939604 | + | 0.939604i | −0.0297278 | + | 0.0297278i |
(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 | 975.2.k.d.343.3 | 28 | ||
5.2 | odd | 4 | 975.2.t.d.382.12 | 28 | |||
5.3 | odd | 4 | 195.2.t.a.187.3 | yes | 28 | ||
5.4 | even | 2 | 195.2.k.a.148.12 | yes | 28 | ||
13.8 | odd | 4 | 975.2.t.d.268.12 | 28 | |||
15.8 | even | 4 | 585.2.w.g.577.12 | 28 | |||
15.14 | odd | 2 | 585.2.n.g.343.3 | 28 | |||
65.8 | even | 4 | 195.2.k.a.112.3 | ✓ | 28 | ||
65.34 | odd | 4 | 195.2.t.a.73.3 | yes | 28 | ||
65.47 | even | 4 | inner | 975.2.k.d.307.12 | 28 | ||
195.8 | odd | 4 | 585.2.n.g.307.12 | 28 | |||
195.164 | even | 4 | 585.2.w.g.73.12 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
195.2.k.a.112.3 | ✓ | 28 | 65.8 | even | 4 | ||
195.2.k.a.148.12 | yes | 28 | 5.4 | even | 2 | ||
195.2.t.a.73.3 | yes | 28 | 65.34 | odd | 4 | ||
195.2.t.a.187.3 | yes | 28 | 5.3 | odd | 4 | ||
585.2.n.g.307.12 | 28 | 195.8 | odd | 4 | |||
585.2.n.g.343.3 | 28 | 15.14 | odd | 2 | |||
585.2.w.g.73.12 | 28 | 195.164 | even | 4 | |||
585.2.w.g.577.12 | 28 | 15.8 | even | 4 | |||
975.2.k.d.307.12 | 28 | 65.47 | even | 4 | inner | ||
975.2.k.d.343.3 | 28 | 1.1 | even | 1 | trivial | ||
975.2.t.d.268.12 | 28 | 13.8 | odd | 4 | |||
975.2.t.d.382.12 | 28 | 5.2 | odd | 4 |