Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1148,2,Mod(1065,1148)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1148, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1148.1065");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1148 = 2^{2} \cdot 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1148.d (of order \(2\), degree \(1\), 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: | \(9.16682615204\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 39 x^{18} + 531 x^{16} + 3488 x^{14} + 12661 x^{12} + 27027 x^{10} + 34540 x^{8} + 25909 x^{6} + 10677 x^{4} + 2092 x^{2} + 144 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1065.9 | ||
Root | \(-0.911088i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1148.1065 |
Dual form | 1148.2.d.a.1065.12 |
$q$-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 \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).
\(n\) | \(493\) | \(575\) | \(785\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 0.162086i | − | 0.0935806i | −0.998905 | − | 0.0467903i | \(-0.985101\pi\) | ||
0.998905 | − | 0.0467903i | \(-0.0148992\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.05958 | −0.473860 | −0.236930 | − | 0.971527i | \(-0.576141\pi\) | ||||
−0.236930 | + | 0.971527i | \(0.576141\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.97373 | 0.991243 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 6.18973i | − | 1.86627i | −0.359520 | − | 0.933137i | \(-0.617059\pi\) | ||
0.359520 | − | 0.933137i | \(-0.382941\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.55048i | 1.53943i | 0.638390 | + | 0.769713i | \(0.279601\pi\) | ||||
−0.638390 | + | 0.769713i | \(0.720399\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.171744i | 0.0443441i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.90747i | 0.947701i | 0.880605 | + | 0.473850i | \(0.157136\pi\) | ||||
−0.880605 | + | 0.473850i | \(0.842864\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 2.97153i | − | 0.681716i | −0.940115 | − | 0.340858i | \(-0.889282\pi\) | ||
0.940115 | − | 0.340858i | \(-0.110718\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.162086 | 0.0353701 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.17619 | 1.49634 | 0.748170 | − | 0.663507i | \(-0.230933\pi\) | ||||
0.748170 | + | 0.663507i | \(0.230933\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.87728 | −0.775457 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 0.968259i | − | 0.186342i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 2.56302i | − | 0.475940i | −0.971272 | − | 0.237970i | \(-0.923518\pi\) | ||
0.971272 | − | 0.237970i | \(-0.0764821\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.343450 | 0.0616854 | 0.0308427 | − | 0.999524i | \(-0.490181\pi\) | ||||
0.0308427 | + | 0.999524i | \(0.490181\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.00327 | −0.174647 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 1.05958i | − | 0.179102i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.19624 | 1.34745 | 0.673727 | − | 0.738981i | \(-0.264692\pi\) | ||||
0.673727 | + | 0.738981i | \(0.264692\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.899657 | 0.144060 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.710016 | − | 6.36364i | 0.110886 | − | 0.993833i | ||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.0205 | 1.52812 | 0.764059 | − | 0.645146i | \(-0.223204\pi\) | ||||
0.764059 | + | 0.645146i | \(0.223204\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.15091 | −0.469710 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.52873i | 1.09818i | 0.835764 | + | 0.549089i | \(0.185025\pi\) | ||||
−0.835764 | + | 0.549089i | \(0.814975\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.633347 | 0.0886864 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 1.52927i | − | 0.210061i | −0.994469 | − | 0.105031i | \(-0.966506\pi\) | ||
0.994469 | − | 0.105031i | \(-0.0334940\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.55854i | 0.884353i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.481644 | −0.0637953 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.7505 | 1.52978 | 0.764891 | − | 0.644160i | \(-0.222793\pi\) | ||||
0.764891 | + | 0.644160i | \(0.222793\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.1776 | 1.43115 | 0.715574 | − | 0.698537i | \(-0.246165\pi\) | ||||
0.715574 | + | 0.698537i | \(0.246165\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.97373i | 0.374655i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 5.88120i | − | 0.729473i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.12911i | 0.504451i | 0.967668 | + | 0.252226i | \(0.0811625\pi\) | ||||
−0.967668 | + | 0.252226i | \(0.918837\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 1.16316i | − | 0.140028i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 7.66832i | − | 0.910062i | −0.890476 | − | 0.455031i | \(-0.849628\pi\) | ||
0.890476 | − | 0.455031i | \(-0.150372\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.2487 | −1.43360 | −0.716802 | − | 0.697277i | \(-0.754395\pi\) | ||||
−0.716802 | + | 0.697277i | \(0.754395\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.628454i | 0.0725677i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.18973 | 0.705386 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.8357i | 1.33162i | 0.746120 | + | 0.665811i | \(0.231914\pi\) | ||||
−0.746120 | + | 0.665811i | \(0.768086\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.76424 | 0.973805 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 14.0549 | 1.54272 | 0.771362 | − | 0.636396i | \(-0.219576\pi\) | ||||
0.771362 | + | 0.636396i | \(0.219576\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 4.14029i | − | 0.449078i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.415430 | −0.0445388 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 1.32263i | − | 0.140199i | −0.997540 | − | 0.0700993i | \(-0.977668\pi\) | ||
0.997540 | − | 0.0700993i | \(-0.0223316\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.55048 | −0.581848 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 0.0556685i | − | 0.00577255i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.14858i | 0.323038i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.93000i | 0.195962i | 0.995188 | + | 0.0979810i | \(0.0312384\pi\) | ||||
−0.995188 | + | 0.0979810i | \(0.968762\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 18.4066i | − | 1.84993i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 7.16465i | − | 0.712909i | −0.934313 | − | 0.356455i | \(-0.883985\pi\) | ||
0.934313 | − | 0.356455i | \(-0.116015\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.161576 | −0.0159206 | −0.00796029 | − | 0.999968i | \(-0.502534\pi\) | ||||
−0.00796029 | + | 0.999968i | \(0.502534\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.171744 | −0.0167605 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.8496 | −1.14554 | −0.572772 | − | 0.819715i | \(-0.694132\pi\) | ||||
−0.572772 | + | 0.819715i | \(0.694132\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 15.2534i | − | 1.46101i | −0.682907 | − | 0.730505i | \(-0.739285\pi\) | ||
0.682907 | − | 0.730505i | \(-0.260715\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 1.32850i | − | 0.126095i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.38582 | −0.694799 | −0.347400 | − | 0.937717i | \(-0.612935\pi\) | ||||
−0.347400 | + | 0.937717i | \(0.612935\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.60378 | −0.709056 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 16.5056i | 1.52594i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.90747 | −0.358197 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −27.3128 | −2.48298 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.03146 | − | 0.115084i | −0.0930035 | − | 0.0103768i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.40622 | 0.841318 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.01362 | −0.267416 | −0.133708 | − | 0.991021i | \(-0.542688\pi\) | ||||
−0.133708 | + | 0.991021i | \(0.542688\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 1.62419i | − | 0.143002i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.02732 | 0.351869 | 0.175934 | − | 0.984402i | \(-0.443705\pi\) | ||||
0.175934 | + | 0.984402i | \(0.443705\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.97153 | 0.257664 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.02595i | 0.0882999i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 3.77667i | − | 0.322663i | −0.986900 | − | 0.161331i | \(-0.948421\pi\) | ||
0.986900 | − | 0.161331i | \(-0.0515788\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.5981 | −0.983742 | −0.491871 | − | 0.870668i | \(-0.663687\pi\) | ||||
−0.491871 | + | 0.870668i | \(0.663687\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.22030 | 0.102768 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 34.3560 | 2.87299 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.71573i | 0.225529i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.162086i | 0.0133687i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 18.2620i | 1.49609i | 0.663651 | + | 0.748043i | \(0.269006\pi\) | ||||
−0.663651 | + | 0.748043i | \(0.730994\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 7.77175i | − | 0.632456i | −0.948683 | − | 0.316228i | \(-0.897584\pi\) | ||
0.948683 | − | 0.316228i | \(-0.102416\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 11.6198i | 0.939401i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.363913 | −0.0292302 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.50772i | 0.758799i | 0.925233 | + | 0.379400i | \(0.123869\pi\) | ||||
−0.925233 | + | 0.379400i | \(0.876131\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.247873 | −0.0196576 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.17619i | 0.565563i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.47898 | −0.664125 | −0.332063 | − | 0.943257i | \(-0.607745\pi\) | ||||
−0.332063 | + | 0.943257i | \(0.607745\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.06305 | 0.0827583 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.73491i | 0.134251i | 0.997745 | + | 0.0671255i | \(0.0213828\pi\) | ||||
−0.997745 | + | 0.0671255i | \(0.978617\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −17.8078 | −1.36983 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 8.83652i | − | 0.675746i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −14.7405 | −1.12070 | −0.560351 | − | 0.828255i | \(-0.689334\pi\) | ||||
−0.560351 | + | 0.828255i | \(0.689334\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 3.87728i | − | 0.293095i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 1.90459i | − | 0.143158i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 23.3480i | 1.74511i | 0.488517 | + | 0.872555i | \(0.337538\pi\) | ||||
−0.488517 | + | 0.872555i | \(0.662462\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.31988i | 0.469753i | 0.972025 | + | 0.234877i | \(0.0754686\pi\) | ||||
−0.972025 | + | 0.234877i | \(0.924531\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 1.81174i | − | 0.133928i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.68460 | −0.638505 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 24.1862 | 1.76867 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.968259 | 0.0704305 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.69246i | 0.339535i | 0.985484 | + | 0.169767i | \(0.0543016\pi\) | ||||
−0.985484 | + | 0.169767i | \(0.945698\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.65756i | 0.479222i | 0.970869 | + | 0.239611i | \(0.0770198\pi\) | ||||
−0.970869 | + | 0.239611i | \(0.922980\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.953261 | −0.0682645 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.88925 | 0.134603 | 0.0673017 | − | 0.997733i | \(-0.478561\pi\) | ||||
0.0673017 | + | 0.997733i | \(0.478561\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 23.9076i | − | 1.69476i | −0.530984 | − | 0.847382i | \(-0.678178\pi\) | ||
0.530984 | − | 0.847382i | \(-0.321822\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.669273 | 0.0472068 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.56302 | 0.179889 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.752321 | + | 6.74281i | −0.0525444 | + | 0.470938i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 21.3400 | 1.48324 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −18.3930 | −1.27227 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 17.8111i | − | 1.22616i | −0.790019 | − | 0.613082i | \(-0.789929\pi\) | ||
0.790019 | − | 0.613082i | \(-0.210071\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.24293 | −0.0851641 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −10.6176 | −0.724114 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.343450i | 0.0233149i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.98535i | 0.134157i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −21.6883 | −1.45892 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.07864 | −0.474021 | −0.237010 | − | 0.971507i | \(-0.576168\pi\) | ||||
−0.237010 | + | 0.971507i | \(0.576168\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −11.5300 | −0.768666 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 16.1206i | − | 1.06996i | −0.844864 | − | 0.534982i | \(-0.820318\pi\) | ||
0.844864 | − | 0.534982i | \(-0.179682\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.51140i | 0.628531i | 0.949335 | + | 0.314266i | \(0.101758\pi\) | ||||
−0.949335 | + | 0.314266i | \(0.898242\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 1.00327i | − | 0.0660104i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 11.4323i | − | 0.748955i | −0.927236 | − | 0.374477i | \(-0.877822\pi\) | ||
0.927236 | − | 0.374477i | \(-0.122178\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 7.97732i | − | 0.520383i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.91841 | 0.124614 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.60112i | 0.297621i | 0.988866 | + | 0.148811i | \(0.0475445\pi\) | ||||
−0.988866 | + | 0.148811i | \(0.952455\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.2766 | −0.855218 | −0.427609 | − | 0.903964i | \(-0.640644\pi\) | ||||
−0.427609 | + | 0.903964i | \(0.640644\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 4.32534i | − | 0.277471i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.05958 | 0.0676943 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 16.4934 | 1.04945 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 2.27810i | − | 0.144369i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.38211 | −0.529074 | −0.264537 | − | 0.964375i | \(-0.585219\pi\) | ||||
−0.264537 | + | 0.964375i | \(0.585219\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 44.4187i | − | 2.79258i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.671084 | −0.0420249 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.60975i | 0.537062i | 0.963271 | + | 0.268531i | \(0.0865381\pi\) | ||||
−0.963271 | + | 0.268531i | \(0.913462\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.19624i | 0.509290i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 7.62172i | − | 0.471772i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.535071i | 0.0329939i | 0.999864 | + | 0.0164970i | \(0.00525138\pi\) | ||||
−0.999864 | + | 0.0164970i | \(0.994749\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.62039i | 0.0995396i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.214380 | −0.0131199 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.12937 | 0.495656 | 0.247828 | − | 0.968804i | \(-0.420283\pi\) | ||||
0.247828 | + | 0.968804i | \(0.420283\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −23.8952 | −1.45153 | −0.725766 | − | 0.687941i | \(-0.758515\pi\) | ||||
−0.725766 | + | 0.687941i | \(0.758515\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.899657i | 0.0544497i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 23.9993i | 1.44722i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −23.8739 | −1.43444 | −0.717221 | − | 0.696846i | \(-0.754586\pi\) | ||||
−0.717221 | + | 0.696846i | \(0.754586\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.02133 | 0.0611452 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 3.98234i | − | 0.237566i | −0.992920 | − | 0.118783i | \(-0.962101\pi\) | ||
0.992920 | − | 0.118783i | \(-0.0378993\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −18.0961 | −1.07570 | −0.537852 | − | 0.843040i | \(-0.680764\pi\) | ||||
−0.537852 | + | 0.843040i | \(0.680764\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.510342 | 0.0302301 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.36364 | + | 0.710016i | 0.375634 | + | 0.0419109i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.73168 | 0.101864 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.312827 | 0.0183382 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 23.3041i | 1.36144i | 0.732544 | + | 0.680720i | \(0.238333\pi\) | ||||
−0.732544 | + | 0.680720i | \(0.761667\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.4506 | −0.724902 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.99327 | −0.347765 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 39.8313i | 2.30350i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.0205i | 0.577574i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.16129 | −0.0667144 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −11.8436 | −0.678164 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.83573 | 0.218917 | 0.109458 | − | 0.993991i | \(-0.465088\pi\) | ||||
0.109458 | + | 0.993991i | \(0.465088\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.0261893i | 0.00148986i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.98814i | 0.169442i | 0.996405 | + | 0.0847210i | \(0.0269999\pi\) | ||||
−0.996405 | + | 0.0847210i | \(0.973000\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 28.5943i | 1.61625i | 0.589014 | + | 0.808123i | \(0.299516\pi\) | ||||
−0.589014 | + | 0.808123i | \(0.700484\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − | 3.15091i | − | 0.177534i | ||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 24.8997i | − | 1.39850i | −0.714875 | − | 0.699252i | \(-0.753516\pi\) | ||
0.714875 | − | 0.699252i | \(-0.246484\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −15.8644 | −0.888236 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.92066i | 0.107201i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 11.6112 | 0.646062 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 21.5208i | − | 1.19376i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.47237 | −0.136722 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.52873 | −0.415072 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.4659i | 0.685189i | 0.939483 | + | 0.342594i | \(0.111306\pi\) | ||||
−0.939483 | + | 0.342594i | \(0.888694\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 24.3734 | 1.33565 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 4.37514i | − | 0.239039i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.8361 | −0.862649 | −0.431325 | − | 0.902197i | \(-0.641954\pi\) | ||||
−0.431325 | + | 0.902197i | \(0.641954\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.19714i | 0.0650197i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 2.12586i | − | 0.115122i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.23247i | 0.0663538i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.19452i | 0.278857i | 0.990232 | + | 0.139428i | \(0.0445265\pi\) | ||||
−0.990232 | + | 0.139428i | \(0.955474\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.4617 | −0.881173 | −0.440586 | − | 0.897710i | \(-0.645229\pi\) | ||||
−0.440586 | + | 0.897710i | \(0.645229\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.37430 | 0.286859 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −18.7888 | −1.00002 | −0.500012 | − | 0.866018i | \(-0.666671\pi\) | ||||
−0.500012 | + | 0.866018i | \(0.666671\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.12522i | 0.431242i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.633347i | 0.0335203i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 26.8931 | 1.41937 | 0.709683 | − | 0.704521i | \(-0.248838\pi\) | ||||
0.709683 | + | 0.704521i | \(0.248838\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.1700 | 0.535264 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.42703i | 0.232359i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12.9785 | 0.679328 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −27.7107 | −1.44648 | −0.723242 | − | 0.690594i | \(-0.757349\pi\) | ||||
−0.723242 | + | 0.690594i | \(0.757349\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.11139 | − | 18.9237i | 0.109915 | − | 0.985130i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.52927 | 0.0793957 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.426013 | −0.0220581 | −0.0110290 | − | 0.999939i | \(-0.503511\pi\) | ||||
−0.0110290 | + | 0.999939i | \(0.503511\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 1.52462i | − | 0.0787310i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 14.2260 | 0.732675 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.0114 | 1.43885 | 0.719425 | − | 0.694570i | \(-0.244405\pi\) | ||||
0.719425 | + | 0.694570i | \(0.244405\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.488467i | 0.0250249i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 14.8248i | − | 0.757511i | −0.925497 | − | 0.378755i | \(-0.876352\pi\) | ||
0.925497 | − | 0.378755i | \(-0.123648\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.55854 | −0.334254 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 29.7984 | 1.51474 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −32.7871 | −1.66237 | −0.831185 | − | 0.555996i | \(-0.812337\pi\) | ||||
−0.831185 | + | 0.555996i | \(0.812337\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 28.0408i | 1.41808i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 0.652774i | − | 0.0329281i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 12.5409i | − | 0.631003i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 16.2173i | − | 0.813923i | −0.913445 | − | 0.406961i | \(-0.866588\pi\) | ||
0.913445 | − | 0.406961i | \(-0.133412\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 0.481644i | − | 0.0241124i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.8298 | 0.790501 | 0.395251 | − | 0.918573i | \(-0.370658\pi\) | ||||
0.395251 | + | 0.918573i | \(0.370658\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.90631i | 0.0949601i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −9.28645 | −0.461447 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 50.7325i | − | 2.51472i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 33.1844 | 1.64086 | 0.820430 | − | 0.571747i | \(-0.193734\pi\) | ||||
0.820430 | + | 0.571747i | \(0.193734\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.612147 | −0.0301950 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11.7505i | 0.578203i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14.8923 | −0.731036 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.87990i | 0.0920591i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.7444 | 0.769166 | 0.384583 | − | 0.923090i | \(-0.374345\pi\) | ||||
0.384583 | + | 0.923090i | \(0.374345\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.43254i | 0.216029i | 0.994149 | + | 0.108014i | \(0.0344493\pi\) | ||||
−0.994149 | + | 0.108014i | \(0.965551\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 22.3884i | 1.08856i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 15.1504i | − | 0.734901i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.1776i | 0.540923i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 5.56864i | − | 0.268856i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.53857 | 0.170447 | 0.0852236 | − | 0.996362i | \(-0.472840\pi\) | ||||
0.0852236 | + | 0.996362i | \(0.472840\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −23.3178 | −1.12058 | −0.560291 | − | 0.828296i | \(-0.689311\pi\) | ||||
−0.560291 | + | 0.828296i | \(0.689311\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.440183 | 0.0211051 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 21.3243i | − | 1.02008i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 28.3096i | − | 1.35114i | −0.737295 | − | 0.675571i | \(-0.763897\pi\) | ||
0.737295 | − | 0.675571i | \(-0.236103\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.97373 | −0.141606 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.43738 | −0.258338 | −0.129169 | − | 0.991623i | \(-0.541231\pi\) | ||||
−0.129169 | + | 0.991623i | \(0.541231\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.40144i | 0.0664345i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.96003 | 0.140004 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 22.3814 | 1.05625 | 0.528123 | − | 0.849168i | \(-0.322896\pi\) | ||||
0.528123 | + | 0.849168i | \(0.322896\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −39.3892 | − | 4.39481i | −1.85477 | − | 0.206943i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.25969 | −0.0591856 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.88120 | 0.275715 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.4445i | 0.909576i | 0.890600 | + | 0.454788i | \(0.150285\pi\) | ||||
−0.890600 | + | 0.454788i | \(0.849715\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.78344 | 0.176596 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 29.2163 | 1.36074 | 0.680368 | − | 0.732870i | \(-0.261820\pi\) | ||||
0.680368 | + | 0.732870i | \(0.261820\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.4977i | 0.766714i | 0.923600 | + | 0.383357i | \(0.125232\pi\) | ||||
−0.923600 | + | 0.383357i | \(0.874768\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.0589854i | 0.00273538i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 18.8138 | 0.870601 | 0.435300 | − | 0.900285i | \(-0.356642\pi\) | ||||
0.435300 | + | 0.900285i | \(0.356642\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.12911 | −0.190665 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.54107 | 0.0710088 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 62.0245i | − | 2.85189i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 11.5215i | 0.528641i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 4.54763i | − | 0.208222i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 18.8829i | − | 0.862781i | −0.902165 | − | 0.431391i | \(-0.858023\pi\) | ||
0.902165 | − | 0.431391i | \(-0.141977\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 45.4931i | 2.07431i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.16316 | 0.0529257 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 2.04500i | − | 0.0928585i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.05043 | −0.183543 | −0.0917713 | − | 0.995780i | \(-0.529253\pi\) | ||||
−0.0917713 | + | 0.995780i | \(0.529253\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.37433i | 0.0621492i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −30.6318 | −1.38239 | −0.691197 | − | 0.722666i | \(-0.742916\pi\) | ||||
−0.691197 | + | 0.722666i | \(0.742916\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.0149 | 0.451049 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 19.5033i | 0.876609i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.66832 | 0.343971 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.27069i | 0.325481i | 0.986669 | + | 0.162741i | \(0.0520333\pi\) | ||||
−0.986669 | + | 0.162741i | \(0.947967\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.281204 | 0.0125633 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 11.5631i | − | 0.515573i | −0.966202 | − | 0.257786i | \(-0.917007\pi\) | ||
0.966202 | − | 0.257786i | \(-0.0829931\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.59154i | 0.337819i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.88641i | 0.128190i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 28.0892i | 1.24503i | 0.782607 | + | 0.622516i | \(0.213889\pi\) | ||||
−0.782607 | + | 0.622516i | \(0.786111\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 12.2487i | − | 0.541851i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.87721 | −0.127032 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.171203 | 0.00754412 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 46.6008 | 2.04950 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.38924i | 0.104876i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 33.3339i | 1.46038i | 0.683243 | + | 0.730191i | \(0.260569\pi\) | ||||
−0.683243 | + | 0.730191i | \(0.739431\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.0223 | −0.525698 | −0.262849 | − | 0.964837i | \(-0.584662\pi\) | ||||
−0.262849 | + | 0.964837i | \(0.584662\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.628454 | −0.0274280 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.34202i | 0.0584593i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 28.4978 | 1.23903 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 34.9427 | 1.51638 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 35.3212 | + | 3.94093i | 1.52993 | + | 0.170701i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.5556 | 0.542828 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.78439 | 0.163308 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.18973i | 0.266611i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.9705 | −0.600640 | −0.300320 | − | 0.953838i | \(-0.597094\pi\) | ||||
−0.300320 | + | 0.953838i | \(0.597094\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.02437 | 0.0439598 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 16.1622i | 0.692315i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 41.6867i | − | 1.78239i | −0.453618 | − | 0.891196i | \(-0.649867\pi\) | ||
0.453618 | − | 0.891196i | \(-0.350133\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 33.2392 | 1.41861 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.61608 | −0.324456 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11.8357 | −0.503306 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.40765i | 0.0597516i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 33.5882i | − | 1.42318i | −0.702595 | − | 0.711590i | \(-0.747976\pi\) | ||
0.702595 | − | 0.711590i | \(-0.252024\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 55.6188i | 2.35243i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 3.92025i | − | 0.165513i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 23.8748i | − | 1.00620i | −0.864227 | − | 0.503101i | \(-0.832192\pi\) | ||
0.864227 | − | 0.503101i | \(-0.167808\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.82589 | 0.329238 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 8.76424i | 0.368064i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.26387 | 0.262595 | 0.131297 | − | 0.991343i | \(-0.458086\pi\) | ||||
0.131297 | + | 0.991343i | \(0.458086\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.98816i | 0.292445i | 0.989252 | + | 0.146223i | \(0.0467116\pi\) | ||||
−0.989252 | + | 0.146223i | \(0.953288\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.760584 | 0.0317738 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −27.8241 | −1.16035 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 0.784626i | − | 0.0326644i | −0.999867 | − | 0.0163322i | \(-0.994801\pi\) | ||
0.999867 | − | 0.0163322i | \(-0.00519893\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.07910 | 0.0448458 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14.0549i | 0.583095i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.46576 | −0.392032 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 17.4891i | − | 0.723085i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 18.5371i | − | 0.765109i | −0.923933 | − | 0.382554i | \(-0.875044\pi\) | ||
0.923933 | − | 0.382554i | \(-0.124956\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 1.02057i | − | 0.0420519i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 0.306221i | − | 0.0125963i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.684309i | 0.0281012i | 0.999901 | + | 0.0140506i | \(0.00447259\pi\) | ||||
−0.999901 | + | 0.0140506i | \(0.995527\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.14029 | 0.169735 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3.87509 | −0.158597 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 32.0764 | 1.31061 | 0.655304 | − | 0.755366i | \(-0.272541\pi\) | ||||
0.655304 | + | 0.755366i | \(0.272541\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 34.7609i | 1.41793i | 0.705246 | + | 0.708963i | \(0.250837\pi\) | ||||
−0.705246 | + | 0.708963i | \(0.749163\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 12.2789i | 0.500034i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 28.9402 | 1.17659 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 32.8192 | 1.33209 | 0.666046 | − | 0.745911i | \(-0.267986\pi\) | ||||
0.666046 | + | 0.745911i | \(0.267986\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 0.415430i | − | 0.0168341i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −41.7881 | −1.69056 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 33.4712 | 1.35189 | 0.675944 | − | 0.736953i | \(-0.263736\pi\) | ||||
0.675944 | + | 0.736953i | \(0.263736\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.09292 | + | 0.121941i | 0.0440706 | + | 0.00491713i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −40.8434 | −1.64429 | −0.822146 | − | 0.569277i | \(-0.807223\pi\) | ||||
−0.822146 | + | 0.569277i | \(0.807223\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23.4192 | 0.941297 | 0.470649 | − | 0.882321i | \(-0.344020\pi\) | ||||
0.470649 | + | 0.882321i | \(0.344020\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 6.94842i | − | 0.278830i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.32263 | 0.0529901 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.41973 | 0.376789 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.98125i | 0.119060i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 32.0266i | 1.27698i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.0864 | −0.481154 | −0.240577 | − | 0.970630i | \(-0.577337\pi\) | ||||
−0.240577 | + | 0.970630i | \(0.577337\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.88693 | −0.114745 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.19318 | 0.126718 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 5.55048i | − | 0.219918i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 22.8035i | − | 0.902092i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.65389i | 0.104822i | 0.998626 | + | 0.0524112i | \(0.0166907\pi\) | ||||
−0.998626 | + | 0.0524112i | \(0.983309\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 48.6653i | − | 1.91917i | −0.281414 | − | 0.959586i | \(-0.590804\pi\) | ||
0.281414 | − | 0.959586i | \(-0.409196\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.72097i | 0.0677630i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 24.9782 | 0.981992 | 0.490996 | − | 0.871162i | \(-0.336633\pi\) | ||||
0.490996 | + | 0.871162i | \(0.336633\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 72.7323i | − | 2.85499i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.0556685 | 0.00218182 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 45.6996i | 1.78836i | 0.447704 | + | 0.894182i | \(0.352242\pi\) | ||||
−0.447704 | + | 0.894182i | \(0.647758\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.26728 | −0.166737 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −36.4244 | −1.42105 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 36.5674i | − | 1.42446i | −0.701944 | − | 0.712232i | \(-0.747684\pi\) | ||
0.701944 | − | 0.712232i | \(-0.252316\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.4438 | 0.600695 | 0.300348 | − | 0.953830i | \(-0.402897\pi\) | ||||
0.300348 | + | 0.953830i | \(0.402897\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.51538i | 0.136526i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.14858 | −0.122097 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 18.3927i | − | 0.712169i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.14735i | 0.0443591i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 69.1865i | − | 2.67092i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 4.03761i | − | 0.155639i | −0.996967 | − | 0.0778193i | \(-0.975204\pi\) | ||
0.996967 | − | 0.0778193i | \(-0.0247957\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.75422i | 0.144500i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 17.9382 | 0.689420 | 0.344710 | − | 0.938709i | \(-0.387977\pi\) | ||||
0.344710 | + | 0.938709i | \(0.387977\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.93000 | −0.0740666 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.61293 | −0.100128 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 1.97784i | − | 0.0756798i | −0.999284 | − | 0.0378399i | \(-0.987952\pi\) | ||
0.999284 | − | 0.0378399i | \(-0.0120477\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.00170i | 0.152897i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.54167 | 0.0588183 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.48817 | 0.323374 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 48.5157i | 1.84563i | 0.385248 | + | 0.922813i | \(0.374116\pi\) | ||||
−0.385248 | + | 0.922813i | \(0.625884\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 18.4066 | 0.699208 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 12.2892 | 0.466156 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 24.8657 | + | 2.77436i | 0.941856 | + | 0.105087i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.85302 | −0.0700876 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.74537 | −0.217000 | −0.108500 | − | 0.994096i | \(-0.534605\pi\) | ||||
−0.108500 | + | 0.994096i | \(0.534605\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 24.3554i | − | 0.918580i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.29301 | −0.0486977 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7.16465 | 0.269454 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 10.8010i | − | 0.405639i | −0.979216 | − | 0.202820i | \(-0.934990\pi\) | ||
0.979216 | − | 0.202820i | \(-0.0650105\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 35.1962i | 1.31996i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.46466 | 0.0923023 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −36.4030 | −1.36140 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.745778 | 0.0278516 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 18.8952i | 0.704674i | 0.935873 | + | 0.352337i | \(0.114613\pi\) | ||||
−0.935873 | + | 0.352337i | \(0.885387\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 0.161576i | − | 0.00601741i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.15195i | 0.0800318i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.93754i | 0.369071i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 28.0884i | − | 1.04174i | −0.853636 | − | 0.520870i | \(-0.825608\pi\) | ||
0.853636 | − | 0.520870i | \(-0.174392\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 25.5916 | 0.947839 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 39.1550i | 1.44820i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −38.5190 | −1.42273 | −0.711365 | − | 0.702823i | \(-0.751923\pi\) | ||||
−0.711365 | + | 0.702823i | \(0.751923\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 0.171744i | − | 0.00633487i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 25.5581 | 0.941445 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −18.3384 | −0.674590 | −0.337295 | − | 0.941399i | \(-0.609512\pi\) | ||||
−0.337295 | + | 0.941399i | \(0.609512\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 2.67336i | − | 0.0982082i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 39.4951 | 1.44894 | 0.724468 | − | 0.689308i | \(-0.242085\pi\) | ||||
0.724468 | + | 0.689308i | \(0.242085\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 19.3502i | − | 0.708935i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 41.7954 | 1.52921 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 11.8496i | − | 0.432975i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.77300i | 0.283641i | 0.989892 | + | 0.141820i | \(0.0452956\pi\) | ||||
−0.989892 | + | 0.141820i | \(0.954704\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.35863i | 0.0495111i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.23482i | 0.299696i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21.1823i | 0.769883i | 0.922941 | + | 0.384941i | \(0.125778\pi\) | ||||
−0.922941 | + | 0.384941i | \(0.874222\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −7.19967 | −0.261331 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −31.5478 | −1.14361 | −0.571804 | − | 0.820390i | \(-0.693756\pi\) | ||||
−0.571804 | + | 0.820390i | \(0.693756\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15.2534 | 0.552210 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − | 12.3121i | − | 0.445145i | ||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 65.2208i | 2.35499i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −24.4006 | −0.879907 | −0.439953 | − | 0.898021i | \(-0.645005\pi\) | ||||
−0.439953 | + | 0.898021i | \(0.645005\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.39552 | 0.0502585 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 24.3531i | 0.875922i | 0.898994 | + | 0.437961i | \(0.144299\pi\) | ||||
−0.898994 | + | 0.437961i | \(0.855701\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.33165 | −0.0478343 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.32850 | 0.0476596 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −18.9097 | − | 2.10983i | −0.677512 | − | 0.0755926i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −47.4648 | −1.69843 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.48167 | −0.0886875 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 10.0742i | − | 0.359565i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −31.7856 | −1.13303 | −0.566517 | − | 0.824050i | \(-0.691710\pi\) | ||||
−0.566517 | + | 0.824050i | \(0.691710\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.0867277 | 0.00308759 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 7.38582i | − | 0.262609i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 62.0412i | 2.20315i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.262643 | 0.00931497 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −8.18095 | −0.289784 | −0.144892 | − | 0.989447i | \(-0.546284\pi\) | ||||
−0.144892 | + | 0.989447i | \(0.546284\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −29.4183 | −1.04074 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 3.93314i | − | 0.138971i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 75.8163i | 2.67550i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 7.60378i | − | 0.267998i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 1.31766i | − | 0.0463838i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 31.1957i | − | 1.09678i | −0.836222 | − | 0.548391i | \(-0.815241\pi\) | ||
0.836222 | − | 0.548391i | \(-0.184759\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −33.1491 | −1.16402 | −0.582012 | − | 0.813180i | \(-0.697734\pi\) | ||||
−0.582012 | + | 0.813180i | \(0.697734\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.87309i | 0.135835i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.98419 | 0.314702 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 29.7763i | − | 1.04174i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −16.5056 | −0.576753 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −32.8670 | −1.14707 | −0.573533 | − | 0.819182i | \(-0.694428\pi\) | ||||
−0.573533 | + | 0.819182i | \(0.694428\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.6445i | 0.440760i | 0.975414 | + | 0.220380i | \(0.0707297\pi\) | ||||
−0.975414 | + | 0.220380i | \(0.929270\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.88996 | 0.135431 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 49.2896i | − | 1.71397i | −0.515343 | − | 0.856984i | \(-0.672335\pi\) | ||
0.515343 | − | 0.856984i | \(-0.327665\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 33.5949 | 1.16680 | 0.583400 | − | 0.812185i | \(-0.301722\pi\) | ||||
0.583400 | + | 0.812185i | \(0.301722\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.86963i | 0.134236i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 3.90747i | − | 0.135386i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 1.83828i | − | 0.0636162i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 0.332548i | − | 0.0114945i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 14.1555i | 0.488701i | 0.969687 | + | 0.244350i | \(0.0785747\pi\) | ||||
−0.969687 | + | 0.244350i | \(0.921425\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.4309 | 0.773481 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.645482 | −0.0222316 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 18.8689 | 0.649109 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 27.3128i | − | 0.938479i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.93313i | 0.100665i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 58.8178 | 2.01625 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.08734 | 0.139948 | 0.0699739 | − | 0.997549i | \(-0.477708\pi\) | ||||
0.0699739 | + | 0.997549i | \(0.477708\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 9.36303i | 0.320209i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −29.3856 | −1.00379 | −0.501896 | − | 0.864928i | \(-0.667364\pi\) | ||||
−0.501896 | + | 0.864928i | \(0.667364\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.25994 | −0.0429885 | −0.0214942 | − | 0.999769i | \(-0.506842\pi\) | ||||
−0.0214942 | + | 0.999769i | \(0.506842\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.115084 | − | 1.03146i | 0.00392205 | − | 0.0351520i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −9.65576 | −0.328686 | −0.164343 | − | 0.986403i | \(-0.552550\pi\) | ||||
−0.164343 | + | 0.986403i | \(0.552550\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15.6188 | 0.531057 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 0.280682i | − | 0.00953245i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 73.2600 | 2.48517 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −22.9186 | −0.776566 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.73930i | 0.194246i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9.40622i | 0.317988i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.8075 | 0.803920 | 0.401960 | − | 0.915657i | \(-0.368329\pi\) | ||||
0.401960 | + | 0.915657i | \(0.368329\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.77727 | 0.127404 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −42.2526 | −1.42353 | −0.711763 | − | 0.702420i | \(-0.752103\pi\) | ||||
−0.711763 | + | 0.702420i | \(0.752103\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 17.4498i | − | 0.587231i | −0.955924 | − | 0.293616i | \(-0.905141\pi\) | ||
0.955924 | − | 0.293616i | \(-0.0948586\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.01807i | 0.0678368i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 29.9859i | 1.00683i | 0.864045 | + | 0.503414i | \(0.167923\pi\) | ||||
−0.864045 | + | 0.503414i | \(0.832077\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 3.01362i | − | 0.101074i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 54.2483i | − | 1.81739i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 22.3718 | 0.748645 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 24.7391i | − | 0.826938i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.45611 | 0.215563 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 0.880267i | − | 0.0293586i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.97557 | 0.199075 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.62419 | 0.0540497 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 6.69644i | − | 0.222597i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −36.3747 | −1.20780 | −0.603901 | − | 0.797059i | \(-0.706388\pi\) | ||||
−0.603901 | + | 0.797059i | \(0.706388\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 21.3057i | − | 0.706666i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16.9860 | −0.562772 | −0.281386 | − | 0.959595i | \(-0.590794\pi\) | ||||
−0.281386 | + | 0.959595i | \(0.590794\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 86.9960i | − | 2.87915i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.91969i | 0.0634630i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.02732i | 0.132994i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 41.1336i | 1.35687i | 0.734660 | + | 0.678436i | \(0.237342\pi\) | ||||
−0.734660 | + | 0.678436i | \(0.762658\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 0.621720i | − | 0.0204864i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 42.5628 | 1.40097 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −31.7791 | −1.04489 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.480484 | −0.0157811 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 7.87488i | − | 0.258366i | −0.991621 | − | 0.129183i | \(-0.958764\pi\) | ||
0.991621 | − | 0.129183i | \(-0.0412355\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.97153i | 0.0973880i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0.484337 | 0.0158565 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −25.6273 | −0.838102 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.54795i | 0.148575i | 0.997237 | + | 0.0742876i | \(0.0236683\pi\) | ||||
−0.997237 | + | 0.0742876i | \(0.976332\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.63474 | 0.151249 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −42.3029 | −1.37903 | −0.689517 | − | 0.724269i | \(-0.742177\pi\) | ||||
−0.689517 | + | 0.724269i | \(0.742177\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.09521 | − | 45.6667i | 0.165923 | − | 1.48711i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.02595 | −0.0333742 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 26.9710 | 0.876439 | 0.438220 | − | 0.898868i | \(-0.355609\pi\) | ||||
0.438220 | + | 0.898868i | \(0.355609\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 67.9863i | − | 2.20693i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.03589 | −0.130873 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −30.8049 | −0.997868 | −0.498934 | − | 0.866640i | \(-0.666275\pi\) | ||||
−0.498934 | + | 0.866640i | \(0.666275\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 4.97206i | − | 0.160892i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.57140i | 0.0831216i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.77667 | 0.121955 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.8820 | −0.996195 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −35.2375 | −1.13551 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 7.05424i | − | 0.227084i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 29.4752i | 0.947859i | 0.880563 | + | 0.473929i | \(0.157165\pi\) | ||||
−0.880563 | + | 0.473929i | \(0.842835\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 1.88201i | − | 0.0604589i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 35.3588i | − | 1.13472i | −0.823470 | − | 0.567359i | \(-0.807965\pi\) | ||
0.823470 | − | 0.567359i | \(-0.192035\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 11.5981i | − | 0.371820i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.48822 | −0.111713 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 45.1187i | 1.44348i | 0.692167 | + | 0.721738i | \(0.256656\pi\) | ||||
−0.692167 | + | 0.721738i | \(0.743344\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.18673 | −0.261649 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 45.3594i | − | 1.44822i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −56.6857 | −1.80799 | −0.903997 | − | 0.427538i | \(-0.859381\pi\) | ||||
−0.903997 | + | 0.427538i | \(0.859381\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.00182 | −0.0637832 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.22030i | 0.0388427i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 71.9093 | 2.28658 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.6231i | 0.877475i | 0.898615 | + | 0.438738i | \(0.144574\pi\) | ||||
−0.898615 | + | 0.438738i | \(0.855426\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.02055 | 0.0641203 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 25.3321i | 0.803081i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 46.1817i | 1.46259i | 0.682061 | + | 0.731295i | \(0.261084\pi\) | ||||
−0.682061 | + | 0.731295i | \(0.738916\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 7.93609i | − | 0.251087i |
(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 | 1148.2.d.a.1065.9 | ✓ | 20 | |
41.40 | even | 2 | inner | 1148.2.d.a.1065.12 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1148.2.d.a.1065.9 | ✓ | 20 | 1.1 | even | 1 | trivial | |
1148.2.d.a.1065.12 | yes | 20 | 41.40 | even | 2 | inner |