Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [483,3,Mod(22,483)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(483, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("483.22");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 483 = 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 483.f (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: | \(13.1607967686\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 22.21 | ||
Character | \(\chi\) | \(=\) | 483.22 |
Dual form | 483.3.f.a.22.22 |
$q$-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 \(\left(\mathbb{Z}/483\mathbb{Z}\right)^\times\).
\(n\) | \(323\) | \(346\) | \(442\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.745761 | −0.372880 | −0.186440 | − | 0.982466i | \(-0.559695\pi\) | ||||
−0.186440 | + | 0.982466i | \(0.559695\pi\) | |||||||
\(3\) | −1.73205 | −0.577350 | ||||||||
\(4\) | −3.44384 | −0.860960 | ||||||||
\(5\) | 8.10909i | 1.62182i | 0.585173 | + | 0.810909i | \(0.301027\pi\) | ||||
−0.585173 | + | 0.810909i | \(0.698973\pi\) | |||||||
\(6\) | 1.29170 | 0.215283 | ||||||||
\(7\) | − | 2.64575i | − | 0.377964i | ||||||
\(8\) | 5.55132 | 0.693916 | ||||||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | − | 6.04744i | − | 0.604744i | ||||||
\(11\) | 17.3590i | 1.57809i | 0.614337 | + | 0.789044i | \(0.289424\pi\) | ||||
−0.614337 | + | 0.789044i | \(0.710576\pi\) | |||||||
\(12\) | 5.96491 | 0.497076 | ||||||||
\(13\) | 11.7963 | 0.907409 | 0.453704 | − | 0.891152i | \(-0.350102\pi\) | ||||
0.453704 | + | 0.891152i | \(0.350102\pi\) | |||||||
\(14\) | 1.97310i | 0.140936i | ||||||||
\(15\) | − | 14.0453i | − | 0.936357i | ||||||
\(16\) | 9.63540 | 0.602213 | ||||||||
\(17\) | 14.5159i | 0.853874i | 0.904281 | + | 0.426937i | \(0.140407\pi\) | ||||
−0.904281 | + | 0.426937i | \(0.859593\pi\) | |||||||
\(18\) | −2.23728 | −0.124293 | ||||||||
\(19\) | − | 7.64785i | − | 0.402519i | −0.979538 | − | 0.201259i | \(-0.935497\pi\) | ||
0.979538 | − | 0.201259i | \(-0.0645034\pi\) | |||||||
\(20\) | − | 27.9264i | − | 1.39632i | ||||||
\(21\) | 4.58258i | 0.218218i | ||||||||
\(22\) | − | 12.9456i | − | 0.588438i | ||||||
\(23\) | −0.920715 | + | 22.9816i | −0.0400311 | + | 0.999198i | ||||
\(24\) | −9.61518 | −0.400632 | ||||||||
\(25\) | −40.7573 | −1.63029 | ||||||||
\(26\) | −8.79723 | −0.338355 | ||||||||
\(27\) | −5.19615 | −0.192450 | ||||||||
\(28\) | 9.11155i | 0.325412i | ||||||||
\(29\) | 4.85267 | 0.167333 | 0.0836667 | − | 0.996494i | \(-0.473337\pi\) | ||||
0.0836667 | + | 0.996494i | \(0.473337\pi\) | |||||||
\(30\) | 10.4745i | 0.349149i | ||||||||
\(31\) | 3.69740 | 0.119271 | 0.0596355 | − | 0.998220i | \(-0.481006\pi\) | ||||
0.0596355 | + | 0.998220i | \(0.481006\pi\) | |||||||
\(32\) | −29.3910 | −0.918469 | ||||||||
\(33\) | − | 30.0666i | − | 0.911110i | ||||||
\(34\) | − | 10.8254i | − | 0.318393i | ||||||
\(35\) | 21.4546 | 0.612989 | ||||||||
\(36\) | −10.3315 | −0.286987 | ||||||||
\(37\) | − | 27.2098i | − | 0.735399i | −0.929945 | − | 0.367700i | \(-0.880145\pi\) | ||
0.929945 | − | 0.367700i | \(-0.119855\pi\) | |||||||
\(38\) | 5.70347i | 0.150091i | ||||||||
\(39\) | −20.4318 | −0.523893 | ||||||||
\(40\) | 45.0162i | 1.12540i | ||||||||
\(41\) | −75.2950 | −1.83646 | −0.918232 | − | 0.396043i | \(-0.870383\pi\) | ||||
−0.918232 | + | 0.396043i | \(0.870383\pi\) | |||||||
\(42\) | − | 3.41751i | − | 0.0813692i | ||||||
\(43\) | − | 10.9461i | − | 0.254561i | −0.991867 | − | 0.127281i | \(-0.959375\pi\) | ||
0.991867 | − | 0.127281i | \(-0.0406248\pi\) | |||||||
\(44\) | − | 59.7815i | − | 1.35867i | ||||||
\(45\) | 24.3273i | 0.540606i | ||||||||
\(46\) | 0.686633 | − | 17.1387i | 0.0149268 | − | 0.372581i | ||||
\(47\) | −63.8078 | −1.35761 | −0.678806 | − | 0.734317i | \(-0.737502\pi\) | ||||
−0.678806 | + | 0.734317i | \(0.737502\pi\) | |||||||
\(48\) | −16.6890 | −0.347688 | ||||||||
\(49\) | −7.00000 | −0.142857 | ||||||||
\(50\) | 30.3952 | 0.607903 | ||||||||
\(51\) | − | 25.1422i | − | 0.492984i | ||||||
\(52\) | −40.6246 | −0.781243 | ||||||||
\(53\) | − | 0.265774i | − | 0.00501460i | −0.999997 | − | 0.00250730i | \(-0.999202\pi\) | ||
0.999997 | − | 0.00250730i | \(-0.000798099\pi\) | |||||||
\(54\) | 3.87509 | 0.0717609 | ||||||||
\(55\) | −140.765 | −2.55937 | ||||||||
\(56\) | − | 14.6874i | − | 0.262275i | ||||||
\(57\) | 13.2465i | 0.232394i | ||||||||
\(58\) | −3.61893 | −0.0623953 | ||||||||
\(59\) | 109.616 | 1.85790 | 0.928950 | − | 0.370206i | \(-0.120713\pi\) | ||||
0.928950 | + | 0.370206i | \(0.120713\pi\) | |||||||
\(60\) | 48.3699i | 0.806166i | ||||||||
\(61\) | 94.2884i | 1.54571i | 0.634582 | + | 0.772855i | \(0.281172\pi\) | ||||
−0.634582 | + | 0.772855i | \(0.718828\pi\) | |||||||
\(62\) | −2.75737 | −0.0444738 | ||||||||
\(63\) | − | 7.93725i | − | 0.125988i | ||||||
\(64\) | −16.6230 | −0.259734 | ||||||||
\(65\) | 95.6573i | 1.47165i | ||||||||
\(66\) | 22.4225i | 0.339735i | ||||||||
\(67\) | 50.6910i | 0.756581i | 0.925687 | + | 0.378291i | \(0.123488\pi\) | ||||
−0.925687 | + | 0.378291i | \(0.876512\pi\) | |||||||
\(68\) | − | 49.9903i | − | 0.735151i | ||||||
\(69\) | 1.59472 | − | 39.8052i | 0.0231120 | − | 0.576887i | ||||
\(70\) | −16.0000 | −0.228572 | ||||||||
\(71\) | 32.1216 | 0.452416 | 0.226208 | − | 0.974079i | \(-0.427367\pi\) | ||||
0.226208 | + | 0.974079i | \(0.427367\pi\) | |||||||
\(72\) | 16.6540 | 0.231305 | ||||||||
\(73\) | −125.902 | −1.72468 | −0.862342 | − | 0.506327i | \(-0.831003\pi\) | ||||
−0.862342 | + | 0.506327i | \(0.831003\pi\) | |||||||
\(74\) | 20.2920i | 0.274216i | ||||||||
\(75\) | 70.5937 | 0.941249 | ||||||||
\(76\) | 26.3380i | 0.346553i | ||||||||
\(77\) | 45.9275 | 0.596461 | ||||||||
\(78\) | 15.2372 | 0.195349 | ||||||||
\(79\) | − | 45.1325i | − | 0.571297i | −0.958334 | − | 0.285648i | \(-0.907791\pi\) | ||
0.958334 | − | 0.285648i | \(-0.0922090\pi\) | |||||||
\(80\) | 78.1343i | 0.976679i | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 56.1521 | 0.684781 | ||||||||
\(83\) | − | 119.398i | − | 1.43853i | −0.694738 | − | 0.719263i | \(-0.744480\pi\) | ||
0.694738 | − | 0.719263i | \(-0.255520\pi\) | |||||||
\(84\) | − | 15.7817i | − | 0.187877i | ||||||
\(85\) | −117.710 | −1.38483 | ||||||||
\(86\) | 8.16319i | 0.0949208i | ||||||||
\(87\) | −8.40507 | −0.0966100 | ||||||||
\(88\) | 96.3653i | 1.09506i | ||||||||
\(89\) | 94.1931i | 1.05835i | 0.848513 | + | 0.529175i | \(0.177498\pi\) | ||||
−0.848513 | + | 0.529175i | \(0.822502\pi\) | |||||||
\(90\) | − | 18.1423i | − | 0.201581i | ||||||
\(91\) | − | 31.2101i | − | 0.342968i | ||||||
\(92\) | 3.17080 | − | 79.1449i | 0.0344652 | − | 0.860270i | ||||
\(93\) | −6.40408 | −0.0688611 | ||||||||
\(94\) | 47.5853 | 0.506227 | ||||||||
\(95\) | 62.0171 | 0.652812 | ||||||||
\(96\) | 50.9067 | 0.530278 | ||||||||
\(97\) | − | 53.8983i | − | 0.555652i | −0.960631 | − | 0.277826i | \(-0.910386\pi\) | ||
0.960631 | − | 0.277826i | \(-0.0896139\pi\) | |||||||
\(98\) | 5.22033 | 0.0532686 | ||||||||
\(99\) | 52.0769i | 0.526029i | ||||||||
\(100\) | 140.362 | 1.40362 | ||||||||
\(101\) | −26.2570 | −0.259970 | −0.129985 | − | 0.991516i | \(-0.541493\pi\) | ||||
−0.129985 | + | 0.991516i | \(0.541493\pi\) | |||||||
\(102\) | 18.7501i | 0.183824i | ||||||||
\(103\) | − | 51.4015i | − | 0.499043i | −0.968369 | − | 0.249522i | \(-0.919727\pi\) | ||
0.968369 | − | 0.249522i | \(-0.0802734\pi\) | |||||||
\(104\) | 65.4851 | 0.629665 | ||||||||
\(105\) | −37.1605 | −0.353910 | ||||||||
\(106\) | 0.198204i | 0.00186984i | ||||||||
\(107\) | − | 187.789i | − | 1.75504i | −0.479540 | − | 0.877520i | \(-0.659196\pi\) | ||
0.479540 | − | 0.877520i | \(-0.340804\pi\) | |||||||
\(108\) | 17.8947 | 0.165692 | ||||||||
\(109\) | − | 79.7085i | − | 0.731271i | −0.930758 | − | 0.365635i | \(-0.880852\pi\) | ||
0.930758 | − | 0.365635i | \(-0.119148\pi\) | |||||||
\(110\) | 104.977 | 0.954339 | ||||||||
\(111\) | 47.1287i | 0.424583i | ||||||||
\(112\) | − | 25.4929i | − | 0.227615i | ||||||
\(113\) | 1.05462i | 0.00933291i | 0.999989 | + | 0.00466645i | \(0.00148538\pi\) | ||||
−0.999989 | + | 0.00466645i | \(0.998515\pi\) | |||||||
\(114\) | − | 9.87870i | − | 0.0866553i | ||||||
\(115\) | −186.359 | − | 7.46616i | −1.62052 | − | 0.0649231i | ||||
\(116\) | −16.7118 | −0.144067 | ||||||||
\(117\) | 35.3889 | 0.302470 | ||||||||
\(118\) | −81.7474 | −0.692774 | ||||||||
\(119\) | 38.4053 | 0.322734 | ||||||||
\(120\) | − | 77.9703i | − | 0.649752i | ||||||
\(121\) | −180.334 | −1.49036 | ||||||||
\(122\) | − | 70.3166i | − | 0.576365i | ||||||
\(123\) | 130.415 | 1.06028 | ||||||||
\(124\) | −12.7333 | −0.102688 | ||||||||
\(125\) | − | 127.777i | − | 1.02222i | ||||||
\(126\) | 5.91929i | 0.0469785i | ||||||||
\(127\) | 221.052 | 1.74057 | 0.870285 | − | 0.492549i | \(-0.163935\pi\) | ||||
0.870285 | + | 0.492549i | \(0.163935\pi\) | |||||||
\(128\) | 129.961 | 1.01532 | ||||||||
\(129\) | 18.9592i | 0.146971i | ||||||||
\(130\) | − | 71.3375i | − | 0.548750i | ||||||
\(131\) | −120.544 | −0.920183 | −0.460091 | − | 0.887872i | \(-0.652183\pi\) | ||||
−0.460091 | + | 0.887872i | \(0.652183\pi\) | |||||||
\(132\) | 103.545i | 0.784429i | ||||||||
\(133\) | −20.2343 | −0.152138 | ||||||||
\(134\) | − | 37.8033i | − | 0.282114i | ||||||
\(135\) | − | 42.1360i | − | 0.312119i | ||||||
\(136\) | 80.5822i | 0.592516i | ||||||||
\(137\) | 6.29977i | 0.0459837i | 0.999736 | + | 0.0229919i | \(0.00731918\pi\) | ||||
−0.999736 | + | 0.0229919i | \(0.992681\pi\) | |||||||
\(138\) | −1.18928 | + | 29.6852i | −0.00861799 | + | 0.215110i | ||||
\(139\) | 87.3445 | 0.628378 | 0.314189 | − | 0.949361i | \(-0.398268\pi\) | ||||
0.314189 | + | 0.949361i | \(0.398268\pi\) | |||||||
\(140\) | −73.8863 | −0.527759 | ||||||||
\(141\) | 110.518 | 0.783818 | ||||||||
\(142\) | −23.9550 | −0.168697 | ||||||||
\(143\) | 204.772i | 1.43197i | ||||||||
\(144\) | 28.9062 | 0.200738 | ||||||||
\(145\) | 39.3507i | 0.271384i | ||||||||
\(146\) | 93.8927 | 0.643101 | ||||||||
\(147\) | 12.1244 | 0.0824786 | ||||||||
\(148\) | 93.7061i | 0.633150i | ||||||||
\(149\) | 75.8390i | 0.508986i | 0.967075 | + | 0.254493i | \(0.0819086\pi\) | ||||
−0.967075 | + | 0.254493i | \(0.918091\pi\) | |||||||
\(150\) | −52.6460 | −0.350973 | ||||||||
\(151\) | 17.1909 | 0.113847 | 0.0569237 | − | 0.998379i | \(-0.481871\pi\) | ||||
0.0569237 | + | 0.998379i | \(0.481871\pi\) | |||||||
\(152\) | − | 42.4557i | − | 0.279314i | ||||||
\(153\) | 43.5476i | 0.284625i | ||||||||
\(154\) | −34.2509 | −0.222409 | ||||||||
\(155\) | 29.9825i | 0.193436i | ||||||||
\(156\) | 70.3639 | 0.451051 | ||||||||
\(157\) | 173.915i | 1.10774i | 0.832603 | + | 0.553870i | \(0.186849\pi\) | ||||
−0.832603 | + | 0.553870i | \(0.813151\pi\) | |||||||
\(158\) | 33.6580i | 0.213025i | ||||||||
\(159\) | 0.460333i | 0.00289518i | ||||||||
\(160\) | − | 238.334i | − | 1.48959i | ||||||
\(161\) | 60.8035 | + | 2.43598i | 0.377662 | + | 0.0151303i | ||||
\(162\) | −6.71185 | −0.0414312 | ||||||||
\(163\) | −61.4799 | −0.377177 | −0.188589 | − | 0.982056i | \(-0.560391\pi\) | ||||
−0.188589 | + | 0.982056i | \(0.560391\pi\) | |||||||
\(164\) | 259.304 | 1.58112 | ||||||||
\(165\) | 243.813 | 1.47765 | ||||||||
\(166\) | 89.0421i | 0.536398i | ||||||||
\(167\) | 194.339 | 1.16371 | 0.581853 | − | 0.813294i | \(-0.302328\pi\) | ||||
0.581853 | + | 0.813294i | \(0.302328\pi\) | |||||||
\(168\) | 25.4394i | 0.151425i | ||||||||
\(169\) | −29.8470 | −0.176610 | ||||||||
\(170\) | 87.7837 | 0.516375 | ||||||||
\(171\) | − | 22.9436i | − | 0.134173i | ||||||
\(172\) | 37.6967i | 0.219167i | ||||||||
\(173\) | −51.7714 | −0.299257 | −0.149628 | − | 0.988742i | \(-0.547808\pi\) | ||||
−0.149628 | + | 0.988742i | \(0.547808\pi\) | |||||||
\(174\) | 6.26817 | 0.0360240 | ||||||||
\(175\) | 107.834i | 0.616192i | ||||||||
\(176\) | 167.261i | 0.950345i | ||||||||
\(177\) | −189.861 | −1.07266 | ||||||||
\(178\) | − | 70.2455i | − | 0.394638i | ||||||
\(179\) | −288.189 | −1.60999 | −0.804997 | − | 0.593279i | \(-0.797833\pi\) | ||||
−0.804997 | + | 0.593279i | \(0.797833\pi\) | |||||||
\(180\) | − | 83.7792i | − | 0.465440i | ||||||
\(181\) | 85.6046i | 0.472954i | 0.971637 | + | 0.236477i | \(0.0759927\pi\) | ||||
−0.971637 | + | 0.236477i | \(0.924007\pi\) | |||||||
\(182\) | 23.2753i | 0.127886i | ||||||||
\(183\) | − | 163.312i | − | 0.892416i | ||||||
\(184\) | −5.11119 | + | 127.578i | −0.0277782 | + | 0.693359i | ||||
\(185\) | 220.646 | 1.19268 | ||||||||
\(186\) | 4.77591 | 0.0256770 | ||||||||
\(187\) | −251.980 | −1.34749 | ||||||||
\(188\) | 219.744 | 1.16885 | ||||||||
\(189\) | 13.7477i | 0.0727393i | ||||||||
\(190\) | −46.2499 | −0.243421 | ||||||||
\(191\) | − | 33.4941i | − | 0.175362i | −0.996149 | − | 0.0876810i | \(-0.972054\pi\) | ||
0.996149 | − | 0.0876810i | \(-0.0279456\pi\) | |||||||
\(192\) | 28.7918 | 0.149957 | ||||||||
\(193\) | 185.943 | 0.963434 | 0.481717 | − | 0.876327i | \(-0.340013\pi\) | ||||
0.481717 | + | 0.876327i | \(0.340013\pi\) | |||||||
\(194\) | 40.1952i | 0.207192i | ||||||||
\(195\) | − | 165.683i | − | 0.849658i | ||||||
\(196\) | 24.1069 | 0.122994 | ||||||||
\(197\) | −192.754 | −0.978449 | −0.489224 | − | 0.872158i | \(-0.662720\pi\) | ||||
−0.489224 | + | 0.872158i | \(0.662720\pi\) | |||||||
\(198\) | − | 38.8369i | − | 0.196146i | ||||||
\(199\) | − | 85.6702i | − | 0.430503i | −0.976559 | − | 0.215252i | \(-0.930943\pi\) | ||
0.976559 | − | 0.215252i | \(-0.0690572\pi\) | |||||||
\(200\) | −226.257 | −1.13128 | ||||||||
\(201\) | − | 87.7993i | − | 0.436813i | ||||||
\(202\) | 19.5814 | 0.0969377 | ||||||||
\(203\) | − | 12.8390i | − | 0.0632461i | ||||||
\(204\) | 86.5857i | 0.424440i | ||||||||
\(205\) | − | 610.574i | − | 2.97841i | ||||||
\(206\) | 38.3332i | 0.186083i | ||||||||
\(207\) | −2.76214 | + | 68.9447i | −0.0133437 | + | 0.333066i | ||||
\(208\) | 113.662 | 0.546453 | ||||||||
\(209\) | 132.759 | 0.635210 | ||||||||
\(210\) | 27.7128 | 0.131966 | ||||||||
\(211\) | −125.041 | −0.592613 | −0.296307 | − | 0.955093i | \(-0.595755\pi\) | ||||
−0.296307 | + | 0.955093i | \(0.595755\pi\) | |||||||
\(212\) | 0.915282i | 0.00431737i | ||||||||
\(213\) | −55.6362 | −0.261203 | ||||||||
\(214\) | 140.046i | 0.654420i | ||||||||
\(215\) | 88.7631 | 0.412851 | ||||||||
\(216\) | −28.8455 | −0.133544 | ||||||||
\(217\) | − | 9.78240i | − | 0.0450802i | ||||||
\(218\) | 59.4435i | 0.272676i | ||||||||
\(219\) | 218.068 | 0.995746 | ||||||||
\(220\) | 484.774 | 2.20352 | ||||||||
\(221\) | 171.234i | 0.774812i | ||||||||
\(222\) | − | 35.1467i | − | 0.158319i | ||||||
\(223\) | 38.1190 | 0.170937 | 0.0854687 | − | 0.996341i | \(-0.472761\pi\) | ||||
0.0854687 | + | 0.996341i | \(0.472761\pi\) | |||||||
\(224\) | 77.7613i | 0.347149i | ||||||||
\(225\) | −122.272 | −0.543430 | ||||||||
\(226\) | − | 0.786493i | − | 0.00348006i | ||||||
\(227\) | 388.681i | 1.71225i | 0.516768 | + | 0.856126i | \(0.327135\pi\) | ||||
−0.516768 | + | 0.856126i | \(0.672865\pi\) | |||||||
\(228\) | − | 45.6187i | − | 0.200082i | ||||||
\(229\) | 347.374i | 1.51692i | 0.651722 | + | 0.758458i | \(0.274047\pi\) | ||||
−0.651722 | + | 0.758458i | \(0.725953\pi\) | |||||||
\(230\) | 138.980 | + | 5.56797i | 0.604259 | + | 0.0242085i | ||||
\(231\) | −79.5488 | −0.344367 | ||||||||
\(232\) | 26.9387 | 0.116115 | ||||||||
\(233\) | −382.241 | −1.64052 | −0.820260 | − | 0.571991i | \(-0.806171\pi\) | ||||
−0.820260 | + | 0.571991i | \(0.806171\pi\) | |||||||
\(234\) | −26.3917 | −0.112785 | ||||||||
\(235\) | − | 517.423i | − | 2.20180i | ||||||
\(236\) | −377.500 | −1.59958 | ||||||||
\(237\) | 78.1717i | 0.329838i | ||||||||
\(238\) | −28.6412 | −0.120341 | ||||||||
\(239\) | 331.712 | 1.38792 | 0.693958 | − | 0.720015i | \(-0.255865\pi\) | ||||
0.693958 | + | 0.720015i | \(0.255865\pi\) | |||||||
\(240\) | − | 135.333i | − | 0.563886i | ||||||
\(241\) | 265.451i | 1.10146i | 0.834685 | + | 0.550728i | \(0.185650\pi\) | ||||
−0.834685 | + | 0.550728i | \(0.814350\pi\) | |||||||
\(242\) | 134.486 | 0.555727 | ||||||||
\(243\) | −15.5885 | −0.0641500 | ||||||||
\(244\) | − | 324.714i | − | 1.33080i | ||||||
\(245\) | − | 56.7636i | − | 0.231688i | ||||||
\(246\) | −97.2583 | −0.395359 | ||||||||
\(247\) | − | 90.2165i | − | 0.365249i | ||||||
\(248\) | 20.5255 | 0.0827639 | ||||||||
\(249\) | 206.803i | 0.830534i | ||||||||
\(250\) | 95.2911i | 0.381164i | ||||||||
\(251\) | − | 229.727i | − | 0.915248i | −0.889146 | − | 0.457624i | \(-0.848701\pi\) | ||
0.889146 | − | 0.457624i | \(-0.151299\pi\) | |||||||
\(252\) | 27.3346i | 0.108471i | ||||||||
\(253\) | −398.936 | − | 15.9827i | −1.57682 | − | 0.0631726i | ||||
\(254\) | −164.852 | −0.649024 | ||||||||
\(255\) | 203.880 | 0.799530 | ||||||||
\(256\) | −30.4278 | −0.118859 | ||||||||
\(257\) | 294.228 | 1.14486 | 0.572428 | − | 0.819955i | \(-0.306001\pi\) | ||||
0.572428 | + | 0.819955i | \(0.306001\pi\) | |||||||
\(258\) | − | 14.1391i | − | 0.0548026i | ||||||
\(259\) | −71.9903 | −0.277955 | ||||||||
\(260\) | − | 329.429i | − | 1.26703i | ||||||
\(261\) | 14.5580 | 0.0557778 | ||||||||
\(262\) | 89.8969 | 0.343118 | ||||||||
\(263\) | − | 49.5368i | − | 0.188353i | −0.995556 | − | 0.0941764i | \(-0.969978\pi\) | ||
0.995556 | − | 0.0941764i | \(-0.0300218\pi\) | |||||||
\(264\) | − | 166.910i | − | 0.632233i | ||||||
\(265\) | 2.15518 | 0.00813276 | ||||||||
\(266\) | 15.0900 | 0.0567292 | ||||||||
\(267\) | − | 163.147i | − | 0.611038i | ||||||
\(268\) | − | 174.572i | − | 0.651387i | ||||||
\(269\) | −407.228 | −1.51386 | −0.756929 | − | 0.653498i | \(-0.773301\pi\) | ||||
−0.756929 | + | 0.653498i | \(0.773301\pi\) | |||||||
\(270\) | 31.4234i | 0.116383i | ||||||||
\(271\) | −136.566 | −0.503932 | −0.251966 | − | 0.967736i | \(-0.581077\pi\) | ||||
−0.251966 | + | 0.967736i | \(0.581077\pi\) | |||||||
\(272\) | 139.866i | 0.514214i | ||||||||
\(273\) | 54.0575i | 0.198013i | ||||||||
\(274\) | − | 4.69812i | − | 0.0171464i | ||||||
\(275\) | − | 707.504i | − | 2.57274i | ||||||
\(276\) | −5.49198 | + | 137.083i | −0.0198985 | + | 0.496677i | ||||
\(277\) | 108.086 | 0.390202 | 0.195101 | − | 0.980783i | \(-0.437497\pi\) | ||||
0.195101 | + | 0.980783i | \(0.437497\pi\) | |||||||
\(278\) | −65.1381 | −0.234310 | ||||||||
\(279\) | 11.0922 | 0.0397570 | ||||||||
\(280\) | 119.102 | 0.425363 | ||||||||
\(281\) | − | 256.248i | − | 0.911915i | −0.890001 | − | 0.455958i | \(-0.849297\pi\) | ||
0.890001 | − | 0.455958i | \(-0.150703\pi\) | |||||||
\(282\) | −82.4202 | −0.292270 | ||||||||
\(283\) | − | 87.9114i | − | 0.310641i | −0.987864 | − | 0.155321i | \(-0.950359\pi\) | ||
0.987864 | − | 0.155321i | \(-0.0496410\pi\) | |||||||
\(284\) | −110.622 | −0.389513 | ||||||||
\(285\) | −107.417 | −0.376901 | ||||||||
\(286\) | − | 152.711i | − | 0.533954i | ||||||
\(287\) | 199.212i | 0.694118i | ||||||||
\(288\) | −88.1730 | −0.306156 | ||||||||
\(289\) | 78.2899 | 0.270899 | ||||||||
\(290\) | − | 29.3462i | − | 0.101194i | ||||||
\(291\) | 93.3545i | 0.320806i | ||||||||
\(292\) | 433.586 | 1.48488 | ||||||||
\(293\) | 553.764i | 1.88998i | 0.327101 | + | 0.944989i | \(0.393928\pi\) | ||||
−0.327101 | + | 0.944989i | \(0.606072\pi\) | |||||||
\(294\) | −9.04187 | −0.0307547 | ||||||||
\(295\) | 888.886i | 3.01317i | ||||||||
\(296\) | − | 151.050i | − | 0.510305i | ||||||
\(297\) | − | 90.1999i | − | 0.303703i | ||||||
\(298\) | − | 56.5577i | − | 0.189791i | ||||||
\(299\) | −10.8610 | + | 271.098i | −0.0363245 | + | 0.906681i | ||||
\(300\) | −243.113 | −0.810378 | ||||||||
\(301\) | −28.9607 | −0.0962150 | ||||||||
\(302\) | −12.8203 | −0.0424514 | ||||||||
\(303\) | 45.4784 | 0.150094 | ||||||||
\(304\) | − | 73.6902i | − | 0.242402i | ||||||
\(305\) | −764.592 | −2.50686 | ||||||||
\(306\) | − | 32.4761i | − | 0.106131i | ||||||
\(307\) | 166.279 | 0.541627 | 0.270813 | − | 0.962632i | \(-0.412707\pi\) | ||||
0.270813 | + | 0.962632i | \(0.412707\pi\) | |||||||
\(308\) | −158.167 | −0.513529 | ||||||||
\(309\) | 89.0299i | 0.288123i | ||||||||
\(310\) | − | 22.3598i | − | 0.0721283i | ||||||
\(311\) | −343.603 | −1.10483 | −0.552417 | − | 0.833568i | \(-0.686294\pi\) | ||||
−0.552417 | + | 0.833568i | \(0.686294\pi\) | |||||||
\(312\) | −113.424 | −0.363537 | ||||||||
\(313\) | 314.795i | 1.00574i | 0.864363 | + | 0.502868i | \(0.167722\pi\) | ||||
−0.864363 | + | 0.502868i | \(0.832278\pi\) | |||||||
\(314\) | − | 129.699i | − | 0.413054i | ||||||
\(315\) | 64.3639 | 0.204330 | ||||||||
\(316\) | 155.429i | 0.491864i | ||||||||
\(317\) | −401.581 | −1.26682 | −0.633409 | − | 0.773818i | \(-0.718345\pi\) | ||||
−0.633409 | + | 0.773818i | \(0.718345\pi\) | |||||||
\(318\) | − | 0.343299i | − | 0.00107956i | ||||||
\(319\) | 84.2373i | 0.264067i | ||||||||
\(320\) | − | 134.797i | − | 0.421241i | ||||||
\(321\) | 325.261i | 1.01327i | ||||||||
\(322\) | −45.3449 | − | 1.81666i | −0.140823 | − | 0.00564180i | ||||
\(323\) | 111.015 | 0.343700 | ||||||||
\(324\) | −30.9946 | −0.0956622 | ||||||||
\(325\) | −480.785 | −1.47934 | ||||||||
\(326\) | 45.8493 | 0.140642 | ||||||||
\(327\) | 138.059i | 0.422199i | ||||||||
\(328\) | −417.987 | −1.27435 | ||||||||
\(329\) | 168.820i | 0.513129i | ||||||||
\(330\) | −181.826 | −0.550988 | ||||||||
\(331\) | −497.047 | −1.50165 | −0.750827 | − | 0.660499i | \(-0.770345\pi\) | ||||
−0.750827 | + | 0.660499i | \(0.770345\pi\) | |||||||
\(332\) | 411.187i | 1.23851i | ||||||||
\(333\) | − | 81.6293i | − | 0.245133i | ||||||
\(334\) | −144.930 | −0.433923 | ||||||||
\(335\) | −411.057 | −1.22704 | ||||||||
\(336\) | 44.1550i | 0.131414i | ||||||||
\(337\) | 357.790i | 1.06169i | 0.847468 | + | 0.530846i | \(0.178126\pi\) | ||||
−0.847468 | + | 0.530846i | \(0.821874\pi\) | |||||||
\(338\) | 22.2588 | 0.0658543 | ||||||||
\(339\) | − | 1.82665i | − | 0.00538836i | ||||||
\(340\) | 405.376 | 1.19228 | ||||||||
\(341\) | 64.1830i | 0.188220i | ||||||||
\(342\) | 17.1104i | 0.0500304i | ||||||||
\(343\) | 18.5203i | 0.0539949i | ||||||||
\(344\) | − | 60.7655i | − | 0.176644i | ||||||
\(345\) | 322.784 | + | 12.9318i | 0.935606 | + | 0.0374834i | ||||
\(346\) | 38.6091 | 0.111587 | ||||||||
\(347\) | 529.547 | 1.52607 | 0.763035 | − | 0.646357i | \(-0.223708\pi\) | ||||
0.763035 | + | 0.646357i | \(0.223708\pi\) | |||||||
\(348\) | 28.9457 | 0.0831773 | ||||||||
\(349\) | 324.799 | 0.930657 | 0.465328 | − | 0.885138i | \(-0.345936\pi\) | ||||
0.465328 | + | 0.885138i | \(0.345936\pi\) | |||||||
\(350\) | − | 80.4181i | − | 0.229766i | ||||||
\(351\) | −61.2954 | −0.174631 | ||||||||
\(352\) | − | 510.198i | − | 1.44942i | ||||||
\(353\) | −119.472 | −0.338447 | −0.169224 | − | 0.985578i | \(-0.554126\pi\) | ||||
−0.169224 | + | 0.985578i | \(0.554126\pi\) | |||||||
\(354\) | 141.591 | 0.399973 | ||||||||
\(355\) | 260.477i | 0.733737i | ||||||||
\(356\) | − | 324.386i | − | 0.911197i | ||||||
\(357\) | −66.5200 | −0.186331 | ||||||||
\(358\) | 214.920 | 0.600335 | ||||||||
\(359\) | 32.2603i | 0.0898616i | 0.998990 | + | 0.0449308i | \(0.0143067\pi\) | ||||
−0.998990 | + | 0.0449308i | \(0.985693\pi\) | |||||||
\(360\) | 135.048i | 0.375135i | ||||||||
\(361\) | 302.510 | 0.837979 | ||||||||
\(362\) | − | 63.8406i | − | 0.176355i | ||||||
\(363\) | 312.347 | 0.860461 | ||||||||
\(364\) | 107.483i | 0.295282i | ||||||||
\(365\) | − | 1020.95i | − | 2.79712i | ||||||
\(366\) | 121.792i | 0.332765i | ||||||||
\(367\) | 10.7331i | 0.0292455i | 0.999893 | + | 0.0146228i | \(0.00465474\pi\) | ||||
−0.999893 | + | 0.0146228i | \(0.995345\pi\) | |||||||
\(368\) | −8.87146 | + | 221.437i | −0.0241072 | + | 0.601730i | ||||
\(369\) | −225.885 | −0.612155 | ||||||||
\(370\) | −164.549 | −0.444728 | ||||||||
\(371\) | −0.703171 | −0.00189534 | ||||||||
\(372\) | 22.0546 | 0.0592867 | ||||||||
\(373\) | − | 209.138i | − | 0.560693i | −0.959899 | − | 0.280346i | \(-0.909551\pi\) | ||
0.959899 | − | 0.280346i | \(-0.0904493\pi\) | |||||||
\(374\) | 187.917 | 0.502452 | ||||||||
\(375\) | 221.316i | 0.590177i | ||||||||
\(376\) | −354.218 | −0.942069 | ||||||||
\(377\) | 57.2436 | 0.151840 | ||||||||
\(378\) | − | 10.2525i | − | 0.0271231i | ||||||
\(379\) | − | 227.488i | − | 0.600232i | −0.953903 | − | 0.300116i | \(-0.902975\pi\) | ||
0.953903 | − | 0.300116i | \(-0.0970254\pi\) | |||||||
\(380\) | −213.577 | −0.562045 | ||||||||
\(381\) | −382.874 | −1.00492 | ||||||||
\(382\) | 24.9786i | 0.0653891i | ||||||||
\(383\) | − | 358.454i | − | 0.935910i | −0.883752 | − | 0.467955i | \(-0.844991\pi\) | ||
0.883752 | − | 0.467955i | \(-0.155009\pi\) | |||||||
\(384\) | −225.099 | −0.586194 | ||||||||
\(385\) | 372.430i | 0.967351i | ||||||||
\(386\) | −138.669 | −0.359246 | ||||||||
\(387\) | − | 32.8384i | − | 0.0848537i | ||||||
\(388\) | 185.617i | 0.478394i | ||||||||
\(389\) | − | 320.157i | − | 0.823025i | −0.911404 | − | 0.411512i | \(-0.865001\pi\) | ||
0.911404 | − | 0.411512i | \(-0.134999\pi\) | |||||||
\(390\) | 123.560i | 0.316821i | ||||||||
\(391\) | −333.597 | − | 13.3650i | −0.853189 | − | 0.0341815i | ||||
\(392\) | −38.8593 | −0.0991308 | ||||||||
\(393\) | 208.788 | 0.531268 | ||||||||
\(394\) | 143.749 | 0.364844 | ||||||||
\(395\) | 365.983 | 0.926539 | ||||||||
\(396\) | − | 179.345i | − | 0.452890i | ||||||
\(397\) | 636.060 | 1.60217 | 0.801083 | − | 0.598554i | \(-0.204258\pi\) | ||||
0.801083 | + | 0.598554i | \(0.204258\pi\) | |||||||
\(398\) | 63.8894i | 0.160526i | ||||||||
\(399\) | 35.0469 | 0.0878368 | ||||||||
\(400\) | −392.713 | −0.981782 | ||||||||
\(401\) | − | 491.403i | − | 1.22544i | −0.790299 | − | 0.612721i | \(-0.790075\pi\) | ||
0.790299 | − | 0.612721i | \(-0.209925\pi\) | |||||||
\(402\) | 65.4773i | 0.162879i | ||||||||
\(403\) | 43.6157 | 0.108227 | ||||||||
\(404\) | 90.4248 | 0.223824 | ||||||||
\(405\) | 72.9818i | 0.180202i | ||||||||
\(406\) | 9.57479i | 0.0235832i | ||||||||
\(407\) | 472.334 | 1.16053 | ||||||||
\(408\) | − | 139.573i | − | 0.342089i | ||||||
\(409\) | −519.008 | −1.26897 | −0.634484 | − | 0.772936i | \(-0.718787\pi\) | ||||
−0.634484 | + | 0.772936i | \(0.718787\pi\) | |||||||
\(410\) | 455.342i | 1.11059i | ||||||||
\(411\) | − | 10.9115i | − | 0.0265487i | ||||||
\(412\) | 177.018i | 0.429656i | ||||||||
\(413\) | − | 290.017i | − | 0.702220i | ||||||
\(414\) | 2.05990 | − | 51.4162i | 0.00497560 | − | 0.124194i | ||||
\(415\) | 968.206 | 2.33303 | ||||||||
\(416\) | −346.705 | −0.833426 | ||||||||
\(417\) | −151.285 | −0.362794 | ||||||||
\(418\) | −99.0064 | −0.236857 | ||||||||
\(419\) | 287.924i | 0.687170i | 0.939122 | + | 0.343585i | \(0.111641\pi\) | ||||
−0.939122 | + | 0.343585i | \(0.888359\pi\) | |||||||
\(420\) | 127.975 | 0.304702 | ||||||||
\(421\) | − | 534.001i | − | 1.26841i | −0.773165 | − | 0.634206i | \(-0.781327\pi\) | ||
0.773165 | − | 0.634206i | \(-0.218673\pi\) | |||||||
\(422\) | 93.2509 | 0.220974 | ||||||||
\(423\) | −191.423 | −0.452538 | ||||||||
\(424\) | − | 1.47540i | − | 0.00347971i | ||||||
\(425\) | − | 591.627i | − | 1.39206i | ||||||
\(426\) | 41.4913 | 0.0973974 | ||||||||
\(427\) | 249.464 | 0.584224 | ||||||||
\(428\) | 646.717i | 1.51102i | ||||||||
\(429\) | − | 354.675i | − | 0.826749i | ||||||
\(430\) | −66.1960 | −0.153944 | ||||||||
\(431\) | 513.030i | 1.19033i | 0.803605 | + | 0.595163i | \(0.202912\pi\) | ||||
−0.803605 | + | 0.595163i | \(0.797088\pi\) | |||||||
\(432\) | −50.0670 | −0.115896 | ||||||||
\(433\) | − | 762.021i | − | 1.75986i | −0.475101 | − | 0.879931i | \(-0.657588\pi\) | ||
0.475101 | − | 0.879931i | \(-0.342412\pi\) | |||||||
\(434\) | 7.29533i | 0.0168095i | ||||||||
\(435\) | − | 68.1574i | − | 0.156684i | ||||||
\(436\) | 274.503i | 0.629595i | ||||||||
\(437\) | 175.760 | + | 7.04149i | 0.402196 | + | 0.0161133i | ||||
\(438\) | −162.627 | −0.371294 | ||||||||
\(439\) | −486.445 | −1.10808 | −0.554038 | − | 0.832492i | \(-0.686914\pi\) | ||||
−0.554038 | + | 0.832492i | \(0.686914\pi\) | |||||||
\(440\) | −781.434 | −1.77599 | ||||||||
\(441\) | −21.0000 | −0.0476190 | ||||||||
\(442\) | − | 127.699i | − | 0.288912i | ||||||
\(443\) | 568.520 | 1.28334 | 0.641670 | − | 0.766981i | \(-0.278242\pi\) | ||||
0.641670 | + | 0.766981i | \(0.278242\pi\) | |||||||
\(444\) | − | 162.304i | − | 0.365549i | ||||||
\(445\) | −763.820 | −1.71645 | ||||||||
\(446\) | −28.4277 | −0.0637392 | ||||||||
\(447\) | − | 131.357i | − | 0.293863i | ||||||
\(448\) | 43.9802i | 0.0981701i | ||||||||
\(449\) | 181.778 | 0.404850 | 0.202425 | − | 0.979298i | \(-0.435118\pi\) | ||||
0.202425 | + | 0.979298i | \(0.435118\pi\) | |||||||
\(450\) | 91.1855 | 0.202634 | ||||||||
\(451\) | − | 1307.04i | − | 2.89810i | ||||||
\(452\) | − | 3.63194i | − | 0.00803526i | ||||||
\(453\) | −29.7756 | −0.0657298 | ||||||||
\(454\) | − | 289.863i | − | 0.638465i | ||||||
\(455\) | 253.085 | 0.556232 | ||||||||
\(456\) | 73.5355i | 0.161262i | ||||||||
\(457\) | 842.429i | 1.84339i | 0.387915 | + | 0.921695i | \(0.373195\pi\) | ||||
−0.387915 | + | 0.921695i | \(0.626805\pi\) | |||||||
\(458\) | − | 259.058i | − | 0.565628i | ||||||
\(459\) | − | 75.4266i | − | 0.164328i | ||||||
\(460\) | 641.792 | + | 25.7123i | 1.39520 | + | 0.0558962i | ||||
\(461\) | −819.955 | −1.77865 | −0.889323 | − | 0.457281i | \(-0.848824\pi\) | ||||
−0.889323 | + | 0.457281i | \(0.848824\pi\) | |||||||
\(462\) | 59.3244 | 0.128408 | ||||||||
\(463\) | 598.844 | 1.29340 | 0.646700 | − | 0.762745i | \(-0.276149\pi\) | ||||
0.646700 | + | 0.762745i | \(0.276149\pi\) | |||||||
\(464\) | 46.7574 | 0.100770 | ||||||||
\(465\) | − | 51.9313i | − | 0.111680i | ||||||
\(466\) | 285.060 | 0.611718 | ||||||||
\(467\) | 688.578i | 1.47447i | 0.675636 | + | 0.737236i | \(0.263869\pi\) | ||||
−0.675636 | + | 0.737236i | \(0.736131\pi\) | |||||||
\(468\) | −121.874 | −0.260414 | ||||||||
\(469\) | 134.116 | 0.285961 | ||||||||
\(470\) | 385.874i | 0.821008i | ||||||||
\(471\) | − | 301.230i | − | 0.639554i | ||||||
\(472\) | 608.514 | 1.28923 | ||||||||
\(473\) | 190.013 | 0.401720 | ||||||||
\(474\) | − | 58.2974i | − | 0.122990i | ||||||
\(475\) | 311.706i | 0.656223i | ||||||||
\(476\) | −132.262 | −0.277861 | ||||||||
\(477\) | − | 0.797321i | − | 0.00167153i | ||||||
\(478\) | −247.378 | −0.517527 | ||||||||
\(479\) | 515.560i | 1.07633i | 0.842841 | + | 0.538163i | \(0.180882\pi\) | ||||
−0.842841 | + | 0.538163i | \(0.819118\pi\) | |||||||
\(480\) | 412.807i | 0.860014i | ||||||||
\(481\) | − | 320.975i | − | 0.667308i | ||||||
\(482\) | − | 197.963i | − | 0.410712i | ||||||
\(483\) | −105.315 | − | 4.21925i | −0.218043 | − | 0.00873550i | ||||
\(484\) | 621.041 | 1.28314 | ||||||||
\(485\) | 437.066 | 0.901166 | ||||||||
\(486\) | 11.6253 | 0.0239203 | ||||||||
\(487\) | 42.9540 | 0.0882013 | 0.0441007 | − | 0.999027i | \(-0.485958\pi\) | ||||
0.0441007 | + | 0.999027i | \(0.485958\pi\) | |||||||
\(488\) | 523.425i | 1.07259i | ||||||||
\(489\) | 106.486 | 0.217763 | ||||||||
\(490\) | 42.3321i | 0.0863920i | ||||||||
\(491\) | 16.5663 | 0.0337400 | 0.0168700 | − | 0.999858i | \(-0.494630\pi\) | ||||
0.0168700 | + | 0.999858i | \(0.494630\pi\) | |||||||
\(492\) | −449.128 | −0.912862 | ||||||||
\(493\) | 70.4406i | 0.142882i | ||||||||
\(494\) | 67.2799i | 0.136194i | ||||||||
\(495\) | −422.296 | −0.853123 | ||||||||
\(496\) | 35.6259 | 0.0718265 | ||||||||
\(497\) | − | 84.9857i | − | 0.170997i | ||||||
\(498\) | − | 154.225i | − | 0.309690i | ||||||
\(499\) | 410.775 | 0.823196 | 0.411598 | − | 0.911366i | \(-0.364971\pi\) | ||||
0.411598 | + | 0.911366i | \(0.364971\pi\) | |||||||
\(500\) | 440.044i | 0.880088i | ||||||||
\(501\) | −336.605 | −0.671866 | ||||||||
\(502\) | 171.322i | 0.341278i | ||||||||
\(503\) | 707.969i | 1.40749i | 0.710452 | + | 0.703746i | \(0.248491\pi\) | ||||
−0.710452 | + | 0.703746i | \(0.751509\pi\) | |||||||
\(504\) | − | 44.0623i | − | 0.0874251i | ||||||
\(505\) | − | 212.920i | − | 0.421624i | ||||||
\(506\) | 297.511 | + | 11.9192i | 0.587966 | + | 0.0235558i | ||||
\(507\) | 51.6966 | 0.101966 | ||||||||
\(508\) | −761.269 | −1.49856 | ||||||||
\(509\) | 928.365 | 1.82390 | 0.911950 | − | 0.410301i | \(-0.134576\pi\) | ||||
0.911950 | + | 0.410301i | \(0.134576\pi\) | |||||||
\(510\) | −152.046 | −0.298129 | ||||||||
\(511\) | 333.105i | 0.651869i | ||||||||
\(512\) | −497.151 | −0.970998 | ||||||||
\(513\) | 39.7394i | 0.0774648i | ||||||||
\(514\) | −219.424 | −0.426895 | ||||||||
\(515\) | 416.819 | 0.809357 | ||||||||
\(516\) | − | 65.2926i | − | 0.126536i | ||||||
\(517\) | − | 1107.64i | − | 2.14243i | ||||||
\(518\) | 53.6875 | 0.103644 | ||||||||
\(519\) | 89.6707 | 0.172776 | ||||||||
\(520\) | 531.025i | 1.02120i | ||||||||
\(521\) | 268.873i | 0.516070i | 0.966136 | + | 0.258035i | \(0.0830750\pi\) | ||||
−0.966136 | + | 0.258035i | \(0.916925\pi\) | |||||||
\(522\) | −10.8568 | −0.0207984 | ||||||||
\(523\) | 807.315i | 1.54362i | 0.635851 | + | 0.771812i | \(0.280649\pi\) | ||||
−0.635851 | + | 0.771812i | \(0.719351\pi\) | |||||||
\(524\) | 415.134 | 0.792241 | ||||||||
\(525\) | − | 186.773i | − | 0.355759i | ||||||
\(526\) | 36.9426i | 0.0702330i | ||||||||
\(527\) | 53.6709i | 0.101842i | ||||||||
\(528\) | − | 289.704i | − | 0.548682i | ||||||
\(529\) | −527.305 | − | 42.3189i | −0.996795 | − | 0.0799980i | ||||
\(530\) | −1.60725 | −0.00303255 | ||||||||
\(531\) | 328.848 | 0.619300 | ||||||||
\(532\) | 69.6838 | 0.130985 | ||||||||
\(533\) | −888.204 | −1.66642 | ||||||||
\(534\) | 121.669i | 0.227844i | ||||||||
\(535\) | 1522.80 | 2.84635 | ||||||||
\(536\) | 281.402i | 0.525004i | ||||||||
\(537\) | 499.158 | 0.929530 | ||||||||
\(538\) | 303.694 | 0.564488 | ||||||||
\(539\) | − | 121.513i | − | 0.225441i | ||||||
\(540\) | 145.110i | 0.268722i | ||||||||
\(541\) | −78.0316 | −0.144236 | −0.0721179 | − | 0.997396i | \(-0.522976\pi\) | ||||
−0.0721179 | + | 0.997396i | \(0.522976\pi\) | |||||||
\(542\) | 101.845 | 0.187906 | ||||||||
\(543\) | − | 148.272i | − | 0.273060i | ||||||
\(544\) | − | 426.636i | − | 0.784257i | ||||||
\(545\) | 646.363 | 1.18599 | ||||||||
\(546\) | − | 40.3140i | − | 0.0738351i | ||||||
\(547\) | 417.888 | 0.763963 | 0.381982 | − | 0.924170i | \(-0.375242\pi\) | ||||
0.381982 | + | 0.924170i | \(0.375242\pi\) | |||||||
\(548\) | − | 21.6954i | − | 0.0395902i | ||||||
\(549\) | 282.865i | 0.515237i | ||||||||
\(550\) | 527.629i | 0.959325i | ||||||||
\(551\) | − | 37.1125i | − | 0.0673548i | ||||||
\(552\) | 8.85284 | − | 220.972i | 0.0160377 | − | 0.400311i | ||||
\(553\) | −119.409 | −0.215930 | ||||||||
\(554\) | −80.6063 | −0.145499 | ||||||||
\(555\) | −382.171 | −0.688596 | ||||||||
\(556\) | −300.801 | −0.541008 | ||||||||
\(557\) | − | 895.207i | − | 1.60719i | −0.595173 | − | 0.803597i | \(-0.702917\pi\) | ||
0.595173 | − | 0.803597i | \(-0.297083\pi\) | |||||||
\(558\) | −8.27212 | −0.0148246 | ||||||||
\(559\) | − | 129.124i | − | 0.230991i | ||||||
\(560\) | 206.724 | 0.369150 | ||||||||
\(561\) | 436.443 | 0.777973 | ||||||||
\(562\) | 191.100i | 0.340035i | ||||||||
\(563\) | 537.325i | 0.954396i | 0.878796 | + | 0.477198i | \(0.158347\pi\) | ||||
−0.878796 | + | 0.477198i | \(0.841653\pi\) | |||||||
\(564\) | −380.608 | −0.674836 | ||||||||
\(565\) | −8.55199 | −0.0151363 | ||||||||
\(566\) | 65.5609i | 0.115832i | ||||||||
\(567\) | − | 23.8118i | − | 0.0419961i | ||||||
\(568\) | 178.317 | 0.313939 | ||||||||
\(569\) | 348.018i | 0.611632i | 0.952091 | + | 0.305816i | \(0.0989292\pi\) | ||||
−0.952091 | + | 0.305816i | \(0.901071\pi\) | |||||||
\(570\) | 80.1072 | 0.140539 | ||||||||
\(571\) | 660.161i | 1.15615i | 0.815984 | + | 0.578075i | \(0.196196\pi\) | ||||
−0.815984 | + | 0.578075i | \(0.803804\pi\) | |||||||
\(572\) | − | 705.202i | − | 1.23287i | ||||||
\(573\) | 58.0136i | 0.101245i | ||||||||
\(574\) | − | 148.564i | − | 0.258823i | ||||||
\(575\) | 37.5258 | − | 936.666i | 0.0652623 | − | 1.62898i | ||||
\(576\) | −49.8689 | −0.0865779 | ||||||||
\(577\) | 285.015 | 0.493960 | 0.246980 | − | 0.969021i | \(-0.420562\pi\) | ||||
0.246980 | + | 0.969021i | \(0.420562\pi\) | |||||||
\(578\) | −58.3856 | −0.101013 | ||||||||
\(579\) | −322.062 | −0.556239 | ||||||||
\(580\) | − | 135.518i | − | 0.233651i | ||||||
\(581\) | −315.897 | −0.543712 | ||||||||
\(582\) | − | 69.6201i | − | 0.119622i | ||||||
\(583\) | 4.61356 | 0.00791347 | ||||||||
\(584\) | −698.922 | −1.19678 | ||||||||
\(585\) | 286.972i | 0.490550i | ||||||||
\(586\) | − | 412.975i | − | 0.704736i | ||||||
\(587\) | −446.694 | −0.760978 | −0.380489 | − | 0.924785i | \(-0.624244\pi\) | ||||
−0.380489 | + | 0.924785i | \(0.624244\pi\) | |||||||
\(588\) | −41.7544 | −0.0710108 | ||||||||
\(589\) | − | 28.2772i | − | 0.0480088i | ||||||
\(590\) | − | 662.896i | − | 1.12355i | ||||||
\(591\) | 333.860 | 0.564908 | ||||||||
\(592\) | − | 262.177i | − | 0.442867i | ||||||
\(593\) | 19.3952 | 0.0327069 | 0.0163534 | − | 0.999866i | \(-0.494794\pi\) | ||||
0.0163534 | + | 0.999866i | \(0.494794\pi\) | |||||||
\(594\) | 67.2675i | 0.113245i | ||||||||
\(595\) | 311.432i | 0.523416i | ||||||||
\(596\) | − | 261.177i | − | 0.438217i | ||||||
\(597\) | 148.385i | 0.248551i | ||||||||
\(598\) | 8.09974 | − | 202.174i | 0.0135447 | − | 0.338084i | ||||
\(599\) | 506.473 | 0.845530 | 0.422765 | − | 0.906239i | \(-0.361059\pi\) | ||||
0.422765 | + | 0.906239i | \(0.361059\pi\) | |||||||
\(600\) | 391.888 | 0.653147 | ||||||||
\(601\) | 425.353 | 0.707742 | 0.353871 | − | 0.935294i | \(-0.384865\pi\) | ||||
0.353871 | + | 0.935294i | \(0.384865\pi\) | |||||||
\(602\) | 21.5978 | 0.0358767 | ||||||||
\(603\) | 152.073i | 0.252194i | ||||||||
\(604\) | −59.2029 | −0.0980180 | ||||||||
\(605\) | − | 1462.34i | − | 2.41710i | ||||||
\(606\) | −33.9160 | −0.0559670 | ||||||||
\(607\) | 633.633 | 1.04388 | 0.521938 | − | 0.852983i | \(-0.325209\pi\) | ||||
0.521938 | + | 0.852983i | \(0.325209\pi\) | |||||||
\(608\) | 224.778i | 0.369701i | ||||||||
\(609\) | 22.2377i | 0.0365151i | ||||||||
\(610\) | 570.203 | 0.934759 | ||||||||
\(611\) | −752.697 | −1.23191 | ||||||||
\(612\) | − | 149.971i | − | 0.245050i | ||||||
\(613\) | − | 25.9856i | − | 0.0423909i | −0.999775 | − | 0.0211954i | \(-0.993253\pi\) | ||
0.999775 | − | 0.0211954i | \(-0.00674722\pi\) | |||||||
\(614\) | −124.005 | −0.201962 | ||||||||
\(615\) | 1057.54i | 1.71959i | ||||||||
\(616\) | 254.959 | 0.413894 | ||||||||
\(617\) | − | 158.782i | − | 0.257345i | −0.991687 | − | 0.128672i | \(-0.958928\pi\) | ||
0.991687 | − | 0.128672i | \(-0.0410715\pi\) | |||||||
\(618\) | − | 66.3950i | − | 0.107435i | ||||||
\(619\) | − | 801.920i | − | 1.29551i | −0.761849 | − | 0.647755i | \(-0.775708\pi\) | ||
0.761849 | − | 0.647755i | \(-0.224292\pi\) | |||||||
\(620\) | − | 103.255i | − | 0.166540i | ||||||
\(621\) | 4.78417 | − | 119.416i | 0.00770399 | − | 0.192296i | ||||
\(622\) | 256.246 | 0.411971 | ||||||||
\(623\) | 249.212 | 0.400018 | ||||||||
\(624\) | −196.869 | −0.315495 | ||||||||
\(625\) | 17.2234 | 0.0275574 | ||||||||
\(626\) | − | 234.762i | − | 0.375019i | ||||||
\(627\) | −229.945 | −0.366739 | ||||||||
\(628\) | − | 598.936i | − | 0.953720i | ||||||
\(629\) | 394.973 | 0.627938 | ||||||||
\(630\) | −48.0000 | −0.0761906 | ||||||||
\(631\) | 755.002i | 1.19652i | 0.801303 | + | 0.598258i | \(0.204140\pi\) | ||||
−0.801303 | + | 0.598258i | \(0.795860\pi\) | |||||||
\(632\) | − | 250.545i | − | 0.396432i | ||||||
\(633\) | 216.578 | 0.342145 | ||||||||
\(634\) | 299.483 | 0.472371 | ||||||||
\(635\) | 1792.53i | 2.82289i | ||||||||
\(636\) | − | 1.58531i | − | 0.00249263i | ||||||
\(637\) | −82.5742 | −0.129630 | ||||||||
\(638\) | − | 62.8209i | − | 0.0984653i | ||||||
\(639\) | 96.3647 | 0.150805 | ||||||||
\(640\) | 1053.86i | 1.64666i | ||||||||
\(641\) | 474.103i | 0.739631i | 0.929105 | + | 0.369815i | \(0.120579\pi\) | ||||
−0.929105 | + | 0.369815i | \(0.879421\pi\) | |||||||
\(642\) | − | 242.567i | − | 0.377830i | ||||||
\(643\) | − | 92.0437i | − | 0.143147i | −0.997435 | − | 0.0715737i | \(-0.977198\pi\) | ||
0.997435 | − | 0.0715737i | \(-0.0228021\pi\) | |||||||
\(644\) | −209.398 | − | 8.38914i | −0.325152 | − | 0.0130266i | ||||
\(645\) | −153.742 | −0.238360 | ||||||||
\(646\) | −82.7907 | −0.128159 | ||||||||
\(647\) | 861.523 | 1.33156 | 0.665782 | − | 0.746146i | \(-0.268098\pi\) | ||||
0.665782 | + | 0.746146i | \(0.268098\pi\) | |||||||
\(648\) | 49.9619 | 0.0771017 | ||||||||
\(649\) | 1902.82i | 2.93193i | ||||||||
\(650\) | 358.551 | 0.551617 | ||||||||
\(651\) | 16.9436i | 0.0260270i | ||||||||
\(652\) | 211.727 | 0.324735 | ||||||||
\(653\) | 946.887 | 1.45006 | 0.725028 | − | 0.688719i | \(-0.241827\pi\) | ||||
0.725028 | + | 0.688719i | \(0.241827\pi\) | |||||||
\(654\) | − | 102.959i | − | 0.157430i | ||||||
\(655\) | − | 977.501i | − | 1.49237i | ||||||
\(656\) | −725.498 | −1.10594 | ||||||||
\(657\) | −377.706 | −0.574894 | ||||||||
\(658\) | − | 125.899i | − | 0.191336i | ||||||
\(659\) | − | 284.771i | − | 0.432126i | −0.976379 | − | 0.216063i | \(-0.930678\pi\) | ||
0.976379 | − | 0.216063i | \(-0.0693217\pi\) | |||||||
\(660\) | −839.652 | −1.27220 | ||||||||
\(661\) | 193.575i | 0.292852i | 0.989222 | + | 0.146426i | \(0.0467771\pi\) | ||||
−0.989222 | + | 0.146426i | \(0.953223\pi\) | |||||||
\(662\) | 370.678 | 0.559937 | ||||||||
\(663\) | − | 296.585i | − | 0.447338i | ||||||
\(664\) | − | 662.815i | − | 0.998216i | ||||||
\(665\) | − | 164.082i | − | 0.246740i | ||||||
\(666\) | 60.8759i | 0.0914053i | ||||||||
\(667\) | −4.46792 | + | 111.522i | −0.00669854 | + | 0.167199i | ||||
\(668\) | −669.272 | −1.00190 | ||||||||
\(669\) | −66.0241 | −0.0986907 | ||||||||
\(670\) | 306.550 | 0.457538 | ||||||||
\(671\) | −1636.75 | −2.43927 | ||||||||
\(672\) | − | 134.686i | − | 0.200426i | ||||||
\(673\) | 913.275 | 1.35702 | 0.678511 | − | 0.734590i | \(-0.262626\pi\) | ||||
0.678511 | + | 0.734590i | \(0.262626\pi\) | |||||||
\(674\) | − | 266.826i | − | 0.395884i | ||||||
\(675\) | 211.781 | 0.313750 | ||||||||
\(676\) | 102.788 | 0.152054 | ||||||||
\(677\) | 286.078i | 0.422567i | 0.977425 | + | 0.211284i | \(0.0677644\pi\) | ||||
−0.977425 | + | 0.211284i | \(0.932236\pi\) | |||||||
\(678\) | 1.36225i | 0.00200921i | ||||||||
\(679\) | −142.601 | −0.210017 | ||||||||
\(680\) | −653.448 | −0.960953 | ||||||||
\(681\) | − | 673.215i | − | 0.988569i | ||||||
\(682\) | − | 47.8652i | − | 0.0701836i | ||||||
\(683\) | 950.616 | 1.39182 | 0.695912 | − | 0.718127i | \(-0.255000\pi\) | ||||
0.695912 | + | 0.718127i | \(0.255000\pi\) | |||||||
\(684\) | 79.0140i | 0.115518i | ||||||||
\(685\) | −51.0854 | −0.0745772 | ||||||||
\(686\) | − | 13.8117i | − | 0.0201336i | ||||||
\(687\) | − | 601.669i | − | 0.875791i | ||||||
\(688\) | − | 105.470i | − | 0.153300i | ||||||
\(689\) | − | 3.13515i | − | 0.00455029i | ||||||
\(690\) | −240.720 | − | 9.64400i | −0.348869 | − | 0.0139768i | ||||
\(691\) | −742.374 | −1.07435 | −0.537174 | − | 0.843472i | \(-0.680508\pi\) | ||||
−0.537174 | + | 0.843472i | \(0.680508\pi\) | |||||||
\(692\) | 178.292 | 0.257648 | ||||||||
\(693\) | 137.783 | 0.198820 | ||||||||
\(694\) | −394.915 | −0.569042 | ||||||||
\(695\) | 708.284i | 1.01911i | ||||||||
\(696\) | −46.6592 | −0.0670391 | ||||||||
\(697\) | − | 1092.97i | − | 1.56811i | ||||||
\(698\) | −242.223 | −0.347024 | ||||||||
\(699\) | 662.061 | 0.947155 | ||||||||
\(700\) | − | 371.362i | − | 0.530517i | ||||||
\(701\) | 270.705i | 0.386169i | 0.981182 | + | 0.193085i | \(0.0618492\pi\) | ||||
−0.981182 | + | 0.193085i | \(0.938151\pi\) | |||||||
\(702\) | 45.7117 | 0.0651164 | ||||||||
\(703\) | −208.096 | −0.296012 | ||||||||
\(704\) | − | 288.557i | − | 0.409883i | ||||||
\(705\) | 896.203i | 1.27121i | ||||||||
\(706\) | 89.0974 | 0.126200 | ||||||||
\(707\) | 69.4694i | 0.0982594i | ||||||||
\(708\) | 653.850 | 0.923517 | ||||||||
\(709\) | 392.483i | 0.553572i | 0.960932 | + | 0.276786i | \(0.0892694\pi\) | ||||
−0.960932 | + | 0.276786i | \(0.910731\pi\) | |||||||
\(710\) | − | 194.253i | − | 0.273596i | ||||||
\(711\) | − | 135.397i | − | 0.190432i | ||||||
\(712\) | 522.896i | 0.734405i | ||||||||
\(713\) | −3.40425 | + | 84.9720i | −0.00477454 | + | 0.119175i | ||||
\(714\) | 49.6080 | 0.0694790 | ||||||||
\(715\) | −1660.51 | −2.32239 | ||||||||
\(716\) | 992.477 | 1.38614 | ||||||||
\(717\) | −574.542 | −0.801314 | ||||||||
\(718\) | − | 24.0585i | − | 0.0335076i | ||||||
\(719\) | 126.909 | 0.176507 | 0.0882536 | − | 0.996098i | \(-0.471871\pi\) | ||||
0.0882536 | + | 0.996098i | \(0.471871\pi\) | |||||||
\(720\) | 234.403i | 0.325560i | ||||||||
\(721\) | −135.995 | −0.188621 | ||||||||
\(722\) | −225.600 | −0.312466 | ||||||||
\(723\) | − | 459.775i | − | 0.635926i | ||||||
\(724\) | − | 294.809i | − | 0.407194i | ||||||
\(725\) | −197.781 | −0.272802 | ||||||||
\(726\) | −232.936 | −0.320849 | ||||||||
\(727\) | − | 335.134i | − | 0.460982i | −0.973075 | − | 0.230491i | \(-0.925967\pi\) | ||
0.973075 | − | 0.230491i | \(-0.0740332\pi\) | |||||||
\(728\) | − | 173.257i | − | 0.237991i | ||||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | 761.384i | 1.04299i | ||||||||
\(731\) | 158.892 | 0.217363 | ||||||||
\(732\) | 562.421i | 0.768335i | ||||||||
\(733\) | − | 839.520i | − | 1.14532i | −0.819793 | − | 0.572660i | \(-0.805911\pi\) | ||
0.819793 | − | 0.572660i | \(-0.194089\pi\) | |||||||
\(734\) | − | 8.00433i | − | 0.0109051i | ||||||
\(735\) | 98.3174i | 0.133765i | ||||||||
\(736\) | 27.0607 | − | 675.451i | 0.0367673 | − | 0.917733i | ||||
\(737\) | −879.943 | −1.19395 | ||||||||
\(738\) | 168.456 | 0.228260 | ||||||||
\(739\) | 146.458 | 0.198184 | 0.0990921 | − | 0.995078i | \(-0.468406\pi\) | ||||
0.0990921 | + | 0.995078i | \(0.468406\pi\) | |||||||
\(740\) | −759.871 | −1.02685 | ||||||||
\(741\) | 156.260i | 0.210877i | ||||||||
\(742\) | 0.524397 | 0.000706735 | ||||||||
\(743\) | − | 1227.58i | − | 1.65219i | −0.563531 | − | 0.826095i | \(-0.690558\pi\) | ||
0.563531 | − | 0.826095i | \(-0.309442\pi\) | |||||||
\(744\) | −35.5511 | −0.0477838 | ||||||||
\(745\) | −614.985 | −0.825483 | ||||||||
\(746\) | 155.967i | 0.209071i | ||||||||
\(747\) | − | 358.193i | − | 0.479509i | ||||||
\(748\) | 867.780 | 1.16013 | ||||||||
\(749\) | −496.844 | −0.663343 | ||||||||
\(750\) | − | 165.049i | − | 0.220065i | ||||||
\(751\) | − | 5.77510i | − | 0.00768987i | −0.999993 | − | 0.00384494i | \(-0.998776\pi\) | ||
0.999993 | − | 0.00384494i | \(-0.00122388\pi\) | |||||||
\(752\) | −614.814 | −0.817572 | ||||||||
\(753\) | 397.899i | 0.528419i | ||||||||
\(754\) | −42.6900 | −0.0566180 | ||||||||
\(755\) | 139.403i | 0.184640i | ||||||||
\(756\) | − | 47.3450i | − | 0.0626256i | ||||||
\(757\) | − | 451.516i | − | 0.596455i | −0.954495 | − | 0.298227i | \(-0.903605\pi\) | ||
0.954495 | − | 0.298227i | \(-0.0963954\pi\) | |||||||
\(758\) | 169.652i | 0.223815i | ||||||||
\(759\) | 690.978 | + | 27.6828i | 0.910379 | + | 0.0364727i | ||||
\(760\) | 344.277 | 0.452996 | ||||||||
\(761\) | 258.765 | 0.340033 | 0.170016 | − | 0.985441i | \(-0.445618\pi\) | ||||
0.170016 | + | 0.985441i | \(0.445618\pi\) | |||||||
\(762\) | 285.532 | 0.374714 | ||||||||
\(763\) | −210.889 | −0.276394 | ||||||||
\(764\) | 115.349i | 0.150980i | ||||||||
\(765\) | −353.131 | −0.461609 | ||||||||
\(766\) | 267.321i | 0.348983i | ||||||||
\(767\) | 1293.07 | 1.68587 | ||||||||
\(768\) | 52.7025 | 0.0686230 | ||||||||
\(769\) | 295.640i | 0.384447i | 0.981351 | + | 0.192223i | \(0.0615698\pi\) | ||||
−0.981351 | + | 0.192223i | \(0.938430\pi\) | |||||||
\(770\) | − | 277.744i | − | 0.360706i | ||||||
\(771\) | −509.618 | −0.660983 | ||||||||
\(772\) | −640.357 | −0.829478 | ||||||||
\(773\) | 1385.11i | 1.79186i | 0.444195 | + | 0.895930i | \(0.353490\pi\) | ||||
−0.444195 | + | 0.895930i | \(0.646510\pi\) | |||||||
\(774\) | 24.4896i | 0.0316403i | ||||||||
\(775\) | −150.696 | −0.194446 | ||||||||
\(776\) | − | 299.207i | − | 0.385576i | ||||||
\(777\) | 124.691 | 0.160477 | ||||||||
\(778\) | 238.760i | 0.306890i | ||||||||
\(779\) | 575.845i | 0.739211i | ||||||||
\(780\) | 570.587i | 0.731522i | ||||||||
\(781\) | 557.597i | 0.713953i | ||||||||
\(782\) | 248.784 | + | 9.96707i | 0.318138 | + | 0.0127456i | ||||
\(783\) | −25.2152 | −0.0322033 | ||||||||
\(784\) | −67.4478 | −0.0860304 | ||||||||
\(785\) | −1410.29 | −1.79655 | ||||||||
\(786\) | −155.706 | −0.198099 | ||||||||
\(787\) | − | 548.275i | − | 0.696665i | −0.937371 | − | 0.348332i | \(-0.886748\pi\) | ||
0.937371 | − | 0.348332i | \(-0.113252\pi\) | |||||||
\(788\) | 663.815 | 0.842405 | ||||||||
\(789\) | 85.8002i | 0.108746i | ||||||||
\(790\) | −272.936 | −0.345488 | ||||||||
\(791\) | 2.79026 | 0.00352751 | ||||||||
\(792\) | 289.096i | 0.365020i | ||||||||
\(793\) | 1112.25i | 1.40259i | ||||||||
\(794\) | −474.348 | −0.597416 | ||||||||
\(795\) | −3.73288 | −0.00469545 | ||||||||
\(796\) | 295.034i | 0.370646i | ||||||||
\(797\) | − | 78.2129i | − | 0.0981341i | −0.998795 | − | 0.0490670i | \(-0.984375\pi\) | ||
0.998795 | − | 0.0490670i | \(-0.0156248\pi\) | |||||||
\(798\) | −26.1366 | −0.0327526 | ||||||||
\(799\) | − | 926.225i | − | 1.15923i | ||||||
\(800\) | 1197.90 | 1.49737 | ||||||||
\(801\) | 282.579i | 0.352783i | ||||||||
\(802\) | 366.469i | 0.456944i | ||||||||
\(803\) | − | 2185.53i | − | 2.72170i | ||||||
\(804\) | 302.367i | 0.376078i | ||||||||
\(805\) | −19.7536 | + | 493.061i | −0.0245386 | + | 0.612498i | ||||
\(806\) | −32.5269 | −0.0403559 | ||||||||
\(807\) | 705.339 | 0.874026 | ||||||||
\(808\) | −145.761 | −0.180397 | ||||||||
\(809\) | 514.417 | 0.635868 | 0.317934 | − | 0.948113i | \(-0.397011\pi\) | ||||
0.317934 | + | 0.948113i | \(0.397011\pi\) | |||||||
\(810\) | − | 54.4269i | − | 0.0671938i | ||||||
\(811\) | 1305.27 | 1.60946 | 0.804731 | − | 0.593640i | \(-0.202310\pi\) | ||||
0.804731 | + | 0.593640i | \(0.202310\pi\) | |||||||
\(812\) | 44.2153i | 0.0544523i | ||||||||
\(813\) | 236.539 | 0.290945 | ||||||||
\(814\) | −352.248 | −0.432737 | ||||||||
\(815\) | − | 498.546i | − | 0.611712i | ||||||
\(816\) | − | 242.255i | − | 0.296881i | ||||||
\(817\) | −83.7144 | −0.102466 | ||||||||
\(818\) | 387.056 | 0.473173 | ||||||||
\(819\) | − | 93.6303i | − | 0.114323i | ||||||
\(820\) | 2102.72i | 2.56429i | ||||||||
\(821\) | −920.132 | −1.12075 | −0.560373 | − | 0.828240i | \(-0.689342\pi\) | ||||
−0.560373 | + | 0.828240i | \(0.689342\pi\) | |||||||
\(822\) | 8.13739i | 0.00989950i | ||||||||
\(823\) | −1234.57 | −1.50009 | −0.750045 | − | 0.661387i | \(-0.769968\pi\) | ||||
−0.750045 | + | 0.661387i | \(0.769968\pi\) | |||||||
\(824\) | − | 285.346i | − | 0.346294i | ||||||
\(825\) | 1225.43i | 1.48537i | ||||||||
\(826\) | 216.283i | 0.261844i | ||||||||
\(827\) | 830.171i | 1.00383i | 0.864916 | + | 0.501917i | \(0.167372\pi\) | ||||
−0.864916 | + | 0.501917i | \(0.832628\pi\) | |||||||
\(828\) | 9.51239 | − | 237.435i | 0.0114884 | − | 0.286757i | ||||
\(829\) | −925.808 | −1.11678 | −0.558388 | − | 0.829580i | \(-0.688580\pi\) | ||||
−0.558388 | + | 0.829580i | \(0.688580\pi\) | |||||||
\(830\) | −722.050 | −0.869940 | ||||||||
\(831\) | −187.210 | −0.225283 | ||||||||
\(832\) | −196.090 | −0.235685 | ||||||||
\(833\) | − | 101.611i | − | 0.121982i | ||||||
\(834\) | 112.822 | 0.135279 | ||||||||
\(835\) | 1575.91i | 1.88732i | ||||||||
\(836\) | −457.200 | −0.546891 | ||||||||
\(837\) | −19.2122 | −0.0229537 | ||||||||
\(838\) | − | 214.723i | − | 0.256232i | ||||||
\(839\) | − | 31.1776i | − | 0.0371604i | −0.999827 | − | 0.0185802i | \(-0.994085\pi\) | ||
0.999827 | − | 0.0185802i | \(-0.00591461\pi\) | |||||||
\(840\) | −206.290 | −0.245583 | ||||||||
\(841\) | −817.452 | −0.972000 | ||||||||
\(842\) | 398.237i | 0.472966i | ||||||||
\(843\) | 443.835i | 0.526495i | ||||||||
\(844\) | 430.623 | 0.510216 | ||||||||
\(845\) | − | 242.032i | − | 0.286429i | ||||||
\(846\) | 142.756 | 0.168742 | ||||||||
\(847\) | 477.118i | 0.563304i | ||||||||
\(848\) | − | 2.56084i | − | 0.00301985i | ||||||
\(849\) | 152.267i | 0.179349i | ||||||||
\(850\) | 441.212i | 0.519073i | ||||||||
\(851\) | 625.323 | + | 25.0524i | 0.734810 | + | 0.0294388i | ||||
\(852\) | 191.602 | 0.224885 | ||||||||
\(853\) | −253.172 | −0.296802 | −0.148401 | − | 0.988927i | \(-0.547413\pi\) | ||||
−0.148401 | + | 0.988927i | \(0.547413\pi\) | |||||||
\(854\) | −186.040 | −0.217846 | ||||||||
\(855\) | 186.051 | 0.217604 | ||||||||
\(856\) | − | 1042.48i | − | 1.21785i | ||||||
\(857\) | −35.3789 | −0.0412823 | −0.0206412 | − | 0.999787i | \(-0.506571\pi\) | ||||
−0.0206412 | + | 0.999787i | \(0.506571\pi\) | |||||||
\(858\) | 264.503i | 0.308278i | ||||||||
\(859\) | −1087.85 | −1.26642 | −0.633210 | − | 0.773980i | \(-0.718263\pi\) | ||||
−0.633210 | + | 0.773980i | \(0.718263\pi\) | |||||||
\(860\) | −305.686 | −0.355449 | ||||||||
\(861\) | − | 345.045i | − | 0.400749i | ||||||
\(862\) | − | 382.598i | − | 0.443849i | ||||||
\(863\) | −76.3577 | −0.0884794 | −0.0442397 | − | 0.999021i | \(-0.514087\pi\) | ||||
−0.0442397 | + | 0.999021i | \(0.514087\pi\) | |||||||
\(864\) | 152.720 | 0.176759 | ||||||||
\(865\) | − | 419.819i | − | 0.485339i | ||||||
\(866\) | 568.285i | 0.656218i | ||||||||
\(867\) | −135.602 | −0.156404 | ||||||||
\(868\) | 33.6890i | 0.0388122i | ||||||||
\(869\) | 783.453 | 0.901557 | ||||||||
\(870\) | 50.8291i | 0.0584243i | ||||||||
\(871\) | 597.966i | 0.686529i | ||||||||
\(872\) | − | 442.488i | − | 0.507440i | ||||||
\(873\) | − | 161.695i | − | 0.185217i | ||||||
\(874\) | −131.075 | − | 5.25127i | −0.149971 | − | 0.00600832i | ||||
\(875\) | −338.066 | −0.386362 | ||||||||
\(876\) | −750.993 | −0.857298 | ||||||||
\(877\) | −260.023 | −0.296491 | −0.148246 | − | 0.988951i | \(-0.547363\pi\) | ||||
−0.148246 | + | 0.988951i | \(0.547363\pi\) | |||||||
\(878\) | 362.772 | 0.413180 | ||||||||
\(879\) | − | 959.147i | − | 1.09118i | ||||||
\(880\) | −1356.33 | −1.54129 | ||||||||
\(881\) | − | 171.372i | − | 0.194520i | −0.995259 | − | 0.0972598i | \(-0.968992\pi\) | ||
0.995259 | − | 0.0972598i | \(-0.0310078\pi\) | |||||||
\(882\) | 15.6610 | 0.0177562 | ||||||||
\(883\) | −1303.61 | −1.47634 | −0.738168 | − | 0.674616i | \(-0.764309\pi\) | ||||
−0.738168 | + | 0.674616i | \(0.764309\pi\) | |||||||
\(884\) | − | 589.701i | − | 0.667083i | ||||||
\(885\) | − | 1539.60i | − | 1.73966i | ||||||
\(886\) | −423.980 | −0.478532 | ||||||||
\(887\) | 10.4214 | 0.0117490 | 0.00587452 | − | 0.999983i | \(-0.498130\pi\) | ||||
0.00587452 | + | 0.999983i | \(0.498130\pi\) | |||||||
\(888\) | 261.627i | 0.294625i | ||||||||
\(889\) | − | 584.850i | − | 0.657873i | ||||||
\(890\) | 569.627 | 0.640030 | ||||||||
\(891\) | 156.231i | 0.175343i | ||||||||
\(892\) | −131.276 | −0.147170 | ||||||||
\(893\) | 487.993i | 0.546464i | ||||||||
\(894\) | 97.9609i | 0.109576i | ||||||||
\(895\) | − | 2336.95i | − | 2.61112i | ||||||
\(896\) | − | 343.844i | − | 0.383754i | ||||||
\(897\) | 18.8119 | − | 469.555i | 0.0209720 | − | 0.523473i | ||||
\(898\) | −135.563 | −0.150961 | ||||||||
\(899\) | 17.9422 | 0.0199580 | ||||||||
\(900\) | 421.085 | 0.467872 | ||||||||
\(901\) | 3.85793 | 0.00428183 | ||||||||
\(902\) | 974.742i | 1.08065i | ||||||||
\(903\) | 50.1614 | 0.0555498 | ||||||||
\(904\) | 5.85453i | 0.00647625i | ||||||||
\(905\) | −694.175 | −0.767044 | ||||||||
\(906\) | 22.2055 | 0.0245093 | ||||||||
\(907\) | − | 1765.32i | − | 1.94633i | −0.230117 | − | 0.973163i | \(-0.573911\pi\) | ||
0.230117 | − | 0.973163i | \(-0.426089\pi\) | |||||||
\(908\) | − | 1338.56i | − | 1.47418i | ||||||
\(909\) | −78.7709 | −0.0866566 | ||||||||
\(910\) | −188.741 | −0.207408 | ||||||||
\(911\) | 1118.37i | 1.22763i | 0.789452 | + | 0.613813i | \(0.210365\pi\) | ||||
−0.789452 | + | 0.613813i | \(0.789635\pi\) | |||||||
\(912\) | 127.635i | 0.139951i | ||||||||
\(913\) | 2072.62 | 2.27012 | ||||||||
\(914\) | − | 628.251i | − | 0.687364i | ||||||
\(915\) | 1324.31 | 1.44734 | ||||||||
\(916\) | − | 1196.30i | − | 1.30600i | ||||||
\(917\) | 318.929i | 0.347796i | ||||||||
\(918\) | 56.2502i | 0.0612747i | ||||||||
\(919\) | − | 324.342i | − | 0.352929i | −0.984307 | − | 0.176464i | \(-0.943534\pi\) | ||
0.984307 | − | 0.176464i | \(-0.0564660\pi\) | |||||||
\(920\) | −1034.54 | − | 41.4471i | −1.12450 | − | 0.0450511i | ||||
\(921\) | −288.004 | −0.312708 | ||||||||
\(922\) | 611.491 | 0.663222 | ||||||||
\(923\) | 378.916 | 0.410527 | ||||||||
\(924\) | 273.953 | 0.296486 | ||||||||
\(925\) | 1109.00i | 1.19891i | ||||||||
\(926\) | −446.594 | −0.482283 | ||||||||
\(927\) | − | 154.204i | − | 0.166348i | ||||||
\(928\) | −142.625 | −0.153690 | ||||||||
\(929\) | 713.804 | 0.768357 | 0.384179 | − | 0.923259i | \(-0.374485\pi\) | ||||
0.384179 | + | 0.923259i | \(0.374485\pi\) | |||||||
\(930\) | 38.7283i | 0.0416433i | ||||||||
\(931\) | 53.5350i | 0.0575027i | ||||||||
\(932\) | 1316.38 | 1.41242 | ||||||||
\(933\) | 595.138 | 0.637876 | ||||||||
\(934\) | − | 513.515i | − | 0.549801i | ||||||
\(935\) | − | 2043.33i | − | 2.18538i | ||||||
\(936\) | 196.455 | 0.209888 | ||||||||
\(937\) | 1505.22i | 1.60642i | 0.595696 | + | 0.803210i | \(0.296876\pi\) | ||||
−0.595696 | + | 0.803210i | \(0.703124\pi\) | |||||||
\(938\) | −100.018 | −0.106629 | ||||||||
\(939\) | − | 545.241i | − | 0.580662i | ||||||
\(940\) | 1781.92i | 1.89566i | ||||||||
\(941\) | 295.128i | 0.313632i | 0.987628 | + | 0.156816i | \(0.0501230\pi\) | ||||
−0.987628 | + | 0.156816i | \(0.949877\pi\) | |||||||
\(942\) | 224.645i | 0.238477i | ||||||||
\(943\) | 69.3253 | − | 1730.40i | 0.0735156 | − | 1.83499i | ||||
\(944\) | 1056.20 | 1.11885 | ||||||||
\(945\) | −111.481 | −0.117970 | ||||||||
\(946\) | −141.705 | −0.149793 | ||||||||
\(947\) | −902.823 | −0.953350 | −0.476675 | − | 0.879080i | \(-0.658158\pi\) | ||||
−0.476675 | + | 0.879080i | \(0.658158\pi\) | |||||||
\(948\) | − | 269.211i | − | 0.283978i | ||||||
\(949\) | −1485.18 | −1.56499 | ||||||||
\(950\) | − | 232.458i | − | 0.244692i | ||||||
\(951\) | 695.559 | 0.731397 | ||||||||
\(952\) | 213.201 | 0.223950 | ||||||||
\(953\) | 511.572i | 0.536802i | 0.963307 | + | 0.268401i | \(0.0864952\pi\) | ||||
−0.963307 | + | 0.268401i | \(0.913505\pi\) | |||||||
\(954\) | 0.594611i | 0.000623281i | ||||||||
\(955\) | 271.607 | 0.284405 | ||||||||
\(956\) | −1142.36 | −1.19494 | ||||||||
\(957\) | − | 145.903i | − | 0.152459i | ||||||
\(958\) | − | 384.484i | − | 0.401341i | ||||||
\(959\) | 16.6676 | 0.0173802 | ||||||||
\(960\) | 233.475i | 0.243203i | ||||||||
\(961\) | −947.329 | −0.985774 | ||||||||
\(962\) | 239.371i | 0.248826i | ||||||||
\(963\) | − | 563.368i | − | 0.585014i | ||||||
\(964\) | − | 914.171i | − | 0.948310i | ||||||
\(965\) | 1507.83i | 1.56251i | ||||||||
\(966\) | 78.5396 | + | 3.14655i | 0.0813039 | + | 0.00325730i | ||||
\(967\) | −341.109 | −0.352750 | −0.176375 | − | 0.984323i | \(-0.556437\pi\) | ||||
−0.176375 | + | 0.984323i | \(0.556437\pi\) | |||||||
\(968\) | −1001.09 | −1.03419 | ||||||||
\(969\) | −192.284 | −0.198435 | ||||||||
\(970\) | −325.946 | −0.336027 | ||||||||
\(971\) | 1720.22i | 1.77160i | 0.464071 | + | 0.885798i | \(0.346388\pi\) | ||||
−0.464071 | + | 0.885798i | \(0.653612\pi\) | |||||||
\(972\) | 53.6842 | 0.0552306 | ||||||||
\(973\) | − | 231.092i | − | 0.237504i | ||||||
\(974\) | −32.0334 | −0.0328885 | ||||||||
\(975\) | 832.745 | 0.854097 | ||||||||
\(976\) | 908.506i | 0.930847i | ||||||||
\(977\) | 241.901i | 0.247596i | 0.992307 | + | 0.123798i | \(0.0395074\pi\) | ||||
−0.992307 | + | 0.123798i | \(0.960493\pi\) | |||||||
\(978\) | −79.4133 | −0.0811997 | ||||||||
\(979\) | −1635.10 | −1.67017 | ||||||||
\(980\) | 195.485i | 0.199474i | ||||||||
\(981\) | − | 239.125i | − | 0.243757i | ||||||
\(982\) | −12.3545 | −0.0125810 | ||||||||
\(983\) | − | 495.443i | − | 0.504011i | −0.967726 | − | 0.252006i | \(-0.918910\pi\) | ||
0.967726 | − | 0.252006i | \(-0.0810901\pi\) | |||||||
\(984\) | 723.975 | 0.735747 | ||||||||
\(985\) | − | 1563.06i | − | 1.58686i | ||||||
\(986\) | − | 52.5318i | − | 0.0532777i | ||||||
\(987\) | − | 292.404i | − | 0.296255i | ||||||
\(988\) | 310.691i | 0.314465i | ||||||||
\(989\) | 251.559 | + | 10.0783i | 0.254357 | + | 0.0101904i | ||||
\(990\) | 314.932 | 0.318113 | ||||||||
\(991\) | −323.525 | −0.326463 | −0.163232 | − | 0.986588i | \(-0.552192\pi\) | ||||
−0.163232 | + | 0.986588i | \(0.552192\pi\) | |||||||
\(992\) | −108.670 | −0.109547 | ||||||||
\(993\) | 860.911 | 0.866980 | ||||||||
\(994\) | 63.3790i | 0.0637616i | ||||||||
\(995\) | 694.707 | 0.698198 | ||||||||
\(996\) | − | 712.196i | − | 0.715056i | ||||||
\(997\) | −1144.19 | −1.14763 | −0.573816 | − | 0.818984i | \(-0.694538\pi\) | ||||
−0.573816 | + | 0.818984i | \(0.694538\pi\) | |||||||
\(998\) | −306.340 | −0.306954 | ||||||||
\(999\) | 141.386i | 0.141528i |
(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 | 483.3.f.a.22.21 | ✓ | 48 | |
23.22 | odd | 2 | inner | 483.3.f.a.22.22 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
483.3.f.a.22.21 | ✓ | 48 | 1.1 | even | 1 | trivial | |
483.3.f.a.22.22 | yes | 48 | 23.22 | odd | 2 | inner |