Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [24,3,Mod(19,24)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(24, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("24.19");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 24 = 2^{3} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 24.b (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: | \(0.653952634465\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.0.4752.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 3x^{2} - 6x + 6 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 19.4 | ||
Root | \(-0.866025 - 1.99551i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 24.19 |
Dual form | 24.3.b.a.19.3 |
$q$-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 \(\left(\mathbb{Z}/24\mathbb{Z}\right)^\times\).
\(n\) | \(7\) | \(13\) | \(17\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.36603 | + | 1.46081i | 0.683013 | + | 0.730406i | ||||
\(3\) | −1.73205 | −0.577350 | ||||||||
\(4\) | −0.267949 | + | 3.99102i | −0.0669873 | + | 0.997754i | ||||
\(5\) | − | 7.98203i | − | 1.59641i | −0.602388 | − | 0.798203i | \(-0.705784\pi\) | ||
0.602388 | − | 0.798203i | \(-0.294216\pi\) | |||||||
\(6\) | −2.36603 | − | 2.53020i | −0.394338 | − | 0.421700i | ||||
\(7\) | 2.13878i | 0.305540i | 0.988262 | + | 0.152770i | \(0.0488193\pi\) | ||||
−0.988262 | + | 0.152770i | \(0.951181\pi\) | |||||||
\(8\) | −6.19615 | + | 5.06040i | −0.774519 | + | 0.632551i | ||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | 11.6603 | − | 10.9037i | 1.16603 | − | 1.09037i | ||||
\(11\) | −8.00000 | −0.727273 | −0.363636 | − | 0.931541i | \(-0.618465\pi\) | ||||
−0.363636 | + | 0.931541i | \(0.618465\pi\) | |||||||
\(12\) | 0.464102 | − | 6.91264i | 0.0386751 | − | 0.576053i | ||||
\(13\) | 11.6865i | 0.898962i | 0.893290 | + | 0.449481i | \(0.148391\pi\) | ||||
−0.893290 | + | 0.449481i | \(0.851609\pi\) | |||||||
\(14\) | −3.12436 | + | 2.92163i | −0.223168 | + | 0.208688i | ||||
\(15\) | 13.8253i | 0.921686i | ||||||||
\(16\) | −15.8564 | − | 2.13878i | −0.991025 | − | 0.133674i | ||||
\(17\) | 11.8564 | 0.697436 | 0.348718 | − | 0.937228i | \(-0.386617\pi\) | ||||
0.348718 | + | 0.937228i | \(0.386617\pi\) | |||||||
\(18\) | 4.09808 | + | 4.38244i | 0.227671 | + | 0.243469i | ||||
\(19\) | 14.9282 | 0.785695 | 0.392847 | − | 0.919604i | \(-0.371490\pi\) | ||||
0.392847 | + | 0.919604i | \(0.371490\pi\) | |||||||
\(20\) | 31.8564 | + | 2.13878i | 1.59282 | + | 0.106939i | ||||
\(21\) | − | 3.70447i | − | 0.176403i | ||||||
\(22\) | −10.9282 | − | 11.6865i | −0.496737 | − | 0.531205i | ||||
\(23\) | − | 4.27756i | − | 0.185981i | −0.995667 | − | 0.0929904i | \(-0.970357\pi\) | ||
0.995667 | − | 0.0929904i | \(-0.0296426\pi\) | |||||||
\(24\) | 10.7321 | − | 8.76488i | 0.447169 | − | 0.365203i | ||||
\(25\) | −38.7128 | −1.54851 | ||||||||
\(26\) | −17.0718 | + | 15.9641i | −0.656608 | + | 0.614002i | ||||
\(27\) | −5.19615 | −0.192450 | ||||||||
\(28\) | −8.53590 | − | 0.573084i | −0.304854 | − | 0.0204673i | ||||
\(29\) | 0.573084i | 0.0197615i | 0.999951 | + | 0.00988076i | \(0.00314519\pi\) | ||||
−0.999951 | + | 0.00988076i | \(0.996855\pi\) | |||||||
\(30\) | −20.1962 | + | 18.8857i | −0.673205 | + | 0.629523i | ||||
\(31\) | − | 57.4399i | − | 1.85290i | −0.376417 | − | 0.926450i | \(-0.622844\pi\) | ||
0.376417 | − | 0.926450i | \(-0.377156\pi\) | |||||||
\(32\) | −18.5359 | − | 26.0849i | −0.579247 | − | 0.815152i | ||||
\(33\) | 13.8564 | 0.419891 | ||||||||
\(34\) | 16.1962 | + | 17.3200i | 0.476357 | + | 0.509412i | ||||
\(35\) | 17.0718 | 0.487766 | ||||||||
\(36\) | −0.803848 | + | 11.9730i | −0.0223291 | + | 0.332585i | ||||
\(37\) | 27.6506i | 0.747313i | 0.927567 | + | 0.373656i | \(0.121896\pi\) | ||||
−0.927567 | + | 0.373656i | \(0.878104\pi\) | |||||||
\(38\) | 20.3923 | + | 21.8073i | 0.536640 | + | 0.573877i | ||||
\(39\) | − | 20.2416i | − | 0.519016i | ||||||
\(40\) | 40.3923 | + | 49.4579i | 1.00981 | + | 1.23645i | ||||
\(41\) | −31.5692 | −0.769981 | −0.384990 | − | 0.922921i | \(-0.625795\pi\) | ||||
−0.384990 | + | 0.922921i | \(0.625795\pi\) | |||||||
\(42\) | 5.41154 | − | 5.06040i | 0.128846 | − | 0.120486i | ||||
\(43\) | 28.7846 | 0.669410 | 0.334705 | − | 0.942323i | \(-0.391363\pi\) | ||||
0.334705 | + | 0.942323i | \(0.391363\pi\) | |||||||
\(44\) | 2.14359 | − | 31.9281i | 0.0487180 | − | 0.725639i | ||||
\(45\) | − | 23.9461i | − | 0.532135i | ||||||
\(46\) | 6.24871 | − | 5.84325i | 0.135842 | − | 0.127027i | ||||
\(47\) | 59.5787i | 1.26763i | 0.773484 | + | 0.633816i | \(0.218512\pi\) | ||||
−0.773484 | + | 0.633816i | \(0.781488\pi\) | |||||||
\(48\) | 27.4641 | + | 3.70447i | 0.572169 | + | 0.0771765i | ||||
\(49\) | 44.4256 | 0.906645 | ||||||||
\(50\) | −52.8827 | − | 56.5522i | −1.05765 | − | 1.13104i | ||||
\(51\) | −20.5359 | −0.402665 | ||||||||
\(52\) | −46.6410 | − | 3.13139i | −0.896943 | − | 0.0602190i | ||||
\(53\) | 31.3550i | 0.591604i | 0.955249 | + | 0.295802i | \(0.0955869\pi\) | ||||
−0.955249 | + | 0.295802i | \(0.904413\pi\) | |||||||
\(54\) | −7.09808 | − | 7.59061i | −0.131446 | − | 0.140567i | ||||
\(55\) | 63.8562i | 1.16102i | ||||||||
\(56\) | −10.8231 | − | 13.2522i | −0.193269 | − | 0.236646i | ||||
\(57\) | −25.8564 | −0.453621 | ||||||||
\(58\) | −0.837169 | + | 0.782847i | −0.0144339 | + | 0.0134974i | ||||
\(59\) | −52.7846 | −0.894654 | −0.447327 | − | 0.894370i | \(-0.647624\pi\) | ||||
−0.447327 | + | 0.894370i | \(0.647624\pi\) | |||||||
\(60\) | −55.1769 | − | 3.70447i | −0.919615 | − | 0.0617412i | ||||
\(61\) | − | 59.5787i | − | 0.976700i | −0.872648 | − | 0.488350i | \(-0.837599\pi\) | ||
0.872648 | − | 0.488350i | \(-0.162401\pi\) | |||||||
\(62\) | 83.9090 | − | 78.4644i | 1.35337 | − | 1.26555i | ||||
\(63\) | 6.41634i | 0.101847i | ||||||||
\(64\) | 12.7846 | − | 62.7101i | 0.199760 | − | 0.979845i | ||||
\(65\) | 93.2820 | 1.43511 | ||||||||
\(66\) | 18.9282 | + | 20.2416i | 0.286791 | + | 0.306691i | ||||
\(67\) | −84.7846 | −1.26544 | −0.632721 | − | 0.774380i | \(-0.718062\pi\) | ||||
−0.632721 | + | 0.774380i | \(0.718062\pi\) | |||||||
\(68\) | −3.17691 | + | 47.3191i | −0.0467193 | + | 0.695869i | ||||
\(69\) | 7.40895i | 0.107376i | ||||||||
\(70\) | 23.3205 | + | 24.9387i | 0.333150 | + | 0.356267i | ||||
\(71\) | − | 42.4685i | − | 0.598147i | −0.954230 | − | 0.299074i | \(-0.903322\pi\) | ||
0.954230 | − | 0.299074i | \(-0.0966776\pi\) | |||||||
\(72\) | −18.5885 | + | 15.1812i | −0.258173 | + | 0.210850i | ||||
\(73\) | −5.42563 | −0.0743236 | −0.0371618 | − | 0.999309i | \(-0.511832\pi\) | ||||
−0.0371618 | + | 0.999309i | \(0.511832\pi\) | |||||||
\(74\) | −40.3923 | + | 37.7714i | −0.545842 | + | 0.510424i | ||||
\(75\) | 67.0526 | 0.894034 | ||||||||
\(76\) | −4.00000 | + | 59.5787i | −0.0526316 | + | 0.783930i | ||||
\(77\) | − | 17.1102i | − | 0.222211i | ||||||
\(78\) | 29.5692 | − | 27.6506i | 0.379093 | − | 0.354494i | ||||
\(79\) | 44.6072i | 0.564649i | 0.959319 | + | 0.282324i | \(0.0911054\pi\) | ||||
−0.959319 | + | 0.282324i | \(0.908895\pi\) | |||||||
\(80\) | −17.0718 | + | 126.566i | −0.213397 | + | 1.58208i | ||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | −43.1244 | − | 46.1167i | −0.525907 | − | 0.562399i | ||||
\(83\) | 67.7128 | 0.815817 | 0.407909 | − | 0.913023i | \(-0.366258\pi\) | ||||
0.407909 | + | 0.913023i | \(0.366258\pi\) | |||||||
\(84\) | 14.7846 | + | 0.992611i | 0.176007 | + | 0.0118168i | ||||
\(85\) | − | 94.6382i | − | 1.11339i | ||||||
\(86\) | 39.3205 | + | 42.0489i | 0.457215 | + | 0.488941i | ||||
\(87\) | − | 0.992611i | − | 0.0114093i | ||||||
\(88\) | 49.5692 | − | 40.4832i | 0.563287 | − | 0.460037i | ||||
\(89\) | −133.138 | −1.49594 | −0.747969 | − | 0.663734i | \(-0.768971\pi\) | ||||
−0.747969 | + | 0.663734i | \(0.768971\pi\) | |||||||
\(90\) | 34.9808 | − | 32.7110i | 0.388675 | − | 0.363455i | ||||
\(91\) | −24.9948 | −0.274669 | ||||||||
\(92\) | 17.0718 | + | 1.14617i | 0.185563 | + | 0.0124583i | ||||
\(93\) | 99.4888i | 1.06977i | ||||||||
\(94\) | −87.0333 | + | 81.3860i | −0.925886 | + | 0.865809i | ||||
\(95\) | − | 119.157i | − | 1.25429i | ||||||
\(96\) | 32.1051 | + | 45.1803i | 0.334428 | + | 0.470628i | ||||
\(97\) | 97.1384 | 1.00143 | 0.500714 | − | 0.865613i | \(-0.333071\pi\) | ||||
0.500714 | + | 0.865613i | \(0.333071\pi\) | |||||||
\(98\) | 60.6865 | + | 64.8975i | 0.619250 | + | 0.662220i | ||||
\(99\) | −24.0000 | −0.242424 | ||||||||
\(100\) | 10.3731 | − | 154.503i | 0.103731 | − | 1.54503i | ||||
\(101\) | − | 62.1370i | − | 0.615218i | −0.951513 | − | 0.307609i | \(-0.900471\pi\) | ||
0.951513 | − | 0.307609i | \(-0.0995288\pi\) | |||||||
\(102\) | −28.0526 | − | 29.9991i | −0.275025 | − | 0.294109i | ||||
\(103\) | − | 27.8041i | − | 0.269943i | −0.990849 | − | 0.134971i | \(-0.956906\pi\) | ||
0.990849 | − | 0.134971i | \(-0.0430943\pi\) | |||||||
\(104\) | −59.1384 | − | 72.4114i | −0.568639 | − | 0.696263i | ||||
\(105\) | −29.5692 | −0.281612 | ||||||||
\(106\) | −45.8038 | + | 42.8318i | −0.432112 | + | 0.404073i | ||||
\(107\) | 37.7795 | 0.353079 | 0.176540 | − | 0.984294i | \(-0.443510\pi\) | ||||
0.176540 | + | 0.984294i | \(0.443510\pi\) | |||||||
\(108\) | 1.39230 | − | 20.7379i | 0.0128917 | − | 0.192018i | ||||
\(109\) | 141.691i | 1.29992i | 0.759968 | + | 0.649960i | \(0.225214\pi\) | ||||
−0.759968 | + | 0.649960i | \(0.774786\pi\) | |||||||
\(110\) | −93.2820 | + | 87.2293i | −0.848018 | + | 0.792993i | ||||
\(111\) | − | 47.8922i | − | 0.431461i | ||||||
\(112\) | 4.57437 | − | 33.9133i | 0.0408426 | − | 0.302798i | ||||
\(113\) | −58.2872 | −0.515816 | −0.257908 | − | 0.966170i | \(-0.583033\pi\) | ||||
−0.257908 | + | 0.966170i | \(0.583033\pi\) | |||||||
\(114\) | −35.3205 | − | 37.7714i | −0.309829 | − | 0.331328i | ||||
\(115\) | −34.1436 | −0.296901 | ||||||||
\(116\) | −2.28719 | − | 0.153557i | −0.0197171 | − | 0.00132377i | ||||
\(117\) | 35.0595i | 0.299654i | ||||||||
\(118\) | −72.1051 | − | 77.1084i | −0.611060 | − | 0.653461i | ||||
\(119\) | 25.3582i | 0.213094i | ||||||||
\(120\) | −69.9615 | − | 85.6636i | −0.583013 | − | 0.713863i | ||||
\(121\) | −57.0000 | −0.471074 | ||||||||
\(122\) | 87.0333 | − | 81.3860i | 0.713388 | − | 0.667098i | ||||
\(123\) | 54.6795 | 0.444549 | ||||||||
\(124\) | 229.244 | + | 15.3910i | 1.84874 | + | 0.124121i | ||||
\(125\) | 109.456i | 0.875649i | ||||||||
\(126\) | −9.37307 | + | 8.76488i | −0.0743894 | + | 0.0695625i | ||||
\(127\) | 185.152i | 1.45789i | 0.684571 | + | 0.728946i | \(0.259990\pi\) | ||||
−0.684571 | + | 0.728946i | \(0.740010\pi\) | |||||||
\(128\) | 109.072 | − | 66.9876i | 0.852123 | − | 0.523341i | ||||
\(129\) | −49.8564 | −0.386484 | ||||||||
\(130\) | 127.426 | + | 136.268i | 0.980197 | + | 1.04821i | ||||
\(131\) | 125.359 | 0.956939 | 0.478469 | − | 0.878104i | \(-0.341192\pi\) | ||||
0.478469 | + | 0.878104i | \(0.341192\pi\) | |||||||
\(132\) | −3.71281 | + | 55.3011i | −0.0281274 | + | 0.418948i | ||||
\(133\) | 31.9281i | 0.240061i | ||||||||
\(134\) | −115.818 | − | 123.854i | −0.864313 | − | 0.924287i | ||||
\(135\) | 41.4758i | 0.307229i | ||||||||
\(136\) | −73.4641 | + | 59.9982i | −0.540177 | + | 0.441163i | ||||
\(137\) | 99.5692 | 0.726783 | 0.363391 | − | 0.931637i | \(-0.381619\pi\) | ||||
0.363391 | + | 0.931637i | \(0.381619\pi\) | |||||||
\(138\) | −10.8231 | + | 10.1208i | −0.0784282 | + | 0.0733392i | ||||
\(139\) | 177.492 | 1.27692 | 0.638461 | − | 0.769654i | \(-0.279571\pi\) | ||||
0.638461 | + | 0.769654i | \(0.279571\pi\) | |||||||
\(140\) | −4.57437 | + | 68.1338i | −0.0326741 | + | 0.486670i | ||||
\(141\) | − | 103.193i | − | 0.731867i | ||||||
\(142\) | 62.0385 | − | 58.0130i | 0.436891 | − | 0.408542i | ||||
\(143\) | − | 93.4920i | − | 0.653790i | ||||||
\(144\) | −47.5692 | − | 6.41634i | −0.330342 | − | 0.0445579i | ||||
\(145\) | 4.57437 | 0.0315474 | ||||||||
\(146\) | −7.41154 | − | 7.92582i | −0.0507640 | − | 0.0542865i | ||||
\(147\) | −76.9474 | −0.523452 | ||||||||
\(148\) | −110.354 | − | 7.40895i | −0.745634 | − | 0.0500605i | ||||
\(149\) | 87.8023i | 0.589277i | 0.955609 | + | 0.294639i | \(0.0951993\pi\) | ||||
−0.955609 | + | 0.294639i | \(0.904801\pi\) | |||||||
\(150\) | 91.5955 | + | 97.9512i | 0.610637 | + | 0.653008i | ||||
\(151\) | − | 219.066i | − | 1.45077i | −0.688345 | − | 0.725383i | \(-0.741663\pi\) | ||
0.688345 | − | 0.725383i | \(-0.258337\pi\) | |||||||
\(152\) | −92.4974 | + | 75.5427i | −0.608536 | + | 0.496992i | ||||
\(153\) | 35.5692 | 0.232479 | ||||||||
\(154\) | 24.9948 | − | 23.3730i | 0.162304 | − | 0.151773i | ||||
\(155\) | −458.487 | −2.95798 | ||||||||
\(156\) | 80.7846 | + | 5.42373i | 0.517850 | + | 0.0347675i | ||||
\(157\) | − | 253.440i | − | 1.61427i | −0.590370 | − | 0.807133i | \(-0.701018\pi\) | ||
0.590370 | − | 0.807133i | \(-0.298982\pi\) | |||||||
\(158\) | −65.1628 | + | 60.9346i | −0.412423 | + | 0.385662i | ||||
\(159\) | − | 54.3085i | − | 0.341563i | ||||||
\(160\) | −208.210 | + | 147.954i | −1.30131 | + | 0.924713i | ||||
\(161\) | 9.14875 | 0.0568245 | ||||||||
\(162\) | 12.2942 | + | 13.1473i | 0.0758903 | + | 0.0811563i | ||||
\(163\) | −102.354 | −0.627938 | −0.313969 | − | 0.949433i | \(-0.601659\pi\) | ||||
−0.313969 | + | 0.949433i | \(0.601659\pi\) | |||||||
\(164\) | 8.45895 | − | 125.993i | 0.0515789 | − | 0.768251i | ||||
\(165\) | − | 110.602i | − | 0.670317i | ||||||
\(166\) | 92.4974 | + | 98.9158i | 0.557213 | + | 0.595878i | ||||
\(167\) | 281.090i | 1.68318i | 0.540120 | + | 0.841588i | \(0.318379\pi\) | ||||
−0.540120 | + | 0.841588i | \(0.681621\pi\) | |||||||
\(168\) | 18.7461 | + | 22.9535i | 0.111584 | + | 0.136628i | ||||
\(169\) | 32.4256 | 0.191868 | ||||||||
\(170\) | 138.249 | − | 129.278i | 0.813228 | − | 0.760460i | ||||
\(171\) | 44.7846 | 0.261898 | ||||||||
\(172\) | −7.71281 | + | 114.880i | −0.0448419 | + | 0.667906i | ||||
\(173\) | − | 242.858i | − | 1.40381i | −0.712273 | − | 0.701903i | \(-0.752334\pi\) | ||
0.712273 | − | 0.701903i | \(-0.247666\pi\) | |||||||
\(174\) | 1.45002 | − | 1.35593i | 0.00833344 | − | 0.00779271i | ||||
\(175\) | − | 82.7981i | − | 0.473132i | ||||||
\(176\) | 126.851 | + | 17.1102i | 0.720746 | + | 0.0972172i | ||||
\(177\) | 91.4256 | 0.516529 | ||||||||
\(178\) | −181.870 | − | 194.490i | −1.02174 | − | 1.09264i | ||||
\(179\) | 318.354 | 1.77851 | 0.889257 | − | 0.457409i | \(-0.151222\pi\) | ||||
0.889257 | + | 0.457409i | \(0.151222\pi\) | |||||||
\(180\) | 95.5692 | + | 6.41634i | 0.530940 | + | 0.0356463i | ||||
\(181\) | 79.5132i | 0.439299i | 0.975579 | + | 0.219650i | \(0.0704914\pi\) | ||||
−0.975579 | + | 0.219650i | \(0.929509\pi\) | |||||||
\(182\) | −34.1436 | − | 36.5128i | −0.187602 | − | 0.200620i | ||||
\(183\) | 103.193i | 0.563898i | ||||||||
\(184\) | 21.6462 | + | 26.5044i | 0.117642 | + | 0.144046i | ||||
\(185\) | 220.708 | 1.19301 | ||||||||
\(186\) | −145.335 | + | 135.904i | −0.781369 | + | 0.730668i | ||||
\(187\) | −94.8513 | −0.507226 | ||||||||
\(188\) | −237.779 | − | 15.9641i | −1.26478 | − | 0.0849152i | ||||
\(189\) | − | 11.1134i | − | 0.0588012i | ||||||
\(190\) | 174.067 | − | 162.772i | 0.916140 | − | 0.856695i | ||||
\(191\) | 352.887i | 1.84758i | 0.382902 | + | 0.923789i | \(0.374925\pi\) | ||||
−0.382902 | + | 0.923789i | \(0.625075\pi\) | |||||||
\(192\) | −22.1436 | + | 108.617i | −0.115331 | + | 0.565714i | ||||
\(193\) | −284.277 | −1.47294 | −0.736469 | − | 0.676472i | \(-0.763508\pi\) | ||||
−0.736469 | + | 0.676472i | \(0.763508\pi\) | |||||||
\(194\) | 132.694 | + | 141.901i | 0.683988 | + | 0.731449i | ||||
\(195\) | −161.569 | −0.828560 | ||||||||
\(196\) | −11.9038 | + | 177.303i | −0.0607337 | + | 0.904609i | ||||
\(197\) | 75.8087i | 0.384816i | 0.981315 | + | 0.192408i | \(0.0616297\pi\) | ||||
−0.981315 | + | 0.192408i | \(0.938370\pi\) | |||||||
\(198\) | −32.7846 | − | 35.0595i | −0.165579 | − | 0.177068i | ||||
\(199\) | − | 104.186i | − | 0.523547i | −0.965129 | − | 0.261774i | \(-0.915693\pi\) | ||
0.965129 | − | 0.261774i | \(-0.0843074\pi\) | |||||||
\(200\) | 239.870 | − | 195.902i | 1.19935 | − | 0.979512i | ||||
\(201\) | 146.851 | 0.730603 | ||||||||
\(202\) | 90.7705 | − | 84.8807i | 0.449359 | − | 0.420202i | ||||
\(203\) | −1.22570 | −0.00603793 | ||||||||
\(204\) | 5.50258 | − | 81.9591i | 0.0269734 | − | 0.401760i | ||||
\(205\) | 251.986i | 1.22920i | ||||||||
\(206\) | 40.6166 | − | 37.9811i | 0.197168 | − | 0.184374i | ||||
\(207\) | − | 12.8327i | − | 0.0619936i | ||||||
\(208\) | 24.9948 | − | 185.306i | 0.120168 | − | 0.890894i | ||||
\(209\) | −119.426 | −0.571414 | ||||||||
\(210\) | −40.3923 | − | 43.1951i | −0.192344 | − | 0.205691i | ||||
\(211\) | 136.918 | 0.648900 | 0.324450 | − | 0.945903i | \(-0.394821\pi\) | ||||
0.324450 | + | 0.945903i | \(0.394821\pi\) | |||||||
\(212\) | −125.138 | − | 8.40156i | −0.590276 | − | 0.0396300i | ||||
\(213\) | 73.5575i | 0.345341i | ||||||||
\(214\) | 51.6077 | + | 55.1887i | 0.241157 | + | 0.257891i | ||||
\(215\) | − | 229.760i | − | 1.06865i | ||||||
\(216\) | 32.1962 | − | 26.2946i | 0.149056 | − | 0.121734i | ||||
\(217\) | 122.851 | 0.566135 | ||||||||
\(218\) | −206.985 | + | 193.554i | −0.949470 | + | 0.887862i | ||||
\(219\) | 9.39746 | 0.0429108 | ||||||||
\(220\) | −254.851 | − | 17.1102i | −1.15841 | − | 0.0777738i | ||||
\(221\) | 138.560i | 0.626968i | ||||||||
\(222\) | 69.9615 | − | 65.4219i | 0.315142 | − | 0.294693i | ||||
\(223\) | − | 53.1624i | − | 0.238396i | −0.992870 | − | 0.119198i | \(-0.961968\pi\) | ||
0.992870 | − | 0.119198i | \(-0.0380324\pi\) | |||||||
\(224\) | 55.7898 | − | 39.6442i | 0.249061 | − | 0.176983i | ||||
\(225\) | −116.138 | −0.516171 | ||||||||
\(226\) | −79.6218 | − | 85.1467i | −0.352309 | − | 0.376755i | ||||
\(227\) | −119.846 | −0.527956 | −0.263978 | − | 0.964529i | \(-0.585035\pi\) | ||||
−0.263978 | + | 0.964529i | \(0.585035\pi\) | |||||||
\(228\) | 6.92820 | − | 103.193i | 0.0303869 | − | 0.452602i | ||||
\(229\) | 214.103i | 0.934946i | 0.884007 | + | 0.467473i | \(0.154836\pi\) | ||||
−0.884007 | + | 0.467473i | \(0.845164\pi\) | |||||||
\(230\) | −46.6410 | − | 49.8774i | −0.202787 | − | 0.216858i | ||||
\(231\) | 29.6358i | 0.128293i | ||||||||
\(232\) | −2.90004 | − | 3.55092i | −0.0125002 | − | 0.0153057i | ||||
\(233\) | −127.436 | −0.546935 | −0.273468 | − | 0.961881i | \(-0.588171\pi\) | ||||
−0.273468 | + | 0.961881i | \(0.588171\pi\) | |||||||
\(234\) | −51.2154 | + | 47.8922i | −0.218869 | + | 0.204667i | ||||
\(235\) | 475.559 | 2.02365 | ||||||||
\(236\) | 14.1436 | − | 210.664i | 0.0599305 | − | 0.892645i | ||||
\(237\) | − | 77.2620i | − | 0.326000i | ||||||
\(238\) | −37.0436 | + | 34.6400i | −0.155646 | + | 0.145546i | ||||
\(239\) | − | 319.281i | − | 1.33590i | −0.744204 | − | 0.667952i | \(-0.767171\pi\) | ||
0.744204 | − | 0.667952i | \(-0.232829\pi\) | |||||||
\(240\) | 29.5692 | − | 219.219i | 0.123205 | − | 0.913414i | ||||
\(241\) | −247.415 | −1.02662 | −0.513310 | − | 0.858203i | \(-0.671581\pi\) | ||||
−0.513310 | + | 0.858203i | \(0.671581\pi\) | |||||||
\(242\) | −77.8634 | − | 83.2663i | −0.321750 | − | 0.344076i | ||||
\(243\) | −15.5885 | −0.0641500 | ||||||||
\(244\) | 237.779 | + | 15.9641i | 0.974506 | + | 0.0654265i | ||||
\(245\) | − | 354.607i | − | 1.44737i | ||||||
\(246\) | 74.6936 | + | 79.8765i | 0.303632 | + | 0.324701i | ||||
\(247\) | 174.459i | 0.706310i | ||||||||
\(248\) | 290.669 | + | 355.906i | 1.17205 | + | 1.43511i | ||||
\(249\) | −117.282 | −0.471012 | ||||||||
\(250\) | −159.895 | + | 149.520i | −0.639580 | + | 0.598079i | ||||
\(251\) | −214.851 | −0.855981 | −0.427991 | − | 0.903783i | \(-0.640778\pi\) | ||||
−0.427991 | + | 0.903783i | \(0.640778\pi\) | |||||||
\(252\) | −25.6077 | − | 1.71925i | −0.101618 | − | 0.00682243i | ||||
\(253\) | 34.2205i | 0.135259i | ||||||||
\(254\) | −270.473 | + | 252.923i | −1.06485 | + | 0.995759i | ||||
\(255\) | 163.918i | 0.642816i | ||||||||
\(256\) | 246.851 | + | 67.8267i | 0.964263 | + | 0.264948i | ||||
\(257\) | −84.2769 | −0.327926 | −0.163963 | − | 0.986467i | \(-0.552428\pi\) | ||||
−0.163963 | + | 0.986467i | \(0.552428\pi\) | |||||||
\(258\) | −68.1051 | − | 72.8309i | −0.263973 | − | 0.282290i | ||||
\(259\) | −59.1384 | −0.228334 | ||||||||
\(260\) | −24.9948 | + | 372.290i | −0.0961340 | + | 1.43188i | ||||
\(261\) | 1.71925i | 0.00658717i | ||||||||
\(262\) | 171.244 | + | 183.126i | 0.653601 | + | 0.698954i | ||||
\(263\) | − | 277.120i | − | 1.05369i | −0.849962 | − | 0.526844i | \(-0.823375\pi\) | ||
0.849962 | − | 0.526844i | \(-0.176625\pi\) | |||||||
\(264\) | −85.8564 | + | 70.1190i | −0.325214 | + | 0.265602i | ||||
\(265\) | 250.277 | 0.944441 | ||||||||
\(266\) | −46.6410 | + | 43.6146i | −0.175342 | + | 0.163965i | ||||
\(267\) | 230.603 | 0.863680 | ||||||||
\(268\) | 22.7180 | − | 338.377i | 0.0847685 | − | 1.26260i | ||||
\(269\) | 123.701i | 0.459855i | 0.973208 | + | 0.229927i | \(0.0738489\pi\) | ||||
−0.973208 | + | 0.229927i | \(0.926151\pi\) | |||||||
\(270\) | −60.5885 | + | 56.6571i | −0.224402 | + | 0.209841i | ||||
\(271\) | − | 197.985i | − | 0.730572i | −0.930895 | − | 0.365286i | \(-0.880971\pi\) | ||
0.930895 | − | 0.365286i | \(-0.119029\pi\) | |||||||
\(272\) | −188.000 | − | 25.3582i | −0.691176 | − | 0.0932288i | ||||
\(273\) | 43.2923 | 0.158580 | ||||||||
\(274\) | 136.014 | + | 145.452i | 0.496402 | + | 0.530847i | ||||
\(275\) | 309.703 | 1.12619 | ||||||||
\(276\) | −29.5692 | − | 1.98522i | −0.107135 | − | 0.00719283i | ||||
\(277\) | − | 247.709i | − | 0.894256i | −0.894470 | − | 0.447128i | \(-0.852447\pi\) | ||
0.894470 | − | 0.447128i | \(-0.147553\pi\) | |||||||
\(278\) | 242.459 | + | 259.283i | 0.872154 | + | 0.932673i | ||||
\(279\) | − | 172.320i | − | 0.617633i | ||||||
\(280\) | −105.779 | + | 86.3902i | −0.377784 | + | 0.308536i | ||||
\(281\) | 443.128 | 1.57697 | 0.788484 | − | 0.615055i | \(-0.210866\pi\) | ||||
0.788484 | + | 0.615055i | \(0.210866\pi\) | |||||||
\(282\) | 150.746 | − | 140.965i | 0.534561 | − | 0.499875i | ||||
\(283\) | −294.620 | −1.04106 | −0.520531 | − | 0.853843i | \(-0.674266\pi\) | ||||
−0.520531 | + | 0.853843i | \(0.674266\pi\) | |||||||
\(284\) | 169.492 | + | 11.3794i | 0.596804 | + | 0.0400683i | ||||
\(285\) | 206.387i | 0.724164i | ||||||||
\(286\) | 136.574 | − | 127.712i | 0.477533 | − | 0.446547i | ||||
\(287\) | − | 67.5196i | − | 0.235260i | ||||||
\(288\) | −55.6077 | − | 78.2546i | −0.193082 | − | 0.271717i | ||||
\(289\) | −148.426 | −0.513583 | ||||||||
\(290\) | 6.24871 | + | 6.68231i | 0.0215473 | + | 0.0230424i | ||||
\(291\) | −168.249 | −0.578174 | ||||||||
\(292\) | 1.45379 | − | 21.6538i | 0.00497874 | − | 0.0741567i | ||||
\(293\) | − | 66.7217i | − | 0.227719i | −0.993497 | − | 0.113859i | \(-0.963679\pi\) | ||
0.993497 | − | 0.113859i | \(-0.0363214\pi\) | |||||||
\(294\) | −105.112 | − | 112.406i | −0.357524 | − | 0.382333i | ||||
\(295\) | 421.328i | 1.42823i | ||||||||
\(296\) | −139.923 | − | 171.327i | −0.472713 | − | 0.578808i | ||||
\(297\) | 41.5692 | 0.139964 | ||||||||
\(298\) | −128.263 | + | 119.940i | −0.430412 | + | 0.402484i | ||||
\(299\) | 49.9897 | 0.167190 | ||||||||
\(300\) | −17.9667 | + | 267.608i | −0.0598889 | + | 0.892026i | ||||
\(301\) | 61.5639i | 0.204531i | ||||||||
\(302\) | 320.014 | − | 299.249i | 1.05965 | − | 0.990892i | ||||
\(303\) | 107.624i | 0.355196i | ||||||||
\(304\) | −236.708 | − | 31.9281i | −0.778644 | − | 0.105027i | ||||
\(305\) | −475.559 | −1.55921 | ||||||||
\(306\) | 48.5885 | + | 51.9600i | 0.158786 | + | 0.169804i | ||||
\(307\) | −524.210 | −1.70753 | −0.853763 | − | 0.520662i | \(-0.825685\pi\) | ||||
−0.853763 | + | 0.520662i | \(0.825685\pi\) | |||||||
\(308\) | 68.2872 | + | 4.58467i | 0.221712 | + | 0.0148853i | ||||
\(309\) | 48.1582i | 0.155852i | ||||||||
\(310\) | −626.305 | − | 669.764i | −2.02034 | − | 2.16053i | ||||
\(311\) | 362.057i | 1.16417i | 0.813128 | + | 0.582085i | \(0.197763\pi\) | ||||
−0.813128 | + | 0.582085i | \(0.802237\pi\) | |||||||
\(312\) | 102.431 | + | 125.420i | 0.328304 | + | 0.401988i | ||||
\(313\) | 252.277 | 0.805996 | 0.402998 | − | 0.915201i | \(-0.367968\pi\) | ||||
0.402998 | + | 0.915201i | \(0.367968\pi\) | |||||||
\(314\) | 370.228 | − | 346.205i | 1.17907 | − | 1.10256i | ||||
\(315\) | 51.2154 | 0.162589 | ||||||||
\(316\) | −178.028 | − | 11.9525i | −0.563380 | − | 0.0378243i | ||||
\(317\) | − | 80.3934i | − | 0.253607i | −0.991928 | − | 0.126803i | \(-0.959528\pi\) | ||
0.991928 | − | 0.126803i | \(-0.0404717\pi\) | |||||||
\(318\) | 79.3346 | − | 74.1868i | 0.249480 | − | 0.233292i | ||||
\(319\) | − | 4.58467i | − | 0.0143720i | ||||||
\(320\) | −500.554 | − | 102.047i | −1.56423 | − | 0.318897i | ||||
\(321\) | −65.4359 | −0.203850 | ||||||||
\(322\) | 12.4974 | + | 13.3646i | 0.0388119 | + | 0.0415050i | ||||
\(323\) | 176.995 | 0.547972 | ||||||||
\(324\) | −2.41154 | + | 35.9191i | −0.00744303 | + | 0.110862i | ||||
\(325\) | − | 452.417i | − | 1.39205i | ||||||
\(326\) | −139.818 | − | 149.520i | −0.428889 | − | 0.458650i | ||||
\(327\) | − | 245.417i | − | 0.750509i | ||||||
\(328\) | 195.608 | − | 159.753i | 0.596365 | − | 0.487052i | ||||
\(329\) | −127.426 | −0.387312 | ||||||||
\(330\) | 161.569 | − | 151.085i | 0.489604 | − | 0.457835i | ||||
\(331\) | 172.056 | 0.519808 | 0.259904 | − | 0.965635i | \(-0.416309\pi\) | ||||
0.259904 | + | 0.965635i | \(0.416309\pi\) | |||||||
\(332\) | −18.1436 | + | 270.243i | −0.0546494 | + | 0.813985i | ||||
\(333\) | 82.9517i | 0.249104i | ||||||||
\(334\) | −410.620 | + | 383.977i | −1.22940 | + | 1.14963i | ||||
\(335\) | 676.753i | 2.02016i | ||||||||
\(336\) | −7.92305 | + | 58.7396i | −0.0235805 | + | 0.174820i | ||||
\(337\) | 564.277 | 1.67441 | 0.837206 | − | 0.546888i | \(-0.184187\pi\) | ||||
0.837206 | + | 0.546888i | \(0.184187\pi\) | |||||||
\(338\) | 44.2942 | + | 47.3678i | 0.131048 | + | 0.140141i | ||||
\(339\) | 100.956 | 0.297806 | ||||||||
\(340\) | 377.703 | + | 25.3582i | 1.11089 | + | 0.0745830i | ||||
\(341\) | 459.519i | 1.34756i | ||||||||
\(342\) | 61.1769 | + | 65.4219i | 0.178880 | + | 0.191292i | ||||
\(343\) | 199.817i | 0.582556i | ||||||||
\(344\) | −178.354 | + | 145.662i | −0.518470 | + | 0.423435i | ||||
\(345\) | 59.1384 | 0.171416 | ||||||||
\(346\) | 354.771 | − | 331.751i | 1.02535 | − | 0.958817i | ||||
\(347\) | −286.123 | −0.824562 | −0.412281 | − | 0.911057i | \(-0.635268\pi\) | ||||
−0.412281 | + | 0.911057i | \(0.635268\pi\) | |||||||
\(348\) | 3.96152 | + | 0.265969i | 0.0113837 | + | 0.000764279i | ||||
\(349\) | − | 421.021i | − | 1.20636i | −0.797603 | − | 0.603182i | \(-0.793899\pi\) | ||
0.797603 | − | 0.603182i | \(-0.206101\pi\) | |||||||
\(350\) | 120.953 | − | 113.104i | 0.345579 | − | 0.323155i | ||||
\(351\) | − | 60.7249i | − | 0.173005i | ||||||
\(352\) | 148.287 | + | 208.679i | 0.421270 | + | 0.592838i | ||||
\(353\) | 429.138 | 1.21569 | 0.607845 | − | 0.794056i | \(-0.292034\pi\) | ||||
0.607845 | + | 0.794056i | \(0.292034\pi\) | |||||||
\(354\) | 124.890 | + | 133.556i | 0.352796 | + | 0.377276i | ||||
\(355\) | −338.985 | −0.954886 | ||||||||
\(356\) | 35.6743 | − | 531.358i | 0.100209 | − | 1.49258i | ||||
\(357\) | − | 43.9217i | − | 0.123030i | ||||||
\(358\) | 434.879 | + | 465.055i | 1.21475 | + | 1.29904i | ||||
\(359\) | − | 263.673i | − | 0.734465i | −0.930129 | − | 0.367233i | \(-0.880305\pi\) | ||
0.930129 | − | 0.367233i | \(-0.119695\pi\) | |||||||
\(360\) | 121.177 | + | 148.374i | 0.336603 | + | 0.412149i | ||||
\(361\) | −138.149 | −0.382684 | ||||||||
\(362\) | −116.154 | + | 108.617i | −0.320867 | + | 0.300047i | ||||
\(363\) | 98.7269 | 0.271975 | ||||||||
\(364\) | 6.69735 | − | 99.7548i | 0.0183993 | − | 0.274052i | ||||
\(365\) | 43.3075i | 0.118651i | ||||||||
\(366\) | −150.746 | + | 140.965i | −0.411875 | + | 0.385149i | ||||
\(367\) | 129.544i | 0.352981i | 0.984302 | + | 0.176491i | \(0.0564745\pi\) | ||||
−0.984302 | + | 0.176491i | \(0.943525\pi\) | |||||||
\(368\) | −9.14875 | + | 67.8267i | −0.0248607 | + | 0.184312i | ||||
\(369\) | −94.7077 | −0.256660 | ||||||||
\(370\) | 301.492 | + | 322.413i | 0.814844 | + | 0.871385i | ||||
\(371\) | −67.0615 | −0.180759 | ||||||||
\(372\) | −397.061 | − | 26.6580i | −1.06737 | − | 0.0716612i | ||||
\(373\) | 302.478i | 0.810933i | 0.914110 | + | 0.405467i | \(0.132891\pi\) | ||||
−0.914110 | + | 0.405467i | \(0.867109\pi\) | |||||||
\(374\) | −129.569 | − | 138.560i | −0.346442 | − | 0.370481i | ||||
\(375\) | − | 189.584i | − | 0.505556i | ||||||
\(376\) | −301.492 | − | 369.159i | −0.801841 | − | 0.981805i | ||||
\(377\) | −6.69735 | −0.0177649 | ||||||||
\(378\) | 16.2346 | − | 15.1812i | 0.0429488 | − | 0.0401619i | ||||
\(379\) | −116.210 | −0.306623 | −0.153312 | − | 0.988178i | \(-0.548994\pi\) | ||||
−0.153312 | + | 0.988178i | \(0.548994\pi\) | |||||||
\(380\) | 475.559 | + | 31.9281i | 1.25147 | + | 0.0840214i | ||||
\(381\) | − | 320.693i | − | 0.841715i | ||||||
\(382\) | −515.503 | + | 482.053i | −1.34948 | + | 1.26192i | ||||
\(383\) | − | 566.151i | − | 1.47820i | −0.673595 | − | 0.739101i | \(-0.735251\pi\) | ||
0.673595 | − | 0.739101i | \(-0.264749\pi\) | |||||||
\(384\) | −188.918 | + | 116.026i | −0.491974 | + | 0.302151i | ||||
\(385\) | −136.574 | −0.354739 | ||||||||
\(386\) | −388.329 | − | 415.275i | −1.00603 | − | 1.07584i | ||||
\(387\) | 86.3538 | 0.223137 | ||||||||
\(388\) | −26.0282 | + | 387.681i | −0.0670829 | + | 0.999178i | ||||
\(389\) | 350.104i | 0.900011i | 0.893026 | + | 0.450006i | \(0.148578\pi\) | ||||
−0.893026 | + | 0.450006i | \(0.851422\pi\) | |||||||
\(390\) | −220.708 | − | 236.022i | −0.565917 | − | 0.605186i | ||||
\(391\) | − | 50.7165i | − | 0.129710i | ||||||
\(392\) | −275.268 | + | 224.812i | −0.702214 | + | 0.573499i | ||||
\(393\) | −217.128 | −0.552489 | ||||||||
\(394\) | −110.742 | + | 103.557i | −0.281072 | + | 0.262834i | ||||
\(395\) | 356.056 | 0.901408 | ||||||||
\(396\) | 6.43078 | − | 95.7844i | 0.0162393 | − | 0.241880i | ||||
\(397\) | − | 544.149i | − | 1.37065i | −0.728236 | − | 0.685326i | \(-0.759660\pi\) | ||
0.728236 | − | 0.685326i | \(-0.240340\pi\) | |||||||
\(398\) | 152.196 | − | 142.321i | 0.382402 | − | 0.357589i | ||||
\(399\) | − | 55.3011i | − | 0.138599i | ||||||
\(400\) | 613.846 | + | 82.7981i | 1.53462 | + | 0.206995i | ||||
\(401\) | −296.431 | −0.739229 | −0.369614 | − | 0.929185i | \(-0.620510\pi\) | ||||
−0.369614 | + | 0.929185i | \(0.620510\pi\) | |||||||
\(402\) | 200.603 | + | 214.522i | 0.499011 | + | 0.533637i | ||||
\(403\) | 671.272 | 1.66569 | ||||||||
\(404\) | 247.990 | + | 16.6496i | 0.613836 | + | 0.0412118i | ||||
\(405\) | − | 71.8383i | − | 0.177378i | ||||||
\(406\) | −1.67434 | − | 1.79052i | −0.00412398 | − | 0.00441014i | ||||
\(407\) | − | 221.205i | − | 0.543500i | ||||||
\(408\) | 127.244 | − | 103.920i | 0.311871 | − | 0.254706i | ||||
\(409\) | −247.415 | −0.604927 | −0.302464 | − | 0.953161i | \(-0.597809\pi\) | ||||
−0.302464 | + | 0.953161i | \(0.597809\pi\) | |||||||
\(410\) | −368.105 | + | 344.220i | −0.897817 | + | 0.839561i | ||||
\(411\) | −172.459 | −0.419608 | ||||||||
\(412\) | 110.967 | + | 7.45009i | 0.269337 | + | 0.0180827i | ||||
\(413\) | − | 112.895i | − | 0.273353i | ||||||
\(414\) | 18.7461 | − | 17.5298i | 0.0452805 | − | 0.0423424i | ||||
\(415\) | − | 540.486i | − | 1.30238i | ||||||
\(416\) | 304.841 | − | 216.620i | 0.732791 | − | 0.520721i | ||||
\(417\) | −307.426 | −0.737232 | ||||||||
\(418\) | −163.138 | − | 174.459i | −0.390283 | − | 0.417365i | ||||
\(419\) | −92.1333 | −0.219889 | −0.109944 | − | 0.993938i | \(-0.535067\pi\) | ||||
−0.109944 | + | 0.993938i | \(0.535067\pi\) | |||||||
\(420\) | 7.92305 | − | 118.011i | 0.0188644 | − | 0.280979i | ||||
\(421\) | 445.540i | 1.05829i | 0.848531 | + | 0.529145i | \(0.177487\pi\) | ||||
−0.848531 | + | 0.529145i | \(0.822513\pi\) | |||||||
\(422\) | 187.033 | + | 200.011i | 0.443207 | + | 0.473961i | ||||
\(423\) | 178.736i | 0.422544i | ||||||||
\(424\) | −158.669 | − | 194.281i | −0.374220 | − | 0.458209i | ||||
\(425\) | −458.995 | −1.07999 | ||||||||
\(426\) | −107.454 | + | 100.481i | −0.252239 | + | 0.235872i | ||||
\(427\) | 127.426 | 0.298421 | ||||||||
\(428\) | −10.1230 | + | 150.778i | −0.0236518 | + | 0.352286i | ||||
\(429\) | 161.933i | 0.377466i | ||||||||
\(430\) | 335.636 | − | 313.857i | 0.780549 | − | 0.729901i | ||||
\(431\) | 186.677i | 0.433125i | 0.976269 | + | 0.216563i | \(0.0694845\pi\) | ||||
−0.976269 | + | 0.216563i | \(0.930515\pi\) | |||||||
\(432\) | 82.3923 | + | 11.1134i | 0.190723 | + | 0.0257255i | ||||
\(433\) | 291.128 | 0.672351 | 0.336176 | − | 0.941799i | \(-0.390866\pi\) | ||||
0.336176 | + | 0.941799i | \(0.390866\pi\) | |||||||
\(434\) | 167.818 | + | 179.463i | 0.386677 | + | 0.413509i | ||||
\(435\) | −7.92305 | −0.0182139 | ||||||||
\(436\) | −565.492 | − | 37.9661i | −1.29700 | − | 0.0870782i | ||||
\(437\) | − | 63.8562i | − | 0.146124i | ||||||
\(438\) | 12.8372 | + | 13.7279i | 0.0293086 | + | 0.0313423i | ||||
\(439\) | − | 87.6899i | − | 0.199749i | −0.995000 | − | 0.0998746i | \(-0.968156\pi\) | ||
0.995000 | − | 0.0998746i | \(-0.0318442\pi\) | |||||||
\(440\) | −323.138 | − | 395.663i | −0.734406 | − | 0.899234i | ||||
\(441\) | 133.277 | 0.302215 | ||||||||
\(442\) | −202.410 | + | 189.276i | −0.457942 | + | 0.428227i | ||||
\(443\) | 20.7077 | 0.0467441 | 0.0233721 | − | 0.999727i | \(-0.492560\pi\) | ||||
0.0233721 | + | 0.999727i | \(0.492560\pi\) | |||||||
\(444\) | 191.138 | + | 12.8327i | 0.430492 | + | 0.0289024i | ||||
\(445\) | 1062.72i | 2.38812i | ||||||||
\(446\) | 77.6603 | − | 72.6211i | 0.174126 | − | 0.162828i | ||||
\(447\) | − | 152.078i | − | 0.340219i | ||||||
\(448\) | 134.123 | + | 27.3435i | 0.299382 | + | 0.0610345i | ||||
\(449\) | 584.410 | 1.30158 | 0.650791 | − | 0.759257i | \(-0.274437\pi\) | ||||
0.650791 | + | 0.759257i | \(0.274437\pi\) | |||||||
\(450\) | −158.648 | − | 169.657i | −0.352551 | − | 0.377015i | ||||
\(451\) | 252.554 | 0.559986 | ||||||||
\(452\) | 15.6180 | − | 232.625i | 0.0345531 | − | 0.514657i | ||||
\(453\) | 379.433i | 0.837600i | ||||||||
\(454\) | −163.713 | − | 175.073i | −0.360601 | − | 0.385623i | ||||
\(455\) | 199.510i | 0.438483i | ||||||||
\(456\) | 160.210 | − | 130.844i | 0.351338 | − | 0.286938i | ||||
\(457\) | −269.692 | −0.590136 | −0.295068 | − | 0.955476i | \(-0.595342\pi\) | ||||
−0.295068 | + | 0.955476i | \(0.595342\pi\) | |||||||
\(458\) | −312.764 | + | 292.470i | −0.682891 | + | 0.638580i | ||||
\(459\) | −61.6077 | −0.134222 | ||||||||
\(460\) | 9.14875 | − | 136.268i | 0.0198886 | − | 0.296234i | ||||
\(461\) | 44.4948i | 0.0965181i | 0.998835 | + | 0.0482590i | \(0.0153673\pi\) | ||||
−0.998835 | + | 0.0482590i | \(0.984633\pi\) | |||||||
\(462\) | −43.2923 | + | 40.4832i | −0.0937064 | + | 0.0876261i | ||||
\(463\) | 611.065i | 1.31980i | 0.751355 | + | 0.659898i | \(0.229400\pi\) | ||||
−0.751355 | + | 0.659898i | \(0.770600\pi\) | |||||||
\(464\) | 1.22570 | − | 9.08705i | 0.00264159 | − | 0.0195842i | ||||
\(465\) | 794.123 | 1.70779 | ||||||||
\(466\) | −174.081 | − | 186.160i | −0.373564 | − | 0.399485i | ||||
\(467\) | 146.410 | 0.313512 | 0.156756 | − | 0.987637i | \(-0.449896\pi\) | ||||
0.156756 | + | 0.987637i | \(0.449896\pi\) | |||||||
\(468\) | −139.923 | − | 9.39417i | −0.298981 | − | 0.0200730i | ||||
\(469\) | − | 181.336i | − | 0.386643i | ||||||
\(470\) | 649.626 | + | 694.703i | 1.38218 | + | 1.47809i | ||||
\(471\) | 438.971i | 0.931997i | ||||||||
\(472\) | 327.061 | − | 267.111i | 0.692927 | − | 0.565914i | ||||
\(473\) | −230.277 | −0.486843 | ||||||||
\(474\) | 112.865 | − | 105.542i | 0.238113 | − | 0.222662i | ||||
\(475\) | −577.913 | −1.21666 | ||||||||
\(476\) | −101.205 | − | 6.79472i | −0.212616 | − | 0.0142746i | ||||
\(477\) | 94.0651i | 0.197201i | ||||||||
\(478\) | 466.410 | − | 436.146i | 0.975753 | − | 0.912440i | ||||
\(479\) | 191.876i | 0.400576i | 0.979737 | + | 0.200288i | \(0.0641878\pi\) | ||||
−0.979737 | + | 0.200288i | \(0.935812\pi\) | |||||||
\(480\) | 360.631 | − | 256.264i | 0.751314 | − | 0.533883i | ||||
\(481\) | −323.138 | −0.671805 | ||||||||
\(482\) | −337.976 | − | 361.428i | −0.701194 | − | 0.749850i | ||||
\(483\) | −15.8461 | −0.0328077 | ||||||||
\(484\) | 15.2731 | − | 227.488i | 0.0315560 | − | 0.470016i | ||||
\(485\) | − | 775.362i | − | 1.59868i | ||||||
\(486\) | −21.2942 | − | 22.7718i | −0.0438153 | − | 0.0468556i | ||||
\(487\) | − | 610.758i | − | 1.25412i | −0.778969 | − | 0.627062i | \(-0.784257\pi\) | ||
0.778969 | − | 0.627062i | \(-0.215743\pi\) | |||||||
\(488\) | 301.492 | + | 369.159i | 0.617812 | + | 0.756473i | ||||
\(489\) | 177.282 | 0.362540 | ||||||||
\(490\) | 518.014 | − | 484.402i | 1.05717 | − | 0.988575i | ||||
\(491\) | −142.354 | −0.289926 | −0.144963 | − | 0.989437i | \(-0.546306\pi\) | ||||
−0.144963 | + | 0.989437i | \(0.546306\pi\) | |||||||
\(492\) | −14.6513 | + | 218.227i | −0.0297791 | + | 0.443550i | ||||
\(493\) | 6.79472i | 0.0137824i | ||||||||
\(494\) | −254.851 | + | 238.315i | −0.515893 | + | 0.482419i | ||||
\(495\) | 191.569i | 0.387008i | ||||||||
\(496\) | −122.851 | + | 910.791i | −0.247684 | + | 1.83627i | ||||
\(497\) | 90.8306 | 0.182758 | ||||||||
\(498\) | −160.210 | − | 171.327i | −0.321707 | − | 0.344030i | ||||
\(499\) | 91.3693 | 0.183105 | 0.0915524 | − | 0.995800i | \(-0.470817\pi\) | ||||
0.0915524 | + | 0.995800i | \(0.470817\pi\) | |||||||
\(500\) | −436.841 | − | 29.3287i | −0.873682 | − | 0.0586573i | ||||
\(501\) | − | 486.863i | − | 0.971782i | ||||||
\(502\) | −293.492 | − | 313.857i | −0.584646 | − | 0.625214i | ||||
\(503\) | 230.067i | 0.457389i | 0.973498 | + | 0.228695i | \(0.0734457\pi\) | ||||
−0.973498 | + | 0.228695i | \(0.926554\pi\) | |||||||
\(504\) | −32.4693 | − | 39.7566i | −0.0644231 | − | 0.0788821i | ||||
\(505\) | −495.979 | −0.982137 | ||||||||
\(506\) | −49.9897 | + | 46.7460i | −0.0987939 | + | 0.0923834i | ||||
\(507\) | −56.1628 | −0.110775 | ||||||||
\(508\) | −738.946 | − | 49.6114i | −1.45462 | − | 0.0976603i | ||||
\(509\) | − | 527.387i | − | 1.03612i | −0.855343 | − | 0.518062i | \(-0.826654\pi\) | ||
0.855343 | − | 0.518062i | \(-0.173346\pi\) | |||||||
\(510\) | −239.454 | + | 223.916i | −0.469517 | + | 0.439052i | ||||
\(511\) | − | 11.6042i | − | 0.0227088i | ||||||
\(512\) | 238.123 | + | 453.256i | 0.465084 | + | 0.885267i | ||||
\(513\) | −77.5692 | −0.151207 | ||||||||
\(514\) | −115.124 | − | 123.113i | −0.223977 | − | 0.239519i | ||||
\(515\) | −221.933 | −0.430939 | ||||||||
\(516\) | 13.3590 | − | 198.978i | 0.0258895 | − | 0.385616i | ||||
\(517\) | − | 476.630i | − | 0.921914i | ||||||
\(518\) | −80.7846 | − | 86.3902i | −0.155955 | − | 0.166776i | ||||
\(519\) | 420.643i | 0.810487i | ||||||||
\(520\) | −577.990 | + | 472.045i | −1.11152 | + | 0.907779i | ||||
\(521\) | 191.856 | 0.368246 | 0.184123 | − | 0.982903i | \(-0.441055\pi\) | ||||
0.184123 | + | 0.982903i | \(0.441055\pi\) | |||||||
\(522\) | −2.51151 | + | 2.34854i | −0.00481131 | + | 0.00449912i | ||||
\(523\) | 105.492 | 0.201706 | 0.100853 | − | 0.994901i | \(-0.467843\pi\) | ||||
0.100853 | + | 0.994901i | \(0.467843\pi\) | |||||||
\(524\) | −33.5898 | + | 500.310i | −0.0641027 | + | 0.954789i | ||||
\(525\) | 143.411i | 0.273163i | ||||||||
\(526\) | 404.820 | − | 378.553i | 0.769620 | − | 0.719682i | ||||
\(527\) | − | 681.031i | − | 1.29228i | ||||||
\(528\) | −219.713 | − | 29.6358i | −0.416123 | − | 0.0561284i | ||||
\(529\) | 510.703 | 0.965411 | ||||||||
\(530\) | 341.885 | + | 365.608i | 0.645065 | + | 0.689826i | ||||
\(531\) | −158.354 | −0.298218 | ||||||||
\(532\) | −127.426 | − | 8.55511i | −0.239522 | − | 0.0160810i | ||||
\(533\) | − | 368.934i | − | 0.692184i | ||||||
\(534\) | 315.009 | + | 336.867i | 0.589904 | + | 0.630837i | ||||
\(535\) | − | 301.557i | − | 0.563658i | ||||||
\(536\) | 525.338 | − | 429.044i | 0.980109 | − | 0.800456i | ||||
\(537\) | −551.405 | −1.02682 | ||||||||
\(538\) | −180.704 | + | 168.979i | −0.335881 | + | 0.314087i | ||||
\(539\) | −355.405 | −0.659378 | ||||||||
\(540\) | −165.531 | − | 11.1134i | −0.306538 | − | 0.0205804i | ||||
\(541\) | 459.744i | 0.849804i | 0.905239 | + | 0.424902i | \(0.139691\pi\) | ||||
−0.905239 | + | 0.424902i | \(0.860309\pi\) | |||||||
\(542\) | 289.219 | − | 270.453i | 0.533615 | − | 0.498990i | ||||
\(543\) | − | 137.721i | − | 0.253630i | ||||||
\(544\) | −219.769 | − | 309.273i | −0.403987 | − | 0.568516i | ||||
\(545\) | 1130.98 | 2.07520 | ||||||||
\(546\) | 59.1384 | + | 63.2420i | 0.108312 | + | 0.115828i | ||||
\(547\) | 67.3693 | 0.123161 | 0.0615807 | − | 0.998102i | \(-0.480386\pi\) | ||||
0.0615807 | + | 0.998102i | \(0.480386\pi\) | |||||||
\(548\) | −26.6795 | + | 397.382i | −0.0486852 | + | 0.725150i | ||||
\(549\) | − | 178.736i | − | 0.325567i | ||||||
\(550\) | 423.061 | + | 452.417i | 0.769203 | + | 0.822577i | ||||
\(551\) | 8.55511i | 0.0155265i | ||||||||
\(552\) | −37.4923 | − | 45.9070i | −0.0679208 | − | 0.0831648i | ||||
\(553\) | −95.4050 | −0.172523 | ||||||||
\(554\) | 361.856 | − | 338.377i | 0.653170 | − | 0.610788i | ||||
\(555\) | −382.277 | −0.688787 | ||||||||
\(556\) | −47.5589 | + | 708.374i | −0.0855376 | + | 1.27405i | ||||
\(557\) | 476.671i | 0.855782i | 0.903830 | + | 0.427891i | \(0.140743\pi\) | ||||
−0.903830 | + | 0.427891i | \(0.859257\pi\) | |||||||
\(558\) | 251.727 | − | 235.393i | 0.451123 | − | 0.421851i | ||||
\(559\) | 336.391i | 0.601774i | ||||||||
\(560\) | −270.697 | − | 36.5128i | −0.483388 | − | 0.0652014i | ||||
\(561\) | 164.287 | 0.292847 | ||||||||
\(562\) | 605.324 | + | 647.327i | 1.07709 | + | 1.15183i | ||||
\(563\) | −910.123 | −1.61656 | −0.808280 | − | 0.588799i | \(-0.799601\pi\) | ||||
−0.808280 | + | 0.588799i | \(0.799601\pi\) | |||||||
\(564\) | 411.846 | + | 27.6506i | 0.730224 | + | 0.0490258i | ||||
\(565\) | 465.250i | 0.823452i | ||||||||
\(566\) | −402.459 | − | 430.385i | −0.711058 | − | 0.760398i | ||||
\(567\) | 19.2490i | 0.0339489i | ||||||||
\(568\) | 214.908 | + | 263.141i | 0.378358 | + | 0.463276i | ||||
\(569\) | −124.123 | −0.218142 | −0.109071 | − | 0.994034i | \(-0.534788\pi\) | ||||
−0.109071 | + | 0.994034i | \(0.534788\pi\) | |||||||
\(570\) | −301.492 | + | 281.929i | −0.528934 | + | 0.494613i | ||||
\(571\) | 945.031 | 1.65504 | 0.827522 | − | 0.561433i | \(-0.189750\pi\) | ||||
0.827522 | + | 0.561433i | \(0.189750\pi\) | |||||||
\(572\) | 373.128 | + | 25.0511i | 0.652322 | + | 0.0437957i | ||||
\(573\) | − | 611.219i | − | 1.06670i | ||||||
\(574\) | 98.6335 | − | 92.2335i | 0.171835 | − | 0.160685i | ||||
\(575\) | 165.596i | 0.287994i | ||||||||
\(576\) | 38.3538 | − | 188.130i | 0.0665865 | − | 0.326615i | ||||
\(577\) | 215.682 | 0.373799 | 0.186899 | − | 0.982379i | \(-0.440156\pi\) | ||||
0.186899 | + | 0.982379i | \(0.440156\pi\) | |||||||
\(578\) | −202.753 | − | 216.822i | −0.350784 | − | 0.375125i | ||||
\(579\) | 492.382 | 0.850401 | ||||||||
\(580\) | −1.22570 | + | 18.2564i | −0.00211328 | + | 0.0314765i | ||||
\(581\) | 144.823i | 0.249265i | ||||||||
\(582\) | −229.832 | − | 245.780i | −0.394900 | − | 0.422302i | ||||
\(583\) | − | 250.840i | − | 0.430258i | ||||||
\(584\) | 33.6180 | − | 27.4559i | 0.0575651 | − | 0.0470135i | ||||
\(585\) | 279.846 | 0.478369 | ||||||||
\(586\) | 97.4679 | − | 91.1435i | 0.166327 | − | 0.155535i | ||||
\(587\) | 900.785 | 1.53456 | 0.767278 | − | 0.641314i | \(-0.221611\pi\) | ||||
0.767278 | + | 0.641314i | \(0.221611\pi\) | |||||||
\(588\) | 20.6180 | − | 307.098i | 0.0350646 | − | 0.522276i | ||||
\(589\) | − | 857.475i | − | 1.45581i | ||||||
\(590\) | −615.482 | + | 575.545i | −1.04319 | + | 0.975500i | ||||
\(591\) | − | 131.305i | − | 0.222174i | ||||||
\(592\) | 59.1384 | − | 438.439i | 0.0998960 | − | 0.740606i | ||||
\(593\) | −508.585 | −0.857647 | −0.428824 | − | 0.903388i | \(-0.641072\pi\) | ||||
−0.428824 | + | 0.903388i | \(0.641072\pi\) | |||||||
\(594\) | 56.7846 | + | 60.7249i | 0.0955970 | + | 0.102230i | ||||
\(595\) | 202.410 | 0.340185 | ||||||||
\(596\) | −350.420 | − | 23.5266i | −0.587954 | − | 0.0394741i | ||||
\(597\) | 180.455i | 0.302270i | ||||||||
\(598\) | 68.2872 | + | 73.0256i | 0.114193 | + | 0.122116i | ||||
\(599\) | 846.934i | 1.41391i | 0.707257 | + | 0.706957i | \(0.249933\pi\) | ||||
−0.707257 | + | 0.706957i | \(0.750067\pi\) | |||||||
\(600\) | −415.468 | + | 339.313i | −0.692446 | + | 0.565522i | ||||
\(601\) | −406.000 | −0.675541 | −0.337770 | − | 0.941229i | \(-0.609673\pi\) | ||||
−0.337770 | + | 0.941229i | \(0.609673\pi\) | |||||||
\(602\) | −89.9334 | + | 84.0979i | −0.149391 | + | 0.139697i | ||||
\(603\) | −254.354 | −0.421814 | ||||||||
\(604\) | 874.295 | + | 58.6985i | 1.44751 | + | 0.0971829i | ||||
\(605\) | 454.976i | 0.752026i | ||||||||
\(606\) | −157.219 | + | 147.018i | −0.259438 | + | 0.242603i | ||||
\(607\) | 771.156i | 1.27044i | 0.772332 | + | 0.635219i | \(0.219090\pi\) | ||||
−0.772332 | + | 0.635219i | \(0.780910\pi\) | |||||||
\(608\) | −276.708 | − | 389.400i | −0.455111 | − | 0.640461i | ||||
\(609\) | 2.12297 | 0.00348600 | ||||||||
\(610\) | −649.626 | − | 694.703i | −1.06496 | − | 1.13886i | ||||
\(611\) | −696.267 | −1.13955 | ||||||||
\(612\) | −9.53074 | + | 141.957i | −0.0155731 | + | 0.231956i | ||||
\(613\) | 336.699i | 0.549264i | 0.961549 | + | 0.274632i | \(0.0885560\pi\) | ||||
−0.961549 | + | 0.274632i | \(0.911444\pi\) | |||||||
\(614\) | −716.084 | − | 765.773i | −1.16626 | − | 1.24719i | ||||
\(615\) | − | 436.453i | − | 0.709680i | ||||||
\(616\) | 86.5847 | + | 106.018i | 0.140560 | + | 0.172106i | ||||
\(617\) | −908.831 | −1.47298 | −0.736492 | − | 0.676447i | \(-0.763519\pi\) | ||||
−0.736492 | + | 0.676447i | \(0.763519\pi\) | |||||||
\(618\) | −70.3501 | + | 65.7853i | −0.113835 | + | 0.106449i | ||||
\(619\) | −1047.77 | −1.69268 | −0.846340 | − | 0.532643i | \(-0.821199\pi\) | ||||
−0.846340 | + | 0.532643i | \(0.821199\pi\) | |||||||
\(620\) | 122.851 | − | 1829.83i | 0.198147 | − | 2.95134i | ||||
\(621\) | 22.2268i | 0.0357920i | ||||||||
\(622\) | −528.897 | + | 494.579i | −0.850317 | + | 0.795143i | ||||
\(623\) | − | 284.754i | − | 0.457068i | ||||||
\(624\) | −43.2923 | + | 320.959i | −0.0693788 | + | 0.514358i | ||||
\(625\) | −94.1384 | −0.150622 | ||||||||
\(626\) | 344.617 | + | 368.529i | 0.550506 | + | 0.588705i | ||||
\(627\) | 206.851 | 0.329906 | ||||||||
\(628\) | 1011.48 | + | 67.9090i | 1.61064 | + | 0.108135i | ||||
\(629\) | 327.836i | 0.521202i | ||||||||
\(630\) | 69.9615 | + | 74.8161i | 0.111050 | + | 0.118756i | ||||
\(631\) | − | 610.758i | − | 0.967921i | −0.875090 | − | 0.483961i | \(-0.839198\pi\) | ||
0.875090 | − | 0.483961i | \(-0.160802\pi\) | |||||||
\(632\) | −225.731 | − | 276.393i | −0.357169 | − | 0.437331i | ||||
\(633\) | −237.149 | −0.374643 | ||||||||
\(634\) | 117.440 | − | 109.819i | 0.185236 | − | 0.173217i | ||||
\(635\) | 1477.89 | 2.32739 | ||||||||
\(636\) | 216.746 | + | 14.5519i | 0.340796 | + | 0.0228804i | ||||
\(637\) | 519.180i | 0.815040i | ||||||||
\(638\) | 6.69735 | − | 6.26278i | 0.0104974 | − | 0.00981627i | ||||
\(639\) | − | 127.405i | − | 0.199382i | ||||||
\(640\) | −534.697 | − | 870.614i | −0.835465 | − | 1.36034i | ||||
\(641\) | 9.60015 | 0.0149768 | 0.00748842 | − | 0.999972i | \(-0.497616\pi\) | ||||
0.00748842 | + | 0.999972i | \(0.497616\pi\) | |||||||
\(642\) | −89.3872 | − | 95.5897i | −0.139232 | − | 0.148894i | ||||
\(643\) | 86.1999 | 0.134059 | 0.0670295 | − | 0.997751i | \(-0.478648\pi\) | ||||
0.0670295 | + | 0.997751i | \(0.478648\pi\) | |||||||
\(644\) | −2.45140 | + | 36.5128i | −0.00380652 | + | 0.0566969i | ||||
\(645\) | 397.955i | 0.616985i | ||||||||
\(646\) | 241.779 | + | 258.556i | 0.374272 | + | 0.400242i | ||||
\(647\) | 352.580i | 0.544946i | 0.962163 | + | 0.272473i | \(0.0878416\pi\) | ||||
−0.962163 | + | 0.272473i | \(0.912158\pi\) | |||||||
\(648\) | −55.7654 | + | 45.5436i | −0.0860577 | + | 0.0702834i | ||||
\(649\) | 422.277 | 0.650658 | ||||||||
\(650\) | 660.897 | − | 618.014i | 1.01677 | − | 0.950790i | ||||
\(651\) | −212.785 | −0.326858 | ||||||||
\(652\) | 27.4256 | − | 408.496i | 0.0420638 | − | 0.626527i | ||||
\(653\) | 319.322i | 0.489008i | 0.969648 | + | 0.244504i | \(0.0786252\pi\) | ||||
−0.969648 | + | 0.244504i | \(0.921375\pi\) | |||||||
\(654\) | 358.508 | − | 335.245i | 0.548177 | − | 0.512607i | ||||
\(655\) | − | 1000.62i | − | 1.52766i | ||||||
\(656\) | 500.574 | + | 67.5196i | 0.763071 | + | 0.102926i | ||||
\(657\) | −16.2769 | −0.0247745 | ||||||||
\(658\) | −174.067 | − | 186.145i | −0.264539 | − | 0.282895i | ||||
\(659\) | 275.328 | 0.417797 | 0.208898 | − | 0.977937i | \(-0.433012\pi\) | ||||
0.208898 | + | 0.977937i | \(0.433012\pi\) | |||||||
\(660\) | 441.415 | + | 29.6358i | 0.668811 | + | 0.0449027i | ||||
\(661\) | 133.668i | 0.202221i | 0.994875 | + | 0.101111i | \(0.0322396\pi\) | ||||
−0.994875 | + | 0.101111i | \(0.967760\pi\) | |||||||
\(662\) | 235.033 | + | 251.342i | 0.355035 | + | 0.379671i | ||||
\(663\) | − | 239.993i | − | 0.361980i | ||||||
\(664\) | −419.559 | + | 342.654i | −0.631866 | + | 0.516046i | ||||
\(665\) | 254.851 | 0.383235 | ||||||||
\(666\) | −121.177 | + | 113.314i | −0.181947 | + | 0.170141i | ||||
\(667\) | 2.45140 | 0.00367526 | ||||||||
\(668\) | −1121.84 | − | 75.3179i | −1.67939 | − | 0.112751i | ||||
\(669\) | 92.0799i | 0.137638i | ||||||||
\(670\) | −988.610 | + | 924.462i | −1.47554 | + | 1.37979i | ||||
\(671\) | 476.630i | 0.710327i | ||||||||
\(672\) | −96.6307 | + | 68.6657i | −0.143796 | + | 0.102181i | ||||
\(673\) | 187.703 | 0.278904 | 0.139452 | − | 0.990229i | \(-0.455466\pi\) | ||||
0.139452 | + | 0.990229i | \(0.455466\pi\) | |||||||
\(674\) | 770.817 | + | 824.303i | 1.14364 | + | 1.22300i | ||||
\(675\) | 201.158 | 0.298011 | ||||||||
\(676\) | −8.68842 | + | 129.411i | −0.0128527 | + | 0.191437i | ||||
\(677\) | 1169.84i | 1.72797i | 0.503515 | + | 0.863986i | \(0.332040\pi\) | ||||
−0.503515 | + | 0.863986i | \(0.667960\pi\) | |||||||
\(678\) | 137.909 | + | 147.478i | 0.203406 | + | 0.217520i | ||||
\(679\) | 207.758i | 0.305976i | ||||||||
\(680\) | 478.908 | + | 586.393i | 0.704276 | + | 0.862342i | ||||
\(681\) | 207.580 | 0.304816 | ||||||||
\(682\) | −671.272 | + | 627.715i | −0.984269 | + | 0.920403i | ||||
\(683\) | 89.4566 | 0.130976 | 0.0654880 | − | 0.997853i | \(-0.479140\pi\) | ||||
0.0654880 | + | 0.997853i | \(0.479140\pi\) | |||||||
\(684\) | −12.0000 | + | 178.736i | −0.0175439 | + | 0.261310i | ||||
\(685\) | − | 794.765i | − | 1.16024i | ||||||
\(686\) | −291.895 | + | 272.955i | −0.425503 | + | 0.397893i | ||||
\(687\) | − | 370.837i | − | 0.539791i | ||||||
\(688\) | −456.420 | − | 61.5639i | −0.663402 | − | 0.0894824i | ||||
\(689\) | −366.431 | −0.531830 | ||||||||
\(690\) | 80.7846 | + | 86.3902i | 0.117079 | + | 0.125203i | ||||
\(691\) | 139.103 | 0.201306 | 0.100653 | − | 0.994922i | \(-0.467907\pi\) | ||||
0.100653 | + | 0.994922i | \(0.467907\pi\) | |||||||
\(692\) | 969.251 | + | 65.0737i | 1.40065 | + | 0.0940371i | ||||
\(693\) | − | 51.3307i | − | 0.0740703i | ||||||
\(694\) | −390.851 | − | 417.972i | −0.563186 | − | 0.602265i | ||||
\(695\) | − | 1416.75i | − | 2.03849i | ||||||
\(696\) | 5.02301 | + | 6.15037i | 0.00721697 | + | 0.00883673i | ||||
\(697\) | −374.297 | −0.537012 | ||||||||
\(698\) | 615.033 | − | 575.126i | 0.881137 | − | 0.823962i | ||||
\(699\) | 220.726 | 0.315773 | ||||||||
\(700\) | 330.449 | + | 22.1857i | 0.472069 | + | 0.0316938i | ||||
\(701\) | − | 1218.34i | − | 1.73801i | −0.494804 | − | 0.869004i | \(-0.664760\pi\) | ||
0.494804 | − | 0.869004i | \(-0.335240\pi\) | |||||||
\(702\) | 88.7077 | − | 82.9517i | 0.126364 | − | 0.118165i | ||||
\(703\) | 412.773i | 0.587160i | ||||||||
\(704\) | −102.277 | + | 501.681i | −0.145280 | + | 0.712615i | ||||
\(705\) | −823.692 | −1.16836 | ||||||||
\(706\) | 586.214 | + | 626.891i | 0.830331 | + | 0.887948i | ||||
\(707\) | 132.897 | 0.187974 | ||||||||
\(708\) | −24.4974 | + | 364.881i | −0.0346009 | + | 0.515369i | ||||
\(709\) | − | 1080.13i | − | 1.52346i | −0.647895 | − | 0.761730i | \(-0.724351\pi\) | ||
0.647895 | − | 0.761730i | \(-0.275649\pi\) | |||||||
\(710\) | −463.061 | − | 495.193i | −0.652199 | − | 0.697455i | ||||
\(711\) | 133.822i | 0.188216i | ||||||||
\(712\) | 824.946 | − | 673.734i | 1.15863 | − | 0.946256i | ||||
\(713\) | −245.703 | −0.344604 | ||||||||
\(714\) | 64.1615 | − | 59.9982i | 0.0898620 | − | 0.0840311i | ||||
\(715\) | −746.256 | −1.04372 | ||||||||
\(716\) | −85.3027 | + | 1270.56i | −0.119138 | + | 1.77452i | ||||
\(717\) | 553.011i | 0.771285i | ||||||||
\(718\) | 385.177 | − | 360.184i | 0.536458 | − | 0.501649i | ||||
\(719\) | − | 20.7736i | − | 0.0288923i | −0.999896 | − | 0.0144461i | \(-0.995401\pi\) | ||
0.999896 | − | 0.0144461i | \(-0.00459851\pi\) | |||||||
\(720\) | −51.2154 | + | 379.699i | −0.0711325 | + | 0.527360i | ||||
\(721\) | 59.4669 | 0.0824783 | ||||||||
\(722\) | −188.715 | − | 201.809i | −0.261378 | − | 0.279515i | ||||
\(723\) | 428.536 | 0.592719 | ||||||||
\(724\) | −317.338 | − | 21.3055i | −0.438313 | − | 0.0294275i | ||||
\(725\) | − | 22.1857i | − | 0.0306010i | ||||||
\(726\) | 134.863 | + | 144.222i | 0.185762 | + | 0.198652i | ||||
\(727\) | 1031.17i | 1.41838i | 0.705015 | + | 0.709192i | \(0.250940\pi\) | ||||
−0.705015 | + | 0.709192i | \(0.749060\pi\) | |||||||
\(728\) | 154.872 | − | 126.484i | 0.212736 | − | 0.173742i | ||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | −63.2642 | + | 59.1592i | −0.0866633 | + | 0.0810399i | ||||
\(731\) | 341.282 | 0.466870 | ||||||||
\(732\) | −411.846 | − | 27.6506i | −0.562631 | − | 0.0377740i | ||||
\(733\) | − | 881.072i | − | 1.20201i | −0.799246 | − | 0.601004i | \(-0.794767\pi\) | ||
0.799246 | − | 0.601004i | \(-0.205233\pi\) | |||||||
\(734\) | −189.240 | + | 176.961i | −0.257820 | + | 0.241091i | ||||
\(735\) | 614.197i | 0.835642i | ||||||||
\(736\) | −111.580 | + | 79.2884i | −0.151603 | + | 0.107729i | ||||
\(737\) | 678.277 | 0.920321 | ||||||||
\(738\) | −129.373 | − | 138.350i | −0.175302 | − | 0.187466i | ||||
\(739\) | −671.195 | −0.908247 | −0.454124 | − | 0.890939i | \(-0.650048\pi\) | ||||
−0.454124 | + | 0.890939i | \(0.650048\pi\) | |||||||
\(740\) | −59.1384 | + | 880.848i | −0.0799168 | + | 1.19033i | ||||
\(741\) | − | 302.171i | − | 0.407788i | ||||||
\(742\) | −91.6077 | − | 97.9643i | −0.123461 | − | 0.132027i | ||||
\(743\) | − | 254.197i | − | 0.342122i | −0.985260 | − | 0.171061i | \(-0.945281\pi\) | ||
0.985260 | − | 0.171061i | \(-0.0547195\pi\) | |||||||
\(744\) | −503.454 | − | 616.448i | −0.676685 | − | 0.828559i | ||||
\(745\) | 700.841 | 0.940726 | ||||||||
\(746\) | −441.864 | + | 413.193i | −0.592311 | + | 0.553878i | ||||
\(747\) | 203.138 | 0.271939 | ||||||||
\(748\) | 25.4153 | − | 378.553i | 0.0339777 | − | 0.506087i | ||||
\(749\) | 80.8019i | 0.107880i | ||||||||
\(750\) | 276.946 | − | 258.976i | 0.369261 | − | 0.345301i | ||||
\(751\) | − | 728.994i | − | 0.970698i | −0.874320 | − | 0.485349i | \(-0.838693\pi\) | ||
0.874320 | − | 0.485349i | \(-0.161307\pi\) | |||||||
\(752\) | 127.426 | − | 944.704i | 0.169449 | − | 1.25626i | ||||
\(753\) | 372.133 | 0.494201 | ||||||||
\(754\) | −9.14875 | − | 9.78357i | −0.0121336 | − | 0.0129756i | ||||
\(755\) | −1748.59 | −2.31601 | ||||||||
\(756\) | 44.3538 | + | 2.97783i | 0.0586691 | + | 0.00393893i | ||||
\(757\) | 372.679i | 0.492311i | 0.969230 | + | 0.246155i | \(0.0791674\pi\) | ||||
−0.969230 | + | 0.246155i | \(0.920833\pi\) | |||||||
\(758\) | −158.746 | − | 169.761i | −0.209428 | − | 0.223960i | ||||
\(759\) | − | 59.2716i | − | 0.0780917i | ||||||
\(760\) | 602.985 | + | 738.317i | 0.793401 | + | 0.971470i | ||||
\(761\) | 1257.80 | 1.65283 | 0.826416 | − | 0.563060i | \(-0.190376\pi\) | ||||
0.826416 | + | 0.563060i | \(0.190376\pi\) | |||||||
\(762\) | 468.473 | − | 438.075i | 0.614794 | − | 0.574902i | ||||
\(763\) | −303.046 | −0.397177 | ||||||||
\(764\) | −1408.38 | − | 94.5559i | −1.84343 | − | 0.123764i | ||||
\(765\) | − | 283.915i | − | 0.371130i | ||||||
\(766\) | 827.041 | − | 773.377i | 1.07969 | − | 1.00963i | ||||
\(767\) | − | 616.868i | − | 0.804260i | ||||||
\(768\) | −427.559 | − | 117.479i | −0.556717 | − | 0.152968i | ||||
\(769\) | 247.703 | 0.322110 | 0.161055 | − | 0.986945i | \(-0.448510\pi\) | ||||
0.161055 | + | 0.986945i | \(0.448510\pi\) | |||||||
\(770\) | −186.564 | − | 199.510i | −0.242291 | − | 0.259103i | ||||
\(771\) | 145.972 | 0.189328 | ||||||||
\(772\) | 76.1718 | − | 1134.55i | 0.0986681 | − | 1.46963i | ||||
\(773\) | − | 587.805i | − | 0.760420i | −0.924900 | − | 0.380210i | \(-0.875852\pi\) | ||
0.924900 | − | 0.380210i | \(-0.124148\pi\) | |||||||
\(774\) | 117.962 | + | 126.147i | 0.152405 | + | 0.162980i | ||||
\(775\) | 2223.66i | 2.86924i | ||||||||
\(776\) | −601.885 | + | 491.560i | −0.775624 | + | 0.633453i | ||||
\(777\) | 102.431 | 0.131829 | ||||||||
\(778\) | −511.437 | + | 478.251i | −0.657374 | + | 0.614719i | ||||
\(779\) | −471.272 | −0.604970 | ||||||||
\(780\) | 43.2923 | − | 644.825i | 0.0555030 | − | 0.826699i | ||||
\(781\) | 339.748i | 0.435016i | ||||||||
\(782\) | 74.0873 | − | 69.2800i | 0.0947407 | − | 0.0885933i | ||||
\(783\) | − | 2.97783i | − | 0.00380311i | ||||||
\(784\) | −704.431 | − | 95.0166i | −0.898509 | − | 0.121195i | ||||
\(785\) | −2022.96 | −2.57702 | ||||||||
\(786\) | −296.603 | − | 317.184i | −0.377357 | − | 0.403541i | ||||
\(787\) | −31.0821 | −0.0394944 | −0.0197472 | − | 0.999805i | \(-0.506286\pi\) | ||||
−0.0197472 | + | 0.999805i | \(0.506286\pi\) | |||||||
\(788\) | −302.554 | − | 20.3129i | −0.383951 | − | 0.0257778i | ||||
\(789\) | 479.986i | 0.608347i | ||||||||
\(790\) | 486.382 | + | 520.132i | 0.615673 | + | 0.658395i | ||||
\(791\) | − | 124.663i | − | 0.157602i | ||||||
\(792\) | 148.708 | − | 121.450i | 0.187762 | − | 0.153346i | ||||
\(793\) | 696.267 | 0.878016 | ||||||||
\(794\) | 794.900 | − | 743.321i | 1.00113 | − | 0.936173i | ||||
\(795\) | −433.492 | −0.545273 | ||||||||
\(796\) | 415.808 | + | 27.9165i | 0.522371 | + | 0.0350710i | ||||
\(797\) | 490.260i | 0.615132i | 0.951527 | + | 0.307566i | \(0.0995145\pi\) | ||||
−0.951527 | + | 0.307566i | \(0.900486\pi\) | |||||||
\(798\) | 80.7846 | − | 75.5427i | 0.101234 | − | 0.0946651i | ||||
\(799\) | 706.389i | 0.884092i | ||||||||
\(800\) | 717.577 | + | 1009.82i | 0.896971 | + | 1.26227i | ||||
\(801\) | −399.415 | −0.498646 | ||||||||
\(802\) | −404.932 | − | 433.030i | −0.504903 | − | 0.539938i | ||||
\(803\) | 43.4050 | 0.0540536 | ||||||||
\(804\) | −39.3487 | + | 586.086i | −0.0489411 | + | 0.728962i | ||||
\(805\) | − | 73.0256i | − | 0.0907150i | ||||||
\(806\) | 916.974 | + | 980.602i | 1.13769 | + | 1.21663i | ||||
\(807\) | − | 214.256i | − | 0.265497i | ||||||
\(808\) | 314.438 | + | 385.010i | 0.389156 | + | 0.476498i | ||||
\(809\) | 676.102 | 0.835726 | 0.417863 | − | 0.908510i | \(-0.362779\pi\) | ||||
0.417863 | + | 0.908510i | \(0.362779\pi\) | |||||||
\(810\) | 104.942 | − | 98.1329i | 0.129558 | − | 0.121152i | ||||
\(811\) | −74.1793 | −0.0914665 | −0.0457332 | − | 0.998954i | \(-0.514562\pi\) | ||||
−0.0457332 | + | 0.998954i | \(0.514562\pi\) | |||||||
\(812\) | 0.328425 | − | 4.89179i | 0.000404465 | − | 0.00602437i | ||||
\(813\) | 342.920i | 0.421796i | ||||||||
\(814\) | 323.138 | − | 302.171i | 0.396976 | − | 0.371217i | ||||
\(815\) | 816.991i | 1.00244i | ||||||||
\(816\) | 325.626 | + | 43.9217i | 0.399051 | + | 0.0538257i | ||||
\(817\) | 429.703 | 0.525952 | ||||||||
\(818\) | −337.976 | − | 361.428i | −0.413173 | − | 0.441843i | ||||
\(819\) | −74.9845 | −0.0915562 | ||||||||
\(820\) | −1005.68 | − | 67.5196i | −1.22644 | − | 0.0823409i | ||||
\(821\) | − | 1130.58i | − | 1.37708i | −0.725198 | − | 0.688540i | \(-0.758252\pi\) | ||
0.725198 | − | 0.688540i | \(-0.241748\pi\) | |||||||
\(822\) | −235.583 | − | 251.930i | −0.286598 | − | 0.306485i | ||||
\(823\) | − | 82.1839i | − | 0.0998589i | −0.998753 | − | 0.0499295i | \(-0.984100\pi\) | ||
0.998753 | − | 0.0499295i | \(-0.0158997\pi\) | |||||||
\(824\) | 140.700 | + | 172.279i | 0.170753 | + | 0.209076i | ||||
\(825\) | −536.420 | −0.650207 | ||||||||
\(826\) | 164.918 | − | 154.217i | 0.199658 | − | 0.186703i | ||||
\(827\) | 1504.57 | 1.81931 | 0.909655 | − | 0.415365i | \(-0.136346\pi\) | ||||
0.909655 | + | 0.415365i | \(0.136346\pi\) | |||||||
\(828\) | 51.2154 | + | 3.43850i | 0.0618543 | + | 0.00415278i | ||||
\(829\) | 1409.65i | 1.70042i | 0.526445 | + | 0.850209i | \(0.323525\pi\) | ||||
−0.526445 | + | 0.850209i | \(0.676475\pi\) | |||||||
\(830\) | 789.549 | − | 738.317i | 0.951263 | − | 0.889539i | ||||
\(831\) | 429.044i | 0.516299i | ||||||||
\(832\) | 732.862 | + | 149.407i | 0.880843 | + | 0.179576i | ||||
\(833\) | 526.728 | 0.632327 | ||||||||
\(834\) | −419.951 | − | 449.091i | −0.503539 | − | 0.538479i | ||||
\(835\) | 2243.67 | 2.68703 | ||||||||
\(836\) | 32.0000 | − | 476.630i | 0.0382775 | − | 0.570131i | ||||
\(837\) | 298.467i | 0.356591i | ||||||||
\(838\) | −125.856 | − | 134.589i | −0.150187 | − | 0.160608i | ||||
\(839\) | − | 288.110i | − | 0.343397i | −0.985150 | − | 0.171698i | \(-0.945075\pi\) | ||
0.985150 | − | 0.171698i | \(-0.0549254\pi\) | |||||||
\(840\) | 183.215 | − | 149.632i | 0.218114 | − | 0.178134i | ||||
\(841\) | 840.672 | 0.999609 | ||||||||
\(842\) | −650.851 | + | 608.620i | −0.772982 | + | 0.722826i | ||||
\(843\) | −767.520 | −0.910463 | ||||||||
\(844\) | −36.6870 | + | 546.441i | −0.0434681 | + | 0.647442i | ||||
\(845\) | − | 258.822i | − | 0.306299i | ||||||
\(846\) | −261.100 | + | 244.158i | −0.308629 | + | 0.288603i | ||||
\(847\) | − | 121.910i | − | 0.143932i | ||||||
\(848\) | 67.0615 | − | 497.178i | 0.0790819 | − | 0.586295i | ||||
\(849\) | 510.297 | 0.601057 | ||||||||
\(850\) | −626.999 | − | 670.506i | −0.737645 | − | 0.788830i | ||||
\(851\) | 118.277 | 0.138986 | ||||||||
\(852\) | −293.569 | − | 19.7097i | −0.344565 | − | 0.0231334i | ||||
\(853\) | − | 645.132i | − | 0.756310i | −0.925742 | − | 0.378155i | \(-0.876559\pi\) | ||
0.925742 | − | 0.378155i | \(-0.123441\pi\) | |||||||
\(854\) | 174.067 | + | 186.145i | 0.203825 | + | 0.217968i | ||||
\(855\) | − | 357.472i | − | 0.418096i | ||||||
\(856\) | −234.087 | + | 191.179i | −0.273466 | + | 0.223340i | ||||
\(857\) | −995.549 | −1.16167 | −0.580833 | − | 0.814022i | \(-0.697273\pi\) | ||||
−0.580833 | + | 0.814022i | \(0.697273\pi\) | |||||||
\(858\) | −236.554 | + | 221.205i | −0.275704 | + | 0.257814i | ||||
\(859\) | −774.354 | −0.901460 | −0.450730 | − | 0.892660i | \(-0.648836\pi\) | ||||
−0.450730 | + | 0.892660i | \(0.648836\pi\) | |||||||
\(860\) | 916.974 | + | 61.5639i | 1.06625 | + | 0.0715859i | ||||
\(861\) | 116.947i | 0.135827i | ||||||||
\(862\) | −272.700 | + | 255.005i | −0.316357 | + | 0.295830i | ||||
\(863\) | 1007.33i | 1.16724i | 0.812025 | + | 0.583622i | \(0.198365\pi\) | ||||
−0.812025 | + | 0.583622i | \(0.801635\pi\) | |||||||
\(864\) | 96.3154 | + | 135.541i | 0.111476 | + | 0.156876i | ||||
\(865\) | −1938.50 | −2.24104 | ||||||||
\(866\) | 397.688 | + | 425.284i | 0.459225 | + | 0.491090i | ||||
\(867\) | 257.081 | 0.296518 | ||||||||
\(868\) | −32.9179 | + | 490.301i | −0.0379238 | + | 0.564863i | ||||
\(869\) | − | 356.858i | − | 0.410654i | ||||||
\(870\) | −10.8231 | − | 11.5741i | −0.0124403 | − | 0.0133036i | ||||
\(871\) | − | 990.836i | − | 1.13758i | ||||||
\(872\) | −717.015 | − | 877.941i | −0.822265 | − | 1.00681i | ||||
\(873\) | 291.415 | 0.333809 | ||||||||
\(874\) | 93.2820 | − | 87.2293i | 0.106730 | − | 0.0998046i | ||||
\(875\) | −234.102 | −0.267546 | ||||||||
\(876\) | −2.51804 | + | 37.5054i | −0.00287448 | + | 0.0428144i | ||||
\(877\) | 681.645i | 0.777246i | 0.921397 | + | 0.388623i | \(0.127049\pi\) | ||||
−0.921397 | + | 0.388623i | \(0.872951\pi\) | |||||||
\(878\) | 128.099 | − | 119.787i | 0.145898 | − | 0.136431i | ||||
\(879\) | 115.565i | 0.131474i | ||||||||
\(880\) | 136.574 | − | 1012.53i | 0.155198 | − | 1.15060i | ||||
\(881\) | −679.108 | −0.770837 | −0.385419 | − | 0.922742i | \(-0.625943\pi\) | ||||
−0.385419 | + | 0.922742i | \(0.625943\pi\) | |||||||
\(882\) | 182.060 | + | 194.693i | 0.206417 | + | 0.220740i | ||||
\(883\) | −1059.44 | −1.19982 | −0.599910 | − | 0.800068i | \(-0.704797\pi\) | ||||
−0.599910 | + | 0.800068i | \(0.704797\pi\) | |||||||
\(884\) | −552.995 | − | 37.1270i | −0.625560 | − | 0.0419989i | ||||
\(885\) | − | 729.762i | − | 0.824590i | ||||||
\(886\) | 28.2872 | + | 30.2500i | 0.0319268 | + | 0.0341422i | ||||
\(887\) | − | 856.411i | − | 0.965514i | −0.875754 | − | 0.482757i | \(-0.839635\pi\) | ||
0.875754 | − | 0.482757i | \(-0.160365\pi\) | |||||||
\(888\) | 242.354 | + | 296.747i | 0.272921 | + | 0.334175i | ||||
\(889\) | −396.000 | −0.445444 | ||||||||
\(890\) | −1552.43 | + | 1451.70i | −1.74430 | + | 1.63112i | ||||
\(891\) | −72.0000 | −0.0808081 | ||||||||
\(892\) | 212.172 | + | 14.2448i | 0.237861 | + | 0.0159695i | ||||
\(893\) | 889.403i | 0.995972i | ||||||||
\(894\) | 222.158 | − | 207.743i | 0.248499 | − | 0.232374i | ||||
\(895\) | − | 2541.11i | − | 2.83923i | ||||||
\(896\) | 143.272 | + | 233.280i | 0.159901 | + | 0.260358i | ||||
\(897\) | −86.5847 | −0.0965270 | ||||||||
\(898\) | 798.319 | + | 853.714i | 0.888997 | + | 0.950684i | ||||
\(899\) | 32.9179 | 0.0366161 | ||||||||
\(900\) | 31.1192 | − | 463.510i | 0.0345769 | − | 0.515011i | ||||
\(901\) | 371.758i | 0.412606i | ||||||||
\(902\) | 344.995 | + | 368.934i | 0.382478 | + | 0.409018i | ||||
\(903\) | − | 106.632i | − | 0.118086i | ||||||
\(904\) | 361.156 | − | 294.957i | 0.399509 | − | 0.326280i | ||||
\(905\) | 634.677 | 0.701300 | ||||||||
\(906\) | −554.281 | + | 518.315i | −0.611789 | + | 0.572092i | ||||
\(907\) | −761.492 | −0.839573 | −0.419786 | − | 0.907623i | \(-0.637895\pi\) | ||||
−0.419786 | + | 0.907623i | \(0.637895\pi\) | |||||||
\(908\) | 32.1127 | − | 478.308i | 0.0353664 | − | 0.526770i | ||||
\(909\) | − | 186.411i | − | 0.205073i | ||||||
\(910\) | −291.446 | + | 272.535i | −0.320271 | + | 0.299489i | ||||
\(911\) | − | 897.344i | − | 0.985009i | −0.870310 | − | 0.492505i | \(-0.836081\pi\) | ||
0.870310 | − | 0.492505i | \(-0.163919\pi\) | |||||||
\(912\) | 409.990 | + | 55.3011i | 0.449550 | + | 0.0606372i | ||||
\(913\) | −541.703 | −0.593321 | ||||||||
\(914\) | −368.406 | − | 393.970i | −0.403070 | − | 0.431039i | ||||
\(915\) | 823.692 | 0.900210 | ||||||||
\(916\) | −854.487 | − | 57.3686i | −0.932846 | − | 0.0626295i | ||||
\(917\) | 268.115i | 0.292383i | ||||||||
\(918\) | −84.1577 | − | 89.9973i | −0.0916750 | − | 0.0980363i | ||||
\(919\) | 62.6388i | 0.0681598i | 0.999419 | + | 0.0340799i | \(0.0108501\pi\) | ||||
−0.999419 | + | 0.0340799i | \(0.989150\pi\) | |||||||
\(920\) | 211.559 | − | 172.780i | 0.229955 | − | 0.187805i | ||||
\(921\) | 907.959 | 0.985840 | ||||||||
\(922\) | −64.9986 | + | 60.7811i | −0.0704974 | + | 0.0659231i | ||||
\(923\) | 496.308 | 0.537712 | ||||||||
\(924\) | −118.277 | − | 7.94089i | −0.128005 | − | 0.00859403i | ||||
\(925\) | − | 1070.43i | − | 1.15722i | ||||||
\(926\) | −892.652 | + | 834.731i | −0.963987 | + | 0.901437i | ||||
\(927\) | − | 83.4124i | − | 0.0899810i | ||||||
\(928\) | 14.9488 | − | 10.6226i | 0.0161086 | − | 0.0114468i | ||||
\(929\) | 253.313 | 0.272673 | 0.136336 | − | 0.990663i | \(-0.456467\pi\) | ||||
0.136336 | + | 0.990663i | \(0.456467\pi\) | |||||||
\(930\) | 1084.79 | + | 1160.07i | 1.16644 | + | 1.24738i | ||||
\(931\) | 663.195 | 0.712347 | ||||||||
\(932\) | 34.1464 | − | 508.599i | 0.0366377 | − | 0.545707i | ||||
\(933\) | − | 627.101i | − | 0.672134i | ||||||
\(934\) | 200.000 | + | 213.878i | 0.214133 | + | 0.228991i | ||||
\(935\) | 757.106i | 0.809739i | ||||||||
\(936\) | −177.415 | − | 217.234i | −0.189546 | − | 0.232088i | ||||
\(937\) | −30.5538 | −0.0326081 | −0.0163040 | − | 0.999867i | \(-0.505190\pi\) | ||||
−0.0163040 | + | 0.999867i | \(0.505190\pi\) | |||||||
\(938\) | 264.897 | − | 247.709i | 0.282406 | − | 0.264082i | ||||
\(939\) | −436.956 | −0.465342 | ||||||||
\(940\) | −127.426 | + | 1897.96i | −0.135559 | + | 2.01911i | ||||
\(941\) | − | 388.745i | − | 0.413119i | −0.978434 | − | 0.206559i | \(-0.933773\pi\) | ||
0.978434 | − | 0.206559i | \(-0.0662267\pi\) | |||||||
\(942\) | −641.254 | + | 599.645i | −0.680737 | + | 0.636566i | ||||
\(943\) | 135.039i | 0.143202i | ||||||||
\(944\) | 836.974 | + | 112.895i | 0.886625 | + | 0.119592i | ||||
\(945\) | −88.7077 | −0.0938705 | ||||||||
\(946\) | −314.564 | − | 336.391i | −0.332520 | − | 0.355594i | ||||
\(947\) | −263.615 | −0.278369 | −0.139184 | − | 0.990266i | \(-0.544448\pi\) | ||||
−0.139184 | + | 0.990266i | \(0.544448\pi\) | |||||||
\(948\) | 308.354 | + | 20.7023i | 0.325268 | + | 0.0218379i | ||||
\(949\) | − | 63.4066i | − | 0.0668141i | ||||||
\(950\) | −789.443 | − | 844.222i | −0.830993 | − | 0.888655i | ||||
\(951\) | 139.245i | 0.146420i | ||||||||
\(952\) | −128.323 | − | 157.123i | −0.134793 | − | 0.165046i | ||||
\(953\) | 1292.41 | 1.35615 | 0.678075 | − | 0.734993i | \(-0.262815\pi\) | ||||
0.678075 | + | 0.734993i | \(0.262815\pi\) | |||||||
\(954\) | −137.412 | + | 128.495i | −0.144037 | + | 0.134691i | ||||
\(955\) | 2816.76 | 2.94949 | ||||||||
\(956\) | 1274.26 | + | 85.5511i | 1.33290 | + | 0.0894886i | ||||
\(957\) | 7.94089i | 0.00829769i | ||||||||
\(958\) | −280.295 | + | 262.107i | −0.292583 | + | 0.273598i | ||||
\(959\) | 212.957i | 0.222061i | ||||||||
\(960\) | 866.985 | + | 176.751i | 0.903109 | + | 0.184115i | ||||
\(961\) | −2338.34 | −2.43324 | ||||||||
\(962\) | −441.415 | − | 472.045i | −0.458852 | − | 0.490691i | ||||
\(963\) | 113.338 | 0.117693 | ||||||||
\(964\) | 66.2947 | − | 987.438i | 0.0687705 | − | 1.02431i | ||||
\(965\) | 2269.11i | 2.35141i | ||||||||
\(966\) | −21.6462 | − | 23.1482i | −0.0224080 | − | 0.0239629i | ||||
\(967\) | − | 1110.00i | − | 1.14788i | −0.818896 | − | 0.573942i | \(-0.805413\pi\) | ||
0.818896 | − | 0.573942i | \(-0.194587\pi\) | |||||||
\(968\) | 353.181 | − | 288.443i | 0.364856 | − | 0.297978i | ||||
\(969\) | −306.564 | −0.316372 | ||||||||
\(970\) | 1132.66 | − | 1059.16i | 1.16769 | − | 1.09192i | ||||
\(971\) | −1341.66 | −1.38173 | −0.690866 | − | 0.722983i | \(-0.742770\pi\) | ||||
−0.690866 | + | 0.722983i | \(0.742770\pi\) | |||||||
\(972\) | 4.17691 | − | 62.2138i | 0.00429724 | − | 0.0640059i | ||||
\(973\) | 379.617i | 0.390151i | ||||||||
\(974\) | 892.204 | − | 834.311i | 0.916020 | − | 0.856583i | ||||
\(975\) | 783.610i | 0.803703i | ||||||||
\(976\) | −127.426 | + | 944.704i | −0.130559 | + | 0.967934i | ||||
\(977\) | −920.431 | −0.942099 | −0.471050 | − | 0.882107i | \(-0.656125\pi\) | ||||
−0.471050 | + | 0.882107i | \(0.656125\pi\) | |||||||
\(978\) | 242.172 | + | 258.976i | 0.247619 | + | 0.264802i | ||||
\(979\) | 1065.11 | 1.08795 | ||||||||
\(980\) | 1415.24 | + | 95.0166i | 1.44412 | + | 0.0969557i | ||||
\(981\) | 425.074i | 0.433307i | ||||||||
\(982\) | −194.459 | − | 207.952i | −0.198023 | − | 0.211764i | ||||
\(983\) | 1697.84i | 1.72720i | 0.504176 | + | 0.863601i | \(0.331796\pi\) | ||||
−0.504176 | + | 0.863601i | \(0.668204\pi\) | |||||||
\(984\) | −338.802 | + | 276.700i | −0.344311 | + | 0.281200i | ||||
\(985\) | 605.108 | 0.614322 | ||||||||
\(986\) | −9.92581 | + | 9.28176i | −0.0100667 | + | 0.00941355i | ||||
\(987\) | 220.708 | 0.223615 | ||||||||
\(988\) | −696.267 | − | 46.7460i | −0.704723 | − | 0.0473138i | ||||
\(989\) | − | 123.128i | − | 0.124497i | ||||||
\(990\) | −279.846 | + | 261.688i | −0.282673 | + | 0.264331i | ||||
\(991\) | 284.765i | 0.287351i | 0.989625 | + | 0.143675i | \(0.0458921\pi\) | ||||
−0.989625 | + | 0.143675i | \(0.954108\pi\) | |||||||
\(992\) | −1498.31 | + | 1064.70i | −1.51040 | + | 1.07329i | ||||
\(993\) | −298.010 | −0.300111 | ||||||||
\(994\) | 124.077 | + | 132.687i | 0.124826 | + | 0.133487i | ||||
\(995\) | −831.615 | −0.835794 | ||||||||
\(996\) | 31.4256 | − | 468.074i | 0.0315518 | − | 0.469954i | ||||
\(997\) | 1093.80i | 1.09710i | 0.836119 | + | 0.548548i | \(0.184819\pi\) | ||||
−0.836119 | + | 0.548548i | \(0.815181\pi\) | |||||||
\(998\) | 124.813 | + | 133.473i | 0.125063 | + | 0.133741i | ||||
\(999\) | − | 143.677i | − | 0.143820i |
(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 | 24.3.b.a.19.4 | yes | 4 | |
3.2 | odd | 2 | 72.3.b.b.19.1 | 4 | |||
4.3 | odd | 2 | 96.3.b.a.79.3 | 4 | |||
5.2 | odd | 4 | 600.3.p.a.499.4 | 8 | |||
5.3 | odd | 4 | 600.3.p.a.499.5 | 8 | |||
5.4 | even | 2 | 600.3.g.a.451.1 | 4 | |||
8.3 | odd | 2 | inner | 24.3.b.a.19.3 | ✓ | 4 | |
8.5 | even | 2 | 96.3.b.a.79.4 | 4 | |||
12.11 | even | 2 | 288.3.b.b.271.4 | 4 | |||
16.3 | odd | 4 | 768.3.g.h.511.5 | 8 | |||
16.5 | even | 4 | 768.3.g.h.511.8 | 8 | |||
16.11 | odd | 4 | 768.3.g.h.511.4 | 8 | |||
16.13 | even | 4 | 768.3.g.h.511.1 | 8 | |||
20.3 | even | 4 | 2400.3.p.a.1999.6 | 8 | |||
20.7 | even | 4 | 2400.3.p.a.1999.3 | 8 | |||
20.19 | odd | 2 | 2400.3.g.a.751.2 | 4 | |||
24.5 | odd | 2 | 288.3.b.b.271.1 | 4 | |||
24.11 | even | 2 | 72.3.b.b.19.2 | 4 | |||
40.3 | even | 4 | 600.3.p.a.499.3 | 8 | |||
40.13 | odd | 4 | 2400.3.p.a.1999.7 | 8 | |||
40.19 | odd | 2 | 600.3.g.a.451.2 | 4 | |||
40.27 | even | 4 | 600.3.p.a.499.6 | 8 | |||
40.29 | even | 2 | 2400.3.g.a.751.1 | 4 | |||
40.37 | odd | 4 | 2400.3.p.a.1999.2 | 8 | |||
48.5 | odd | 4 | 2304.3.g.z.1279.1 | 8 | |||
48.11 | even | 4 | 2304.3.g.z.1279.2 | 8 | |||
48.29 | odd | 4 | 2304.3.g.z.1279.7 | 8 | |||
48.35 | even | 4 | 2304.3.g.z.1279.8 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
24.3.b.a.19.3 | ✓ | 4 | 8.3 | odd | 2 | inner | |
24.3.b.a.19.4 | yes | 4 | 1.1 | even | 1 | trivial | |
72.3.b.b.19.1 | 4 | 3.2 | odd | 2 | |||
72.3.b.b.19.2 | 4 | 24.11 | even | 2 | |||
96.3.b.a.79.3 | 4 | 4.3 | odd | 2 | |||
96.3.b.a.79.4 | 4 | 8.5 | even | 2 | |||
288.3.b.b.271.1 | 4 | 24.5 | odd | 2 | |||
288.3.b.b.271.4 | 4 | 12.11 | even | 2 | |||
600.3.g.a.451.1 | 4 | 5.4 | even | 2 | |||
600.3.g.a.451.2 | 4 | 40.19 | odd | 2 | |||
600.3.p.a.499.3 | 8 | 40.3 | even | 4 | |||
600.3.p.a.499.4 | 8 | 5.2 | odd | 4 | |||
600.3.p.a.499.5 | 8 | 5.3 | odd | 4 | |||
600.3.p.a.499.6 | 8 | 40.27 | even | 4 | |||
768.3.g.h.511.1 | 8 | 16.13 | even | 4 | |||
768.3.g.h.511.4 | 8 | 16.11 | odd | 4 | |||
768.3.g.h.511.5 | 8 | 16.3 | odd | 4 | |||
768.3.g.h.511.8 | 8 | 16.5 | even | 4 | |||
2304.3.g.z.1279.1 | 8 | 48.5 | odd | 4 | |||
2304.3.g.z.1279.2 | 8 | 48.11 | even | 4 | |||
2304.3.g.z.1279.7 | 8 | 48.29 | odd | 4 | |||
2304.3.g.z.1279.8 | 8 | 48.35 | even | 4 | |||
2400.3.g.a.751.1 | 4 | 40.29 | even | 2 | |||
2400.3.g.a.751.2 | 4 | 20.19 | odd | 2 | |||
2400.3.p.a.1999.2 | 8 | 40.37 | odd | 4 | |||
2400.3.p.a.1999.3 | 8 | 20.7 | even | 4 | |||
2400.3.p.a.1999.6 | 8 | 20.3 | even | 4 | |||
2400.3.p.a.1999.7 | 8 | 40.13 | odd | 4 |