Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [630,3,Mod(127,630)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(630, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 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("630.127");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 630.o (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(17.1662566547\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 32 x^{14} + 152 x^{13} + 1954 x^{12} - 12664 x^{11} + 50336 x^{10} + 231896 x^{9} + \cdots + 2560000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{14}\cdot 5 \) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 253.1 | ||
Root | \(-0.394902 + 0.394902i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 630.253 |
Dual form | 630.3.o.f.127.1 |
$q$-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 \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(281\) | \(451\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | − | 1.00000i | 0.500000 | − | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | − | 2.00000i | − | 0.500000i | ||||||
\(5\) | −4.80148 | + | 1.39490i | −0.960297 | + | 0.278980i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.87083 | − | 1.87083i | 0.267261 | − | 0.267261i | ||||
\(8\) | −2.00000 | − | 2.00000i | −0.250000 | − | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.40658 | + | 6.19639i | −0.340658 | + | 0.619639i | ||||
\(11\) | 11.5078 | 1.04617 | 0.523083 | − | 0.852282i | \(-0.324782\pi\) | ||||
0.523083 | + | 0.852282i | \(0.324782\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −7.70521 | − | 7.70521i | −0.592708 | − | 0.592708i | 0.345654 | − | 0.938362i | \(-0.387657\pi\) |
−0.938362 | + | 0.345654i | \(0.887657\pi\) | |||||||
\(14\) | − | 3.74166i | − | 0.267261i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | −21.0749 | + | 21.0749i | −1.23970 | + | 1.23970i | −0.279579 | + | 0.960123i | \(0.590195\pi\) |
−0.960123 | + | 0.279579i | \(0.909805\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 24.1173i | − | 1.26933i | −0.772786 | − | 0.634666i | \(-0.781138\pi\) | ||
0.772786 | − | 0.634666i | \(-0.218862\pi\) | |||||||
\(20\) | 2.78980 | + | 9.60297i | 0.139490 | + | 0.480148i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 11.5078 | − | 11.5078i | 0.523083 | − | 0.523083i | ||||
\(23\) | −30.1762 | − | 30.1762i | −1.31201 | − | 1.31201i | −0.919934 | − | 0.392073i | \(-0.871758\pi\) |
−0.392073 | − | 0.919934i | \(-0.628242\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 21.1085 | − | 13.3952i | 0.844340 | − | 0.535808i | ||||
\(26\) | −15.4104 | −0.592708 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.74166 | − | 3.74166i | −0.133631 | − | 0.133631i | ||||
\(29\) | 51.1392i | 1.76342i | 0.471790 | + | 0.881711i | \(0.343608\pi\) | ||||
−0.471790 | + | 0.881711i | \(0.656392\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −46.9852 | −1.51565 | −0.757826 | − | 0.652457i | \(-0.773738\pi\) | ||||
−0.757826 | + | 0.652457i | \(0.773738\pi\) | |||||||
\(32\) | −4.00000 | + | 4.00000i | −0.125000 | + | 0.125000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 42.1499i | 1.23970i | ||||||||
\(35\) | −6.37313 | + | 11.5924i | −0.182089 | + | 0.331211i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.50020 | + | 8.50020i | −0.229735 | + | 0.229735i | −0.812582 | − | 0.582847i | \(-0.801939\pi\) |
0.582847 | + | 0.812582i | \(0.301939\pi\) | |||||||
\(38\) | −24.1173 | − | 24.1173i | −0.634666 | − | 0.634666i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 12.3928 | + | 6.81316i | 0.309819 | + | 0.170329i | ||||
\(41\) | −18.6089 | −0.453875 | −0.226937 | − | 0.973909i | \(-0.572871\pi\) | ||||
−0.226937 | + | 0.973909i | \(0.572871\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −26.1383 | − | 26.1383i | −0.607867 | − | 0.607867i | 0.334522 | − | 0.942388i | \(-0.391425\pi\) |
−0.942388 | + | 0.334522i | \(0.891425\pi\) | |||||||
\(44\) | − | 23.0156i | − | 0.523083i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −60.3523 | −1.31201 | ||||||||
\(47\) | −50.1311 | + | 50.1311i | −1.06662 | + | 1.06662i | −0.0690016 | + | 0.997617i | \(0.521981\pi\) |
−0.997617 | + | 0.0690016i | \(0.978019\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 7.00000i | − | 0.142857i | ||||||
\(50\) | 7.71330 | − | 34.5037i | 0.154266 | − | 0.690074i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −15.4104 | + | 15.4104i | −0.296354 | + | 0.296354i | ||||
\(53\) | −7.08527 | − | 7.08527i | −0.133684 | − | 0.133684i | 0.637098 | − | 0.770783i | \(-0.280135\pi\) |
−0.770783 | + | 0.637098i | \(0.780135\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −55.2546 | + | 16.0523i | −1.00463 | + | 0.291860i | ||||
\(56\) | −7.48331 | −0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 51.1392 | + | 51.1392i | 0.881711 | + | 0.881711i | ||||
\(59\) | − | 94.3487i | − | 1.59913i | −0.600579 | − | 0.799565i | \(-0.705063\pi\) | ||
0.600579 | − | 0.799565i | \(-0.294937\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.09003 | 0.132623 | 0.0663117 | − | 0.997799i | \(-0.478877\pi\) | ||||
0.0663117 | + | 0.997799i | \(0.478877\pi\) | |||||||
\(62\) | −46.9852 | + | 46.9852i | −0.757826 | + | 0.757826i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000i | 0.125000i | ||||||||
\(65\) | 47.7445 | + | 26.2484i | 0.734530 | + | 0.403822i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −20.6469 | + | 20.6469i | −0.308163 | + | 0.308163i | −0.844197 | − | 0.536034i | \(-0.819922\pi\) |
0.536034 | + | 0.844197i | \(0.319922\pi\) | |||||||
\(68\) | 42.1499 | + | 42.1499i | 0.619851 | + | 0.619851i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 5.21925 | + | 17.9655i | 0.0745607 | + | 0.256650i | ||||
\(71\) | 63.7595 | 0.898021 | 0.449011 | − | 0.893526i | \(-0.351777\pi\) | ||||
0.449011 | + | 0.893526i | \(0.351777\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 50.1883 | + | 50.1883i | 0.687511 | + | 0.687511i | 0.961681 | − | 0.274170i | \(-0.0884031\pi\) |
−0.274170 | + | 0.961681i | \(0.588403\pi\) | |||||||
\(74\) | 17.0004i | 0.229735i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −48.2346 | −0.634666 | ||||||||
\(77\) | 21.5292 | − | 21.5292i | 0.279599 | − | 0.279599i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 1.06121i | − | 0.0134331i | −0.999977 | − | 0.00671653i | \(-0.997862\pi\) | ||
0.999977 | − | 0.00671653i | \(-0.00213796\pi\) | |||||||
\(80\) | 19.2059 | − | 5.57961i | 0.240074 | − | 0.0697451i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −18.6089 | + | 18.6089i | −0.226937 | + | 0.226937i | ||||
\(83\) | −53.6243 | − | 53.6243i | −0.646075 | − | 0.646075i | 0.305967 | − | 0.952042i | \(-0.401020\pi\) |
−0.952042 | + | 0.305967i | \(0.901020\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 71.7935 | − | 130.588i | 0.844629 | − | 1.53633i | ||||
\(86\) | −52.2765 | −0.607867 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −23.0156 | − | 23.0156i | −0.261541 | − | 0.261541i | ||||
\(89\) | − | 145.154i | − | 1.63095i | −0.578794 | − | 0.815473i | \(-0.696477\pi\) | ||
0.578794 | − | 0.815473i | \(-0.303523\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −28.8303 | −0.316816 | ||||||||
\(92\) | −60.3523 | + | 60.3523i | −0.656003 | + | 0.656003i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 100.262i | 1.06662i | ||||||||
\(95\) | 33.6413 | + | 115.799i | 0.354119 | + | 1.21894i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 23.7872 | − | 23.7872i | 0.245229 | − | 0.245229i | −0.573780 | − | 0.819009i | \(-0.694524\pi\) |
0.819009 | + | 0.573780i | \(0.194524\pi\) | |||||||
\(98\) | −7.00000 | − | 7.00000i | −0.0714286 | − | 0.0714286i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −26.7904 | − | 42.2170i | −0.267904 | − | 0.422170i | ||||
\(101\) | −50.1467 | −0.496502 | −0.248251 | − | 0.968696i | \(-0.579856\pi\) | ||||
−0.248251 | + | 0.968696i | \(0.579856\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 56.3876 | + | 56.3876i | 0.547453 | + | 0.547453i | 0.925703 | − | 0.378251i | \(-0.123474\pi\) |
−0.378251 | + | 0.925703i | \(0.623474\pi\) | |||||||
\(104\) | 30.8208i | 0.296354i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −14.1705 | −0.133684 | ||||||||
\(107\) | 135.365 | − | 135.365i | 1.26510 | − | 1.26510i | 0.316506 | − | 0.948590i | \(-0.397490\pi\) |
0.948590 | − | 0.316506i | \(-0.102510\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 100.934i | 0.926001i | 0.886358 | + | 0.463001i | \(0.153227\pi\) | ||||
−0.886358 | + | 0.463001i | \(0.846773\pi\) | |||||||
\(110\) | −39.2023 | + | 71.3069i | −0.356385 | + | 0.648245i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −7.48331 | + | 7.48331i | −0.0668153 | + | 0.0668153i | ||||
\(113\) | −25.3174 | − | 25.3174i | −0.224048 | − | 0.224048i | 0.586153 | − | 0.810201i | \(-0.300642\pi\) |
−0.810201 | + | 0.586153i | \(0.800642\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 186.983 | + | 102.798i | 1.62594 | + | 0.893892i | ||||
\(116\) | 102.278 | 0.881711 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −94.3487 | − | 94.3487i | −0.799565 | − | 0.799565i | ||||
\(119\) | 78.8552i | 0.662649i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.4299 | 0.0944623 | ||||||||
\(122\) | 8.09003 | − | 8.09003i | 0.0663117 | − | 0.0663117i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 93.9704i | 0.757826i | ||||||||
\(125\) | −82.6671 | + | 93.7611i | −0.661337 | + | 0.750089i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 116.746 | − | 116.746i | 0.919262 | − | 0.919262i | −0.0777140 | − | 0.996976i | \(-0.524762\pi\) |
0.996976 | + | 0.0777140i | \(0.0247621\pi\) | |||||||
\(128\) | 8.00000 | + | 8.00000i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 73.9929 | − | 21.4960i | 0.569176 | − | 0.165354i | ||||
\(131\) | −34.8004 | −0.265652 | −0.132826 | − | 0.991139i | \(-0.542405\pi\) | ||||
−0.132826 | + | 0.991139i | \(0.542405\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −45.1194 | − | 45.1194i | −0.339243 | − | 0.339243i | ||||
\(134\) | 41.2938i | 0.308163i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 84.2997 | 0.619851 | ||||||||
\(137\) | −131.552 | + | 131.552i | −0.960235 | + | 0.960235i | −0.999239 | − | 0.0390044i | \(-0.987581\pi\) |
0.0390044 | + | 0.999239i | \(0.487581\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 89.4407i | − | 0.643458i | −0.946832 | − | 0.321729i | \(-0.895736\pi\) | ||
0.946832 | − | 0.321729i | \(-0.104264\pi\) | |||||||
\(140\) | 23.1848 | + | 12.7463i | 0.165605 | + | 0.0910447i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 63.7595 | − | 63.7595i | 0.449011 | − | 0.449011i | ||||
\(143\) | −88.6702 | − | 88.6702i | −0.620071 | − | 0.620071i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −71.3342 | − | 245.544i | −0.491960 | − | 1.69341i | ||||
\(146\) | 100.377 | 0.687511 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 17.0004 | + | 17.0004i | 0.114868 | + | 0.114868i | ||||
\(149\) | − | 55.7399i | − | 0.374093i | −0.982351 | − | 0.187047i | \(-0.940108\pi\) | ||
0.982351 | − | 0.187047i | \(-0.0598915\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 82.9665 | 0.549447 | 0.274724 | − | 0.961523i | \(-0.411414\pi\) | ||||
0.274724 | + | 0.961523i | \(0.411414\pi\) | |||||||
\(152\) | −48.2346 | + | 48.2346i | −0.317333 | + | 0.317333i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | − | 43.0583i | − | 0.279599i | ||||||
\(155\) | 225.599 | − | 65.5398i | 1.45548 | − | 0.422837i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −99.7950 | + | 99.7950i | −0.635637 | + | 0.635637i | −0.949476 | − | 0.313839i | \(-0.898385\pi\) |
0.313839 | + | 0.949476i | \(0.398385\pi\) | |||||||
\(158\) | −1.06121 | − | 1.06121i | −0.00671653 | − | 0.00671653i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 13.6263 | − | 24.7855i | 0.0851645 | − | 0.154910i | ||||
\(161\) | −112.909 | −0.701297 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −45.3884 | − | 45.3884i | −0.278457 | − | 0.278457i | 0.554036 | − | 0.832493i | \(-0.313087\pi\) |
−0.832493 | + | 0.554036i | \(0.813087\pi\) | |||||||
\(164\) | 37.2177i | 0.226937i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −107.249 | −0.646075 | ||||||||
\(167\) | 99.2501 | − | 99.2501i | 0.594312 | − | 0.594312i | −0.344481 | − | 0.938793i | \(-0.611945\pi\) |
0.938793 | + | 0.344481i | \(0.111945\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 50.2595i | − | 0.297393i | ||||||
\(170\) | −58.7949 | − | 202.382i | −0.345853 | − | 1.19048i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −52.2765 | + | 52.2765i | −0.303933 | + | 0.303933i | ||||
\(173\) | 80.5404 | + | 80.5404i | 0.465551 | + | 0.465551i | 0.900470 | − | 0.434919i | \(-0.143223\pi\) |
−0.434919 | + | 0.900470i | \(0.643223\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 14.4303 | − | 64.5505i | 0.0824586 | − | 0.368860i | ||||
\(176\) | −46.0313 | −0.261541 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −145.154 | − | 145.154i | −0.815473 | − | 0.815473i | ||||
\(179\) | 154.267i | 0.861824i | 0.902394 | + | 0.430912i | \(0.141808\pi\) | ||||
−0.902394 | + | 0.430912i | \(0.858192\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 166.548 | 0.920155 | 0.460078 | − | 0.887879i | \(-0.347822\pi\) | ||||
0.460078 | + | 0.887879i | \(0.347822\pi\) | |||||||
\(182\) | −28.8303 | + | 28.8303i | −0.158408 | + | 0.158408i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 120.705i | 0.656003i | ||||||||
\(185\) | 28.9566 | − | 52.6705i | 0.156522 | − | 0.284705i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −242.527 | + | 242.527i | −1.29693 | + | 1.29693i | ||||
\(188\) | 100.262 | + | 100.262i | 0.533309 | + | 0.533309i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 149.440 | + | 82.1576i | 0.786528 | + | 0.432409i | ||||
\(191\) | 235.646 | 1.23375 | 0.616873 | − | 0.787063i | \(-0.288399\pi\) | ||||
0.616873 | + | 0.787063i | \(0.288399\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.2211 | − | 16.2211i | −0.0840471 | − | 0.0840471i | 0.663833 | − | 0.747880i | \(-0.268928\pi\) |
−0.747880 | + | 0.663833i | \(0.768928\pi\) | |||||||
\(194\) | − | 47.5744i | − | 0.245229i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −14.0000 | −0.0714286 | ||||||||
\(197\) | 6.68134 | − | 6.68134i | 0.0339154 | − | 0.0339154i | −0.689946 | − | 0.723861i | \(-0.742366\pi\) |
0.723861 | + | 0.689946i | \(0.242366\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 32.0712i | 0.161162i | 0.996748 | + | 0.0805808i | \(0.0256775\pi\) | ||||
−0.996748 | + | 0.0805808i | \(0.974322\pi\) | |||||||
\(200\) | −69.0074 | − | 15.4266i | −0.345037 | − | 0.0771330i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −50.1467 | + | 50.1467i | −0.248251 | + | 0.248251i | ||||
\(203\) | 95.6728 | + | 95.6728i | 0.471294 | + | 0.471294i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 89.3502 | − | 25.9575i | 0.435855 | − | 0.126622i | ||||
\(206\) | 112.775 | 0.547453 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 30.8208 | + | 30.8208i | 0.148177 | + | 0.148177i | ||||
\(209\) | − | 277.538i | − | 1.32793i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 123.531 | 0.585457 | 0.292728 | − | 0.956196i | \(-0.405437\pi\) | ||||
0.292728 | + | 0.956196i | \(0.405437\pi\) | |||||||
\(212\) | −14.1705 | + | 14.1705i | −0.0668422 | + | 0.0668422i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 270.731i | − | 1.26510i | ||||||
\(215\) | 161.963 | + | 89.0421i | 0.753315 | + | 0.414149i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −87.9013 | + | 87.9013i | −0.405075 | + | 0.405075i | ||||
\(218\) | 100.934 | + | 100.934i | 0.463001 | + | 0.463001i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 32.1046 | + | 110.509i | 0.145930 | + | 0.502315i | ||||
\(221\) | 324.774 | 1.46956 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −81.9590 | − | 81.9590i | −0.367529 | − | 0.367529i | 0.499046 | − | 0.866575i | \(-0.333684\pi\) |
−0.866575 | + | 0.499046i | \(0.833684\pi\) | |||||||
\(224\) | 14.9666i | 0.0668153i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −50.6348 | −0.224048 | ||||||||
\(227\) | −93.6089 | + | 93.6089i | −0.412374 | + | 0.412374i | −0.882565 | − | 0.470191i | \(-0.844185\pi\) |
0.470191 | + | 0.882565i | \(0.344185\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 348.973i | 1.52390i | 0.647635 | + | 0.761950i | \(0.275758\pi\) | ||||
−0.647635 | + | 0.761950i | \(0.724242\pi\) | |||||||
\(230\) | 289.781 | − | 84.1856i | 1.25992 | − | 0.366024i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 102.278 | − | 102.278i | 0.440856 | − | 0.440856i | ||||
\(233\) | −208.319 | − | 208.319i | −0.894074 | − | 0.894074i | 0.100829 | − | 0.994904i | \(-0.467850\pi\) |
−0.994904 | + | 0.100829i | \(0.967850\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 170.776 | − | 310.631i | 0.726704 | − | 1.32184i | ||||
\(236\) | −188.697 | −0.799565 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 78.8552 | + | 78.8552i | 0.331324 | + | 0.331324i | ||||
\(239\) | − | 330.793i | − | 1.38407i | −0.721864 | − | 0.692035i | \(-0.756715\pi\) | ||
0.721864 | − | 0.692035i | \(-0.243285\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 375.584 | 1.55844 | 0.779221 | − | 0.626749i | \(-0.215615\pi\) | ||||
0.779221 | + | 0.626749i | \(0.215615\pi\) | |||||||
\(242\) | 11.4299 | − | 11.4299i | 0.0472312 | − | 0.0472312i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 16.1801i | − | 0.0663117i | ||||||
\(245\) | 9.76432 | + | 33.6104i | 0.0398543 | + | 0.137185i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −185.829 | + | 185.829i | −0.752344 | + | 0.752344i | ||||
\(248\) | 93.9704 | + | 93.9704i | 0.378913 | + | 0.378913i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 11.0940 | + | 176.428i | 0.0443761 | + | 0.705713i | ||||
\(251\) | −41.2876 | −0.164493 | −0.0822463 | − | 0.996612i | \(-0.526209\pi\) | ||||
−0.0822463 | + | 0.996612i | \(0.526209\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −347.262 | − | 347.262i | −1.37258 | − | 1.37258i | ||||
\(254\) | − | 233.492i | − | 0.919262i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 101.370 | − | 101.370i | 0.394437 | − | 0.394437i | −0.481828 | − | 0.876266i | \(-0.660027\pi\) |
0.876266 | + | 0.481828i | \(0.160027\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 31.8048i | 0.122799i | ||||||||
\(260\) | 52.4969 | − | 95.4889i | 0.201911 | − | 0.367265i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −34.8004 | + | 34.8004i | −0.132826 | + | 0.132826i | ||||
\(263\) | −164.594 | − | 164.594i | −0.625833 | − | 0.625833i | 0.321184 | − | 0.947017i | \(-0.395919\pi\) |
−0.947017 | + | 0.321184i | \(0.895919\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 43.9031 | + | 24.1366i | 0.165672 | + | 0.0910813i | ||||
\(266\) | −90.2387 | −0.339243 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 41.2938 | + | 41.2938i | 0.154081 | + | 0.154081i | ||||
\(269\) | 254.148i | 0.944788i | 0.881387 | + | 0.472394i | \(0.156610\pi\) | ||||
−0.881387 | + | 0.472394i | \(0.843390\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 22.4723 | 0.0829237 | 0.0414619 | − | 0.999140i | \(-0.486798\pi\) | ||||
0.0414619 | + | 0.999140i | \(0.486798\pi\) | |||||||
\(272\) | 84.2997 | − | 84.2997i | 0.309925 | − | 0.309925i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 263.104i | 0.960235i | ||||||||
\(275\) | 242.913 | − | 154.150i | 0.883319 | − | 0.560544i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 47.3949 | − | 47.3949i | 0.171101 | − | 0.171101i | −0.616362 | − | 0.787463i | \(-0.711394\pi\) |
0.787463 | + | 0.616362i | \(0.211394\pi\) | |||||||
\(278\) | −89.4407 | − | 89.4407i | −0.321729 | − | 0.321729i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 35.9310 | − | 10.4385i | 0.128325 | − | 0.0372803i | ||||
\(281\) | 18.8810 | 0.0671920 | 0.0335960 | − | 0.999435i | \(-0.489304\pi\) | ||||
0.0335960 | + | 0.999435i | \(0.489304\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −115.825 | − | 115.825i | −0.409277 | − | 0.409277i | 0.472209 | − | 0.881486i | \(-0.343457\pi\) |
−0.881486 | + | 0.472209i | \(0.843457\pi\) | |||||||
\(284\) | − | 127.519i | − | 0.449011i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −177.340 | −0.620071 | ||||||||
\(287\) | −34.8140 | + | 34.8140i | −0.121303 | + | 0.121303i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 599.306i | − | 2.07372i | ||||||
\(290\) | −316.879 | − | 174.210i | −1.09268 | − | 0.600724i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 100.377 | − | 100.377i | 0.343756 | − | 0.343756i | ||||
\(293\) | −224.451 | − | 224.451i | −0.766043 | − | 0.766043i | 0.211364 | − | 0.977407i | \(-0.432209\pi\) |
−0.977407 | + | 0.211364i | \(0.932209\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 131.607 | + | 453.014i | 0.446126 | + | 1.53564i | ||||
\(296\) | 34.0008 | 0.114868 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −55.7399 | − | 55.7399i | −0.187047 | − | 0.187047i | ||||
\(299\) | 465.027i | 1.55528i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −97.8004 | −0.324918 | ||||||||
\(302\) | 82.9665 | − | 82.9665i | 0.274724 | − | 0.274724i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 96.4693i | 0.317333i | ||||||||
\(305\) | −38.8441 | + | 11.2848i | −0.127358 | + | 0.0369993i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −42.5120 | + | 42.5120i | −0.138476 | + | 0.138476i | −0.772947 | − | 0.634471i | \(-0.781218\pi\) |
0.634471 | + | 0.772947i | \(0.281218\pi\) | |||||||
\(308\) | −43.0583 | − | 43.0583i | −0.139800 | − | 0.139800i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 160.059 | − | 291.139i | 0.516319 | − | 0.939157i | ||||
\(311\) | 97.1353 | 0.312332 | 0.156166 | − | 0.987731i | \(-0.450086\pi\) | ||||
0.156166 | + | 0.987731i | \(0.450086\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −94.4913 | − | 94.4913i | −0.301889 | − | 0.301889i | 0.539863 | − | 0.841753i | \(-0.318476\pi\) |
−0.841753 | + | 0.539863i | \(0.818476\pi\) | |||||||
\(314\) | 199.590i | 0.635637i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.12242 | −0.00671653 | ||||||||
\(317\) | −146.150 | + | 146.150i | −0.461040 | + | 0.461040i | −0.898996 | − | 0.437956i | \(-0.855703\pi\) |
0.437956 | + | 0.898996i | \(0.355703\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 588.501i | 1.84483i | ||||||||
\(320\) | −11.1592 | − | 38.4119i | −0.0348726 | − | 0.120037i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −112.909 | + | 112.909i | −0.350649 | + | 0.350649i | ||||
\(323\) | 508.271 | + | 508.271i | 1.57359 | + | 1.57359i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −265.858 | − | 59.4326i | −0.818025 | − | 0.182869i | ||||
\(326\) | −90.7768 | −0.278457 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 37.2177 | + | 37.2177i | 0.113469 | + | 0.113469i | ||||
\(329\) | 187.573i | 0.570131i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 223.981 | 0.676679 | 0.338339 | − | 0.941024i | \(-0.390135\pi\) | ||||
0.338339 | + | 0.941024i | \(0.390135\pi\) | |||||||
\(332\) | −107.249 | + | 107.249i | −0.323038 | + | 0.323038i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 198.500i | − | 0.594312i | ||||||
\(335\) | 70.3354 | − | 127.936i | 0.209956 | − | 0.381899i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −41.7444 | + | 41.7444i | −0.123871 | + | 0.123871i | −0.766324 | − | 0.642454i | \(-0.777916\pi\) |
0.642454 | + | 0.766324i | \(0.277916\pi\) | |||||||
\(338\) | −50.2595 | − | 50.2595i | −0.148697 | − | 0.148697i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −261.177 | − | 143.587i | −0.768167 | − | 0.422315i | ||||
\(341\) | −540.697 | −1.58562 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.0958 | − | 13.0958i | −0.0381802 | − | 0.0381802i | ||||
\(344\) | 104.553i | 0.303933i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 161.081 | 0.465551 | ||||||||
\(347\) | −283.163 | + | 283.163i | −0.816031 | + | 0.816031i | −0.985530 | − | 0.169500i | \(-0.945785\pi\) |
0.169500 | + | 0.985530i | \(0.445785\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 73.8529i | − | 0.211613i | −0.994387 | − | 0.105807i | \(-0.966258\pi\) | ||
0.994387 | − | 0.105807i | \(-0.0337424\pi\) | |||||||
\(350\) | −50.1203 | − | 78.9808i | −0.143201 | − | 0.225659i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −46.0313 | + | 46.0313i | −0.130771 | + | 0.130771i | ||||
\(353\) | 221.700 | + | 221.700i | 0.628047 | + | 0.628047i | 0.947576 | − | 0.319530i | \(-0.103525\pi\) |
−0.319530 | + | 0.947576i | \(0.603525\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −306.140 | + | 88.9383i | −0.862367 | + | 0.250530i | ||||
\(356\) | −290.309 | −0.815473 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 154.267 | + | 154.267i | 0.430912 | + | 0.430912i | ||||
\(359\) | 351.735i | 0.979764i | 0.871789 | + | 0.489882i | \(0.162960\pi\) | ||||
−0.871789 | + | 0.489882i | \(0.837040\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −220.645 | −0.611205 | ||||||||
\(362\) | 166.548 | − | 166.548i | 0.460078 | − | 0.460078i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 57.6605i | 0.158408i | ||||||||
\(365\) | −310.986 | − | 170.971i | −0.852017 | − | 0.468413i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.03767 | − | 9.03767i | 0.0246258 | − | 0.0246258i | −0.694687 | − | 0.719312i | \(-0.744457\pi\) |
0.719312 | + | 0.694687i | \(0.244457\pi\) | |||||||
\(368\) | 120.705 | + | 120.705i | 0.328002 | + | 0.328002i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −23.7139 | − | 81.6271i | −0.0640916 | − | 0.220614i | ||||
\(371\) | −26.5107 | −0.0714573 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −151.095 | − | 151.095i | −0.405079 | − | 0.405079i | 0.474939 | − | 0.880019i | \(-0.342470\pi\) |
−0.880019 | + | 0.474939i | \(0.842470\pi\) | |||||||
\(374\) | 485.053i | 1.29693i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 200.524 | 0.533309 | ||||||||
\(377\) | 394.039 | − | 394.039i | 1.04520 | − | 1.04520i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 268.787i | − | 0.709201i | −0.935018 | − | 0.354601i | \(-0.884617\pi\) | ||
0.935018 | − | 0.354601i | \(-0.115383\pi\) | |||||||
\(380\) | 231.598 | − | 67.2826i | 0.609468 | − | 0.177059i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 235.646 | − | 235.646i | 0.616873 | − | 0.616873i | ||||
\(383\) | −304.341 | − | 304.341i | −0.794625 | − | 0.794625i | 0.187618 | − | 0.982242i | \(-0.439923\pi\) |
−0.982242 | + | 0.187618i | \(0.939923\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −73.3408 | + | 133.403i | −0.190496 | + | 0.346501i | ||||
\(386\) | −32.4422 | −0.0840471 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −47.5744 | − | 47.5744i | −0.122614 | − | 0.122614i | ||||
\(389\) | − | 50.0127i | − | 0.128567i | −0.997932 | − | 0.0642837i | \(-0.979524\pi\) | ||
0.997932 | − | 0.0642837i | \(-0.0204763\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1271.92 | 3.25299 | ||||||||
\(392\) | −14.0000 | + | 14.0000i | −0.0357143 | + | 0.0357143i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 13.3627i | − | 0.0339154i | ||||||
\(395\) | 1.48029 | + | 5.09539i | 0.00374756 | + | 0.0128997i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −325.002 | + | 325.002i | −0.818644 | + | 0.818644i | −0.985912 | − | 0.167268i | \(-0.946506\pi\) |
0.167268 | + | 0.985912i | \(0.446506\pi\) | |||||||
\(398\) | 32.0712 | + | 32.0712i | 0.0805808 | + | 0.0805808i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −84.4340 | + | 53.5808i | −0.211085 | + | 0.133952i | ||||
\(401\) | 462.981 | 1.15457 | 0.577283 | − | 0.816544i | \(-0.304113\pi\) | ||||
0.577283 | + | 0.816544i | \(0.304113\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 362.031 | + | 362.031i | 0.898340 | + | 0.898340i | ||||
\(404\) | 100.293i | 0.248251i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 191.346 | 0.471294 | ||||||||
\(407\) | −97.8188 | + | 97.8188i | −0.240341 | + | 0.240341i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 131.630i | − | 0.321834i | −0.986968 | − | 0.160917i | \(-0.948555\pi\) | ||
0.986968 | − | 0.160917i | \(-0.0514451\pi\) | |||||||
\(410\) | 63.3926 | − | 115.308i | 0.154616 | − | 0.281238i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 112.775 | − | 112.775i | 0.273726 | − | 0.273726i | ||||
\(413\) | −176.510 | − | 176.510i | −0.427386 | − | 0.427386i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 332.277 | + | 182.675i | 0.800667 | + | 0.440182i | ||||
\(416\) | 61.6417 | 0.148177 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −277.538 | − | 277.538i | −0.663966 | − | 0.663966i | ||||
\(419\) | 536.418i | 1.28023i | 0.768277 | + | 0.640117i | \(0.221114\pi\) | ||||
−0.768277 | + | 0.640117i | \(0.778886\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −508.770 | −1.20848 | −0.604240 | − | 0.796803i | \(-0.706523\pi\) | ||||
−0.604240 | + | 0.796803i | \(0.706523\pi\) | |||||||
\(422\) | 123.531 | − | 123.531i | 0.292728 | − | 0.292728i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 28.3411i | 0.0668422i | ||||||||
\(425\) | −162.557 | + | 727.163i | −0.382487 | + | 1.71097i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 15.1351 | − | 15.1351i | 0.0354451 | − | 0.0354451i | ||||
\(428\) | −270.731 | − | 270.731i | −0.632548 | − | 0.632548i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 251.005 | − | 72.9206i | 0.583732 | − | 0.169583i | ||||
\(431\) | −467.561 | −1.08483 | −0.542414 | − | 0.840111i | \(-0.682490\pi\) | ||||
−0.542414 | + | 0.840111i | \(0.682490\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −129.391 | − | 129.391i | −0.298825 | − | 0.298825i | 0.541729 | − | 0.840554i | \(-0.317770\pi\) |
−0.840554 | + | 0.541729i | \(0.817770\pi\) | |||||||
\(434\) | 175.803i | 0.405075i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 201.868 | 0.463001 | ||||||||
\(437\) | −727.768 | + | 727.768i | −1.66537 | + | 1.66537i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 51.7818i | 0.117954i | 0.998259 | + | 0.0589770i | \(0.0187839\pi\) | ||||
−0.998259 | + | 0.0589770i | \(0.981216\pi\) | |||||||
\(440\) | 142.614 | + | 78.4047i | 0.324122 | + | 0.178192i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 324.774 | − | 324.774i | 0.734782 | − | 0.734782i | ||||
\(443\) | −357.514 | − | 357.514i | −0.807029 | − | 0.807029i | 0.177154 | − | 0.984183i | \(-0.443311\pi\) |
−0.984183 | + | 0.177154i | \(0.943311\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 202.476 | + | 696.956i | 0.455002 | + | 1.56619i | ||||
\(446\) | −163.918 | −0.367529 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 14.9666 | + | 14.9666i | 0.0334077 | + | 0.0334077i | ||||
\(449\) | − | 615.742i | − | 1.37136i | −0.727902 | − | 0.685681i | \(-0.759504\pi\) | ||
0.727902 | − | 0.685681i | \(-0.240496\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −214.148 | −0.474828 | ||||||||
\(452\) | −50.6348 | + | 50.6348i | −0.112024 | + | 0.112024i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 187.218i | 0.412374i | ||||||||
\(455\) | 138.428 | − | 40.2154i | 0.304237 | − | 0.0883855i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −502.144 | + | 502.144i | −1.09878 | + | 1.09878i | −0.104230 | + | 0.994553i | \(0.533238\pi\) |
−0.994553 | + | 0.104230i | \(0.966762\pi\) | |||||||
\(458\) | 348.973 | + | 348.973i | 0.761950 | + | 0.761950i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 205.595 | − | 373.966i | 0.446946 | − | 0.812970i | ||||
\(461\) | −100.965 | −0.219012 | −0.109506 | − | 0.993986i | \(-0.534927\pi\) | ||||
−0.109506 | + | 0.993986i | \(0.534927\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 312.235 | + | 312.235i | 0.674374 | + | 0.674374i | 0.958721 | − | 0.284347i | \(-0.0917768\pi\) |
−0.284347 | + | 0.958721i | \(0.591777\pi\) | |||||||
\(464\) | − | 204.557i | − | 0.440856i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −416.639 | −0.894074 | ||||||||
\(467\) | −502.571 | + | 502.571i | −1.07617 | + | 1.07617i | −0.0793198 | + | 0.996849i | \(0.525275\pi\) |
−0.996849 | + | 0.0793198i | \(0.974725\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 77.2537i | 0.164720i | ||||||||
\(470\) | −139.856 | − | 481.407i | −0.297566 | − | 1.02427i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −188.697 | + | 188.697i | −0.399783 | + | 0.399783i | ||||
\(473\) | −300.794 | − | 300.794i | −0.635929 | − | 0.635929i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −323.056 | − | 509.080i | −0.680119 | − | 1.07175i | ||||
\(476\) | 157.710 | 0.331324 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −330.793 | − | 330.793i | −0.692035 | − | 0.692035i | ||||
\(479\) | 270.133i | 0.563952i | 0.959421 | + | 0.281976i | \(0.0909899\pi\) | ||||
−0.959421 | + | 0.281976i | \(0.909010\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 130.992 | 0.272332 | ||||||||
\(482\) | 375.584 | − | 375.584i | 0.779221 | − | 0.779221i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 22.8599i | − | 0.0472312i | ||||||
\(485\) | −81.0330 | + | 147.395i | −0.167078 | + | 0.303906i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −227.632 | + | 227.632i | −0.467417 | + | 0.467417i | −0.901077 | − | 0.433660i | \(-0.857222\pi\) |
0.433660 | + | 0.901077i | \(0.357222\pi\) | |||||||
\(488\) | −16.1801 | − | 16.1801i | −0.0331559 | − | 0.0331559i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 43.3747 | + | 23.8461i | 0.0885198 | + | 0.0486655i | ||||
\(491\) | 23.2563 | 0.0473652 | 0.0236826 | − | 0.999720i | \(-0.492461\pi\) | ||||
0.0236826 | + | 0.999720i | \(0.492461\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1077.76 | − | 1077.76i | −2.18612 | − | 2.18612i | ||||
\(494\) | 371.658i | 0.752344i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 187.941 | 0.378913 | ||||||||
\(497\) | 119.283 | − | 119.283i | 0.240006 | − | 0.240006i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 319.077i | − | 0.639433i | −0.947513 | − | 0.319717i | \(-0.896412\pi\) | ||
0.947513 | − | 0.319717i | \(-0.103588\pi\) | |||||||
\(500\) | 187.522 | + | 165.334i | 0.375045 | + | 0.330668i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −41.2876 | + | 41.2876i | −0.0822463 | + | 0.0822463i | ||||
\(503\) | −585.731 | − | 585.731i | −1.16448 | − | 1.16448i | −0.983485 | − | 0.180990i | \(-0.942070\pi\) |
−0.180990 | − | 0.983485i | \(-0.557930\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 240.779 | − | 69.9498i | 0.476789 | − | 0.138514i | ||||
\(506\) | −694.524 | −1.37258 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −233.492 | − | 233.492i | −0.459631 | − | 0.459631i | ||||
\(509\) | 266.157i | 0.522902i | 0.965217 | + | 0.261451i | \(0.0842009\pi\) | ||||
−0.965217 | + | 0.261451i | \(0.915799\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 187.787 | 0.367490 | ||||||||
\(512\) | 16.0000 | − | 16.0000i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 202.741i | − | 0.394437i | ||||||
\(515\) | −349.399 | − | 192.089i | −0.678446 | − | 0.372988i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −576.899 | + | 576.899i | −1.11586 | + | 1.11586i | ||||
\(518\) | 31.8048 | + | 31.8048i | 0.0613993 | + | 0.0613993i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −42.9921 | − | 147.986i | −0.0826770 | − | 0.284588i | ||||
\(521\) | 1.52542 | 0.00292786 | 0.00146393 | − | 0.999999i | \(-0.499534\pi\) | ||||
0.00146393 | + | 0.999999i | \(0.499534\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 260.120 | + | 260.120i | 0.497362 | + | 0.497362i | 0.910616 | − | 0.413254i | \(-0.135608\pi\) |
−0.413254 | + | 0.910616i | \(0.635608\pi\) | |||||||
\(524\) | 69.6007i | 0.132826i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −329.188 | −0.625833 | ||||||||
\(527\) | 990.210 | − | 990.210i | 1.87896 | − | 1.87896i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1292.20i | 2.44272i | ||||||||
\(530\) | 68.0396 | − | 19.7665i | 0.128377 | − | 0.0372953i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −90.2387 | + | 90.2387i | −0.169622 | + | 0.169622i | ||||
\(533\) | 143.385 | + | 143.385i | 0.269015 | + | 0.269015i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −461.133 | + | 838.776i | −0.861931 | + | 1.56781i | ||||
\(536\) | 82.5877 | 0.154081 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 254.148 | + | 254.148i | 0.472394 | + | 0.472394i | ||||
\(539\) | − | 80.5547i | − | 0.149452i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −273.648 | −0.505820 | −0.252910 | − | 0.967490i | \(-0.581388\pi\) | ||||
−0.252910 | + | 0.967490i | \(0.581388\pi\) | |||||||
\(542\) | 22.4723 | − | 22.4723i | 0.0414619 | − | 0.0414619i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 168.599i | − | 0.309925i | ||||||
\(545\) | −140.793 | − | 484.634i | −0.258336 | − | 0.889236i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 355.490 | − | 355.490i | 0.649890 | − | 0.649890i | −0.303077 | − | 0.952966i | \(-0.598014\pi\) |
0.952966 | + | 0.303077i | \(0.0980138\pi\) | |||||||
\(548\) | 263.104 | + | 263.104i | 0.480117 | + | 0.480117i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 88.7632 | − | 397.062i | 0.161388 | − | 0.721932i | ||||
\(551\) | 1233.34 | 2.23837 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.98535 | − | 1.98535i | −0.00359014 | − | 0.00359014i | ||||
\(554\) | − | 94.7898i | − | 0.171101i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −178.881 | −0.321729 | ||||||||
\(557\) | 270.897 | − | 270.897i | 0.486350 | − | 0.486350i | −0.420802 | − | 0.907152i | \(-0.638251\pi\) |
0.907152 | + | 0.420802i | \(0.138251\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 402.802i | 0.720575i | ||||||||
\(560\) | 25.4925 | − | 46.3695i | 0.0455224 | − | 0.0828027i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 18.8810 | − | 18.8810i | 0.0335960 | − | 0.0335960i | ||||
\(563\) | −73.1143 | − | 73.1143i | −0.129866 | − | 0.129866i | 0.639186 | − | 0.769052i | \(-0.279271\pi\) |
−0.769052 | + | 0.639186i | \(0.779271\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 156.876 | + | 86.2458i | 0.277657 | + | 0.152647i | ||||
\(566\) | −231.651 | −0.409277 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −127.519 | − | 127.519i | −0.224505 | − | 0.224505i | ||||
\(569\) | − | 1018.55i | − | 1.79007i | −0.445992 | − | 0.895037i | \(-0.647149\pi\) | ||
0.445992 | − | 0.895037i | \(-0.352851\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −621.517 | −1.08847 | −0.544236 | − | 0.838932i | \(-0.683180\pi\) | ||||
−0.544236 | + | 0.838932i | \(0.683180\pi\) | |||||||
\(572\) | −177.340 | + | 177.340i | −0.310036 | + | 0.310036i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 69.6280i | 0.121303i | ||||||||
\(575\) | −1041.19 | − | 232.758i | −1.81076 | − | 0.404796i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 760.301 | − | 760.301i | 1.31768 | − | 1.31768i | 0.402071 | − | 0.915608i | \(-0.368290\pi\) |
0.915608 | − | 0.402071i | \(-0.131710\pi\) | |||||||
\(578\) | −599.306 | − | 599.306i | −1.03686 | − | 1.03686i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −491.089 | + | 142.668i | −0.846704 | + | 0.245980i | ||||
\(581\) | −200.644 | −0.345342 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −81.5360 | − | 81.5360i | −0.139856 | − | 0.139856i | ||||
\(584\) | − | 200.753i | − | 0.343756i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −448.901 | −0.766043 | ||||||||
\(587\) | −5.94607 | + | 5.94607i | −0.0101296 | + | 0.0101296i | −0.712153 | − | 0.702024i | \(-0.752280\pi\) |
0.702024 | + | 0.712153i | \(0.252280\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1133.16i | 1.92387i | ||||||||
\(590\) | 584.621 | + | 321.407i | 0.990883 | + | 0.544757i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 34.0008 | − | 34.0008i | 0.0574338 | − | 0.0574338i | ||||
\(593\) | 463.916 | + | 463.916i | 0.782320 | + | 0.782320i | 0.980222 | − | 0.197902i | \(-0.0634127\pi\) |
−0.197902 | + | 0.980222i | \(0.563413\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −109.995 | − | 378.622i | −0.184866 | − | 0.636339i | ||||
\(596\) | −111.480 | −0.187047 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 465.027 | + | 465.027i | 0.777638 | + | 0.777638i | ||||
\(599\) | 660.745i | 1.10308i | 0.834148 | + | 0.551540i | \(0.185960\pi\) | ||||
−0.834148 | + | 0.551540i | \(0.814040\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −905.439 | −1.50655 | −0.753277 | − | 0.657704i | \(-0.771528\pi\) | ||||
−0.753277 | + | 0.657704i | \(0.771528\pi\) | |||||||
\(602\) | −97.8004 | + | 97.8004i | −0.162459 | + | 0.162459i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 165.933i | − | 0.274724i | ||||||
\(605\) | −54.8807 | + | 15.9436i | −0.0907119 | + | 0.0263531i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 518.514 | − | 518.514i | 0.854224 | − | 0.854224i | −0.136426 | − | 0.990650i | \(-0.543562\pi\) |
0.990650 | + | 0.136426i | \(0.0435615\pi\) | |||||||
\(608\) | 96.4693 | + | 96.4693i | 0.158667 | + | 0.158667i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −27.5593 | + | 50.1289i | −0.0451792 | + | 0.0821786i | ||||
\(611\) | 772.541 | 1.26439 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −500.739 | − | 500.739i | −0.816867 | − | 0.816867i | 0.168786 | − | 0.985653i | \(-0.446015\pi\) |
−0.985653 | + | 0.168786i | \(0.946015\pi\) | |||||||
\(614\) | 85.0240i | 0.138476i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −86.1166 | −0.139800 | ||||||||
\(617\) | −122.242 | + | 122.242i | −0.198123 | + | 0.198123i | −0.799195 | − | 0.601072i | \(-0.794740\pi\) |
0.601072 | + | 0.799195i | \(0.294740\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 320.914i | 0.518440i | 0.965818 | + | 0.259220i | \(0.0834655\pi\) | ||||
−0.965818 | + | 0.259220i | \(0.916534\pi\) | |||||||
\(620\) | −131.080 | − | 451.198i | −0.211419 | − | 0.727738i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 97.1353 | − | 97.1353i | 0.156166 | − | 0.156166i | ||||
\(623\) | −271.559 | − | 271.559i | −0.435889 | − | 0.435889i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 266.137 | − | 565.505i | 0.425820 | − | 0.904808i | ||||
\(626\) | −188.983 | −0.301889 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 199.590 | + | 199.590i | 0.317818 | + | 0.317818i | ||||
\(629\) | − | 358.282i | − | 0.569606i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −636.141 | −1.00815 | −0.504074 | − | 0.863661i | \(-0.668166\pi\) | ||||
−0.504074 | + | 0.863661i | \(0.668166\pi\) | |||||||
\(632\) | −2.12242 | + | 2.12242i | −0.00335827 | + | 0.00335827i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 292.300i | 0.461040i | ||||||||
\(635\) | −397.706 | + | 723.405i | −0.626308 | + | 1.13922i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −53.9365 | + | 53.9365i | −0.0846726 | + | 0.0846726i | ||||
\(638\) | 588.501 | + | 588.501i | 0.922416 | + | 0.922416i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −49.5711 | − | 27.2527i | −0.0774548 | − | 0.0425823i | ||||
\(641\) | 682.051 | 1.06404 | 0.532021 | − | 0.846731i | \(-0.321433\pi\) | ||||
0.532021 | + | 0.846731i | \(0.321433\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.33298 | − | 5.33298i | −0.00829390 | − | 0.00829390i | 0.702948 | − | 0.711242i | \(-0.251867\pi\) |
−0.711242 | + | 0.702948i | \(0.751867\pi\) | |||||||
\(644\) | 225.818i | 0.350649i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1016.54 | 1.57359 | ||||||||
\(647\) | −285.931 | + | 285.931i | −0.441933 | + | 0.441933i | −0.892661 | − | 0.450728i | \(-0.851164\pi\) |
0.450728 | + | 0.892661i | \(0.351164\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 1085.75i | − | 1.67296i | ||||||
\(650\) | −325.291 | + | 206.426i | −0.500447 | + | 0.317578i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −90.7768 | + | 90.7768i | −0.139228 | + | 0.139228i | ||||
\(653\) | −199.462 | − | 199.462i | −0.305455 | − | 0.305455i | 0.537689 | − | 0.843144i | \(-0.319298\pi\) |
−0.843144 | + | 0.537689i | \(0.819298\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 167.093 | − | 48.5431i | 0.255104 | − | 0.0741116i | ||||
\(656\) | 74.4355 | 0.113469 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 187.573 | + | 187.573i | 0.285066 | + | 0.285066i | ||||
\(659\) | − | 204.685i | − | 0.310599i | −0.987867 | − | 0.155300i | \(-0.950366\pi\) | ||
0.987867 | − | 0.155300i | \(-0.0496343\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 143.044 | 0.216406 | 0.108203 | − | 0.994129i | \(-0.465490\pi\) | ||||
0.108203 | + | 0.994129i | \(0.465490\pi\) | |||||||
\(662\) | 223.981 | − | 223.981i | 0.338339 | − | 0.338339i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 214.497i | 0.323038i | ||||||||
\(665\) | 279.577 | + | 153.703i | 0.420417 | + | 0.231132i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1543.19 | − | 1543.19i | 2.31362 | − | 2.31362i | ||||
\(668\) | −198.500 | − | 198.500i | −0.297156 | − | 0.297156i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −57.6008 | − | 198.272i | −0.0859714 | − | 0.295928i | ||||
\(671\) | 93.0986 | 0.138746 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −317.527 | − | 317.527i | −0.471808 | − | 0.471808i | 0.430691 | − | 0.902499i | \(-0.358270\pi\) |
−0.902499 | + | 0.430691i | \(0.858270\pi\) | |||||||
\(674\) | 83.4888i | 0.123871i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −100.519 | −0.148697 | ||||||||
\(677\) | 272.663 | − | 272.663i | 0.402752 | − | 0.402752i | −0.476450 | − | 0.879202i | \(-0.658077\pi\) |
0.879202 | + | 0.476450i | \(0.158077\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 89.0035i | − | 0.131080i | ||||||
\(680\) | −404.764 | + | 117.590i | −0.595241 | + | 0.172926i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −540.697 | + | 540.697i | −0.792812 | + | 0.792812i | ||||
\(683\) | 449.231 | + | 449.231i | 0.657732 | + | 0.657732i | 0.954843 | − | 0.297111i | \(-0.0960232\pi\) |
−0.297111 | + | 0.954843i | \(0.596023\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 448.143 | − | 815.148i | 0.654224 | − | 1.19000i | ||||
\(686\) | −26.1916 | −0.0381802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 104.553 | + | 104.553i | 0.151967 | + | 0.151967i | ||||
\(689\) | 109.187i | 0.158472i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1004.13 | 1.45316 | 0.726578 | − | 0.687084i | \(-0.241109\pi\) | ||||
0.726578 | + | 0.687084i | \(0.241109\pi\) | |||||||
\(692\) | 161.081 | − | 161.081i | 0.232776 | − | 0.232776i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 566.325i | 0.816031i | ||||||||
\(695\) | 124.761 | + | 429.448i | 0.179512 | + | 0.617911i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 392.181 | − | 392.181i | 0.562669 | − | 0.562669i | ||||
\(698\) | −73.8529 | − | 73.8529i | −0.105807 | − | 0.105807i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −129.101 | − | 28.8605i | −0.184430 | − | 0.0412293i | ||||
\(701\) | 869.248 | 1.24001 | 0.620006 | − | 0.784597i | \(-0.287130\pi\) | ||||
0.620006 | + | 0.784597i | \(0.287130\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 205.002 | + | 205.002i | 0.291610 | + | 0.291610i | ||||
\(704\) | 92.0626i | 0.130771i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 443.401 | 0.628047 | ||||||||
\(707\) | −93.8159 | + | 93.8159i | −0.132696 | + | 0.132696i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 79.6980i | 0.112409i | 0.998419 | + | 0.0562045i | \(0.0178999\pi\) | ||||
−0.998419 | + | 0.0562045i | \(0.982100\pi\) | |||||||
\(710\) | −217.202 | + | 395.078i | −0.305918 | + | 0.556449i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −290.309 | + | 290.309i | −0.407737 | + | 0.407737i | ||||
\(713\) | 1417.83 | + | 1417.83i | 1.98855 | + | 1.98855i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 549.435 | + | 302.062i | 0.768440 | + | 0.422465i | ||||
\(716\) | 308.533 | 0.430912 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 351.735 | + | 351.735i | 0.489882 | + | 0.489882i | ||||
\(719\) | − | 1081.03i | − | 1.50351i | −0.659440 | − | 0.751757i | \(-0.729207\pi\) | ||
0.659440 | − | 0.751757i | \(-0.270793\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 210.983 | 0.292626 | ||||||||
\(722\) | −220.645 | + | 220.645i | −0.305603 | + | 0.305603i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 333.096i | − | 0.460078i | ||||||
\(725\) | 685.020 | + | 1079.47i | 0.944856 | + | 1.48893i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 281.701 | − | 281.701i | 0.387484 | − | 0.387484i | −0.486305 | − | 0.873789i | \(-0.661656\pi\) |
0.873789 | + | 0.486305i | \(0.161656\pi\) | |||||||
\(728\) | 57.6605 | + | 57.6605i | 0.0792040 | + | 0.0792040i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −481.957 | + | 140.016i | −0.660215 | + | 0.191802i | ||||
\(731\) | 1101.72 | 1.50715 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1016.28 | + | 1016.28i | 1.38647 | + | 1.38647i | 0.832611 | + | 0.553858i | \(0.186845\pi\) |
0.553858 | + | 0.832611i | \(0.313155\pi\) | |||||||
\(734\) | − | 18.0753i | − | 0.0246258i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 241.409 | 0.328002 | ||||||||
\(737\) | −237.601 | + | 237.601i | −0.322389 | + | 0.322389i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 289.140i | 0.391258i | 0.980678 | + | 0.195629i | \(0.0626749\pi\) | ||||
−0.980678 | + | 0.195629i | \(0.937325\pi\) | |||||||
\(740\) | −105.341 | − | 57.9132i | −0.142353 | − | 0.0782611i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −26.5107 | + | 26.5107i | −0.0357286 | + | 0.0357286i | ||||
\(743\) | −290.501 | − | 290.501i | −0.390984 | − | 0.390984i | 0.484054 | − | 0.875038i | \(-0.339164\pi\) |
−0.875038 | + | 0.484054i | \(0.839164\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 77.7517 | + | 267.634i | 0.104365 | + | 0.359240i | ||||
\(746\) | −302.189 | −0.405079 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 485.053 | + | 485.053i | 0.648467 | + | 0.648467i | ||||
\(749\) | − | 506.491i | − | 0.676223i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 688.089 | 0.916231 | 0.458115 | − | 0.888893i | \(-0.348525\pi\) | ||||
0.458115 | + | 0.888893i | \(0.348525\pi\) | |||||||
\(752\) | 200.524 | − | 200.524i | 0.266655 | − | 0.266655i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 788.077i | − | 1.04520i | ||||||
\(755\) | −398.363 | + | 115.730i | −0.527632 | + | 0.153285i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 180.960 | − | 180.960i | 0.239049 | − | 0.239049i | −0.577408 | − | 0.816456i | \(-0.695936\pi\) |
0.816456 | + | 0.577408i | \(0.195936\pi\) | |||||||
\(758\) | −268.787 | − | 268.787i | −0.354601 | − | 0.354601i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 164.315 | − | 298.880i | 0.216204 | − | 0.393264i | ||||
\(761\) | −1096.09 | −1.44033 | −0.720163 | − | 0.693805i | \(-0.755933\pi\) | ||||
−0.720163 | + | 0.693805i | \(0.755933\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 188.831 | + | 188.831i | 0.247484 | + | 0.247484i | ||||
\(764\) | − | 471.291i | − | 0.616873i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −608.682 | −0.794625 | ||||||||
\(767\) | −726.977 | + | 726.977i | −0.947818 | + | 0.947818i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 892.540i | − | 1.16065i | −0.814385 | − | 0.580325i | \(-0.802925\pi\) | ||
0.814385 | − | 0.580325i | \(-0.197075\pi\) | |||||||
\(770\) | 60.0621 | + | 206.744i | 0.0780028 | + | 0.268499i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −32.4422 | + | 32.4422i | −0.0420235 | + | 0.0420235i | ||||
\(773\) | −836.773 | − | 836.773i | −1.08250 | − | 1.08250i | −0.996276 | − | 0.0862244i | \(-0.972520\pi\) |
−0.0862244 | − | 0.996276i | \(-0.527480\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −991.787 | + | 629.376i | −1.27973 | + | 0.812099i | ||||
\(776\) | −95.1487 | −0.122614 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −50.0127 | − | 50.0127i | −0.0642837 | − | 0.0642837i | ||||
\(779\) | 448.796i | 0.576118i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 733.733 | 0.939479 | ||||||||
\(782\) | 1271.92 | − | 1271.92i | 1.62650 | − | 1.62650i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 28.0000i | 0.0357143i | ||||||||
\(785\) | 339.960 | − | 618.368i | 0.433070 | − | 0.787730i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −226.485 | + | 226.485i | −0.287782 | + | 0.287782i | −0.836203 | − | 0.548420i | \(-0.815229\pi\) |
0.548420 | + | 0.836203i | \(0.315229\pi\) | |||||||
\(788\) | −13.3627 | − | 13.3627i | −0.0169577 | − | 0.0169577i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 6.57568 | + | 3.61511i | 0.00832365 | + | 0.00457608i | ||||
\(791\) | −94.7290 | −0.119759 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −62.3354 | − | 62.3354i | −0.0786070 | − | 0.0786070i | ||||
\(794\) | 650.003i | 0.818644i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 64.1423 | 0.0805808 | ||||||||
\(797\) | 728.914 | − | 728.914i | 0.914572 | − | 0.914572i | −0.0820555 | − | 0.996628i | \(-0.526148\pi\) |
0.996628 | + | 0.0820555i | \(0.0261485\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 2113.02i | − | 2.64458i | ||||||
\(800\) | −30.8532 | + | 138.015i | −0.0385665 | + | 0.172518i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 462.981 | − | 462.981i | 0.577283 | − | 0.577283i | ||||
\(803\) | 577.558 | + | 577.558i | 0.719250 | + | 0.719250i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 542.130 | − | 157.497i | 0.673453 | − | 0.195648i | ||||
\(806\) | 724.062 | 0.898340 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 100.293 | + | 100.293i | 0.124126 | + | 0.124126i | ||||
\(809\) | − | 1196.38i | − | 1.47884i | −0.673247 | − | 0.739418i | \(-0.735101\pi\) | ||
0.673247 | − | 0.739418i | \(-0.264899\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1180.03 | −1.45503 | −0.727513 | − | 0.686094i | \(-0.759324\pi\) | ||||
−0.727513 | + | 0.686094i | \(0.759324\pi\) | |||||||
\(812\) | 191.346 | − | 191.346i | 0.235647 | − | 0.235647i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 195.638i | 0.240341i | ||||||||
\(815\) | 281.244 | + | 154.619i | 0.345085 | + | 0.189717i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −630.385 | + | 630.385i | −0.771585 | + | 0.771585i | ||||
\(818\) | −131.630 | − | 131.630i | −0.160917 | − | 0.160917i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −51.9151 | − | 178.700i | −0.0633111 | − | 0.217927i | ||||
\(821\) | −35.8305 | −0.0436425 | −0.0218212 | − | 0.999762i | \(-0.506946\pi\) | ||||
−0.0218212 | + | 0.999762i | \(0.506946\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 448.829 | + | 448.829i | 0.545357 | + | 0.545357i | 0.925094 | − | 0.379737i | \(-0.123986\pi\) |
−0.379737 | + | 0.925094i | \(0.623986\pi\) | |||||||
\(824\) | − | 225.550i | − | 0.273726i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −353.021 | −0.427386 | ||||||||
\(827\) | −874.926 | + | 874.926i | −1.05795 | + | 1.05795i | −0.0597373 | + | 0.998214i | \(0.519026\pi\) |
−0.998214 | + | 0.0597373i | \(0.980974\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 934.022i | − | 1.12669i | −0.826223 | − | 0.563343i | \(-0.809515\pi\) | ||
0.826223 | − | 0.563343i | \(-0.190485\pi\) | |||||||
\(830\) | 514.952 | − | 149.601i | 0.620424 | − | 0.180242i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 61.6417 | − | 61.6417i | 0.0740886 | − | 0.0740886i | ||||
\(833\) | 147.525 | + | 147.525i | 0.177100 | + | 0.177100i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −338.104 | + | 614.992i | −0.404915 | + | 0.736517i | ||||
\(836\) | −555.076 | −0.663966 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 536.418 | + | 536.418i | 0.640117 | + | 0.640117i | ||||
\(839\) | − | 10.5147i | − | 0.0125324i | −0.999980 | − | 0.00626621i | \(-0.998005\pi\) | ||
0.999980 | − | 0.00626621i | \(-0.00199461\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1774.22 | −2.10966 | ||||||||
\(842\) | −508.770 | + | 508.770i | −0.604240 | + | 0.604240i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 247.063i | − | 0.292728i | ||||||
\(845\) | 70.1071 | + | 241.320i | 0.0829670 | + | 0.285586i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 21.3835 | − | 21.3835i | 0.0252461 | − | 0.0252461i | ||||
\(848\) | 28.3411 | + | 28.3411i | 0.0334211 | + | 0.0334211i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 564.606 | + | 889.720i | 0.664242 | + | 1.04673i | ||||
\(851\) | 513.007 | 0.602828 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1082.57 | + | 1082.57i | 1.26914 | + | 1.26914i | 0.946534 | + | 0.322603i | \(0.104558\pi\) |
0.322603 | + | 0.946534i | \(0.395442\pi\) | |||||||
\(854\) | − | 30.2701i | − | 0.0354451i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −541.461 | −0.632548 | ||||||||
\(857\) | −506.843 | + | 506.843i | −0.591416 | + | 0.591416i | −0.938014 | − | 0.346598i | \(-0.887337\pi\) |
0.346598 | + | 0.938014i | \(0.387337\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 471.172i | 0.548512i | 0.961657 | + | 0.274256i | \(0.0884315\pi\) | ||||
−0.961657 | + | 0.274256i | \(0.911568\pi\) | |||||||
\(860\) | 178.084 | − | 323.926i | 0.207075 | − | 0.376658i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −467.561 | + | 467.561i | −0.542414 | + | 0.542414i | ||||
\(863\) | −352.570 | − | 352.570i | −0.408540 | − | 0.408540i | 0.472689 | − | 0.881229i | \(-0.343283\pi\) |
−0.881229 | + | 0.472689i | \(0.843283\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −499.059 | − | 274.367i | −0.576947 | − | 0.317188i | ||||
\(866\) | −258.782 | −0.298825 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 175.803 | + | 175.803i | 0.202538 | + | 0.202538i | ||||
\(869\) | − | 12.2122i | − | 0.0140532i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 318.178 | 0.365301 | ||||||||
\(872\) | 201.868 | − | 201.868i | 0.231500 | − | 0.231500i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1455.54i | 1.66537i | ||||||||
\(875\) | 20.7550 | + | 330.067i | 0.0237200 | + | 0.377219i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1223.94 | + | 1223.94i | −1.39560 | + | 1.39560i | −0.583467 | + | 0.812137i | \(0.698304\pi\) |
−0.812137 | + | 0.583467i | \(0.801696\pi\) | |||||||
\(878\) | 51.7818 | + | 51.7818i | 0.0589770 | + | 0.0589770i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 221.018 | − | 64.2091i | 0.251157 | − | 0.0729649i | ||||
\(881\) | 635.103 | 0.720889 | 0.360444 | − | 0.932781i | \(-0.382625\pi\) | ||||
0.360444 | + | 0.932781i | \(0.382625\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −230.546 | − | 230.546i | −0.261094 | − | 0.261094i | 0.564405 | − | 0.825498i | \(-0.309106\pi\) |
−0.825498 | + | 0.564405i | \(0.809106\pi\) | |||||||
\(884\) | − | 649.547i | − | 0.734782i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −715.028 | −0.807029 | ||||||||
\(887\) | 1224.61 | − | 1224.61i | 1.38062 | − | 1.38062i | 0.537101 | − | 0.843518i | \(-0.319520\pi\) |
0.843518 | − | 0.537101i | \(-0.180480\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 436.824i | − | 0.491366i | ||||||
\(890\) | 899.432 | + | 494.480i | 1.01060 | + | 0.555595i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −163.918 | + | 163.918i | −0.183765 | + | 0.183765i | ||||
\(893\) | 1209.03 | + | 1209.03i | 1.35389 | + | 1.35389i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −215.187 | − | 740.708i | −0.240432 | − | 0.827607i | ||||
\(896\) | 29.9333 | 0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −615.742 | − | 615.742i | −0.685681 | − | 0.685681i | ||||
\(899\) | − | 2402.79i | − | 2.67273i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 298.643 | 0.331457 | ||||||||
\(902\) | −214.148 | + | 214.148i | −0.237414 | + | 0.237414i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 101.270i | 0.112024i | ||||||||
\(905\) | −799.678 | + | 232.318i | −0.883622 | + | 0.256705i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 766.713 | − | 766.713i | 0.845329 | − | 0.845329i | −0.144217 | − | 0.989546i | \(-0.546066\pi\) |
0.989546 | + | 0.144217i | \(0.0460664\pi\) | |||||||
\(908\) | 187.218 | + | 187.218i | 0.206187 | + | 0.206187i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 98.2126 | − | 178.643i | 0.107926 | − | 0.196311i | ||||
\(911\) | 754.441 | 0.828146 | 0.414073 | − | 0.910244i | \(-0.364106\pi\) | ||||
0.414073 | + | 0.910244i | \(0.364106\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −617.098 | − | 617.098i | −0.675902 | − | 0.675902i | ||||
\(914\) | 1004.29i | 1.09878i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 697.947 | 0.761950 | ||||||||
\(917\) | −65.1055 | + | 65.1055i | −0.0709984 | + | 0.0709984i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 858.117i | 0.933750i | 0.884323 | + | 0.466875i | \(0.154620\pi\) | ||||
−0.884323 | + | 0.466875i | \(0.845380\pi\) | |||||||
\(920\) | −168.371 | − | 579.561i | −0.183012 | − | 0.629958i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −100.965 | + | 100.965i | −0.109506 | + | 0.109506i | ||||
\(923\) | −491.280 | − | 491.280i | −0.532265 | − | 0.532265i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −65.5645 | + | 293.288i | −0.0708806 | + | 0.317068i | ||||
\(926\) | 624.471 | 0.674374 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −204.557 | − | 204.557i | −0.220428 | − | 0.220428i | ||||
\(929\) | − | 631.542i | − | 0.679809i | −0.940460 | − | 0.339904i | \(-0.889605\pi\) | ||
0.940460 | − | 0.339904i | \(-0.110395\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −168.821 | −0.181333 | ||||||||
\(932\) | −416.639 | + | 416.639i | −0.447037 | + | 0.447037i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1005.14i | 1.07617i | ||||||||
\(935\) | 826.186 | − | 1502.79i | 0.883622 | − | 1.60726i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1167.50 | − | 1167.50i | 1.24599 | − | 1.24599i | 0.288519 | − | 0.957474i | \(-0.406837\pi\) |
0.957474 | − | 0.288519i | \(-0.0931630\pi\) | |||||||
\(938\) | 77.2537 | + | 77.2537i | 0.0823600 | + | 0.0823600i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −621.263 | − | 341.551i | −0.660918 | − | 0.363352i | ||||
\(941\) | 614.550 | 0.653082 | 0.326541 | − | 0.945183i | \(-0.394117\pi\) | ||||
0.326541 | + | 0.945183i | \(0.394117\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 561.544 | + | 561.544i | 0.595487 | + | 0.595487i | ||||
\(944\) | 377.395i | 0.399783i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −601.589 | −0.635929 | ||||||||
\(947\) | 635.282 | − | 635.282i | 0.670837 | − | 0.670837i | −0.287072 | − | 0.957909i | \(-0.592682\pi\) |
0.957909 | + | 0.287072i | \(0.0926820\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 773.423i | − | 0.814987i | ||||||
\(950\) | −832.137 | − | 186.024i | −0.875933 | − | 0.195815i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 157.710 | − | 157.710i | 0.165662 | − | 0.165662i | ||||
\(953\) | −350.517 | − | 350.517i | −0.367803 | − | 0.367803i | 0.498872 | − | 0.866676i | \(-0.333748\pi\) |
−0.866676 | + | 0.498872i | \(0.833748\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1131.45 | + | 328.703i | −1.18476 | + | 0.344191i | ||||
\(956\) | −661.585 | −0.692035 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 270.133 | + | 270.133i | 0.281976 | + | 0.281976i | ||||
\(959\) | 492.223i | 0.513267i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1246.61 | 1.29720 | ||||||||
\(962\) | 130.992 | − | 130.992i | 0.136166 | − | 0.136166i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 751.169i | − | 0.779221i | ||||||
\(965\) | 100.512 | + | 55.2585i | 0.104158 | + | 0.0572627i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 435.204 | − | 435.204i | 0.450056 | − | 0.450056i | −0.445317 | − | 0.895373i | \(-0.646909\pi\) |
0.895373 | + | 0.445317i | \(0.146909\pi\) | |||||||
\(968\) | −22.8599 | − | 22.8599i | −0.0236156 | − | 0.0236156i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 66.3616 | + | 228.428i | 0.0684140 | + | 0.235492i | ||||
\(971\) | −218.866 | −0.225403 | −0.112701 | − | 0.993629i | \(-0.535950\pi\) | ||||
−0.112701 | + | 0.993629i | \(0.535950\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −167.328 | − | 167.328i | −0.171971 | − | 0.171971i | ||||
\(974\) | 455.264i | 0.467417i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −32.3601 | −0.0331559 | ||||||||
\(977\) | −1000.73 | + | 1000.73i | −1.02429 | + | 1.02429i | −0.0245886 | + | 0.999698i | \(0.507828\pi\) |
−0.999698 | + | 0.0245886i | \(0.992172\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 1670.41i | − | 1.70624i | ||||||
\(980\) | 67.2208 | − | 19.5286i | 0.0685926 | − | 0.0199272i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 23.2563 | − | 23.2563i | 0.0236826 | − | 0.0236826i | ||||
\(983\) | −915.596 | − | 915.596i | −0.931431 | − | 0.931431i | 0.0663648 | − | 0.997795i | \(-0.478860\pi\) |
−0.997795 | + | 0.0663648i | \(0.978860\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −22.7605 | + | 41.4001i | −0.0231071 | + | 0.0420306i | ||||
\(986\) | −2155.51 | −2.18612 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 371.658 | + | 371.658i | 0.376172 | + | 0.376172i | ||||
\(989\) | 1577.50i | 1.59505i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −437.633 | −0.441608 | −0.220804 | − | 0.975318i | \(-0.570868\pi\) | ||||
−0.220804 | + | 0.975318i | \(0.570868\pi\) | |||||||
\(992\) | 187.941 | − | 187.941i | 0.189457 | − | 0.189457i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | − | 238.566i | − | 0.240006i | ||||||
\(995\) | −44.7361 | − | 153.989i | −0.0449609 | − | 0.154763i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 180.748 | − | 180.748i | 0.181292 | − | 0.181292i | −0.610627 | − | 0.791919i | \(-0.709082\pi\) |
0.791919 | + | 0.610627i | \(0.209082\pi\) | |||||||
\(998\) | −319.077 | − | 319.077i | −0.319717 | − | 0.319717i | ||||
\(999\) | 0 | 0 |
(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 | 630.3.o.f.253.1 | 16 | ||
3.2 | odd | 2 | 210.3.l.b.43.4 | ✓ | 16 | ||
5.2 | odd | 4 | inner | 630.3.o.f.127.1 | 16 | ||
15.2 | even | 4 | 210.3.l.b.127.4 | yes | 16 | ||
15.8 | even | 4 | 1050.3.l.h.757.5 | 16 | |||
15.14 | odd | 2 | 1050.3.l.h.43.5 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.l.b.43.4 | ✓ | 16 | 3.2 | odd | 2 | ||
210.3.l.b.127.4 | yes | 16 | 15.2 | even | 4 | ||
630.3.o.f.127.1 | 16 | 5.2 | odd | 4 | inner | ||
630.3.o.f.253.1 | 16 | 1.1 | even | 1 | trivial | ||
1050.3.l.h.43.5 | 16 | 15.14 | odd | 2 | |||
1050.3.l.h.757.5 | 16 | 15.8 | even | 4 |