Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2151,2,Mod(2150,2151)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2151, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2151.2150");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2151 = 3^{2} \cdot 239 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2151.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: | \(17.1758214748\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2150.5 | ||
Character | \(\chi\) | \(=\) | 2151.2150 |
Dual form | 2151.2.b.a.2150.76 |
$q$-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 \(\left(\mathbb{Z}/2151\mathbb{Z}\right)^\times\).
\(n\) | \(479\) | \(1441\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.54042i | − | 1.79634i | −0.439643 | − | 0.898172i | \(-0.644895\pi\) | ||
0.439643 | − | 0.898172i | \(-0.355105\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −4.45371 | −2.22685 | ||||||||
\(5\) | 2.74390i | 1.22711i | 0.789653 | + | 0.613554i | \(0.210261\pi\) | ||||
−0.789653 | + | 0.613554i | \(0.789739\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 3.15846i | − | 1.19378i | −0.802322 | − | 0.596892i | \(-0.796402\pi\) | ||
0.802322 | − | 0.596892i | \(-0.203598\pi\) | |||||||
\(8\) | 6.23344i | 2.20385i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 6.97064 | 2.20431 | ||||||||
\(11\) | − | 3.61764i | − | 1.09076i | −0.838189 | − | 0.545380i | \(-0.816385\pi\) | ||
0.838189 | − | 0.545380i | \(-0.183615\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.68097i | 1.85297i | 0.376333 | + | 0.926484i | \(0.377185\pi\) | ||||
−0.376333 | + | 0.926484i | \(0.622815\pi\) | |||||||
\(14\) | −8.02379 | −2.14445 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 6.92810 | 1.73203 | ||||||||
\(17\) | 1.88970i | 0.458320i | 0.973389 | + | 0.229160i | \(0.0735979\pi\) | ||||
−0.973389 | + | 0.229160i | \(0.926402\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 1.30591i | − | 0.299596i | −0.988717 | − | 0.149798i | \(-0.952138\pi\) | ||
0.988717 | − | 0.149798i | \(-0.0478623\pi\) | |||||||
\(20\) | − | 12.2205i | − | 2.73259i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −9.19031 | −1.95938 | ||||||||
\(23\) | −0.0247915 | −0.00516939 | −0.00258469 | − | 0.999997i | \(-0.500823\pi\) | ||||
−0.00258469 | + | 0.999997i | \(0.500823\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.52897 | −0.505795 | ||||||||
\(26\) | 16.9724 | 3.32857 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 14.0668i | 2.65838i | ||||||||
\(29\) | 7.25544i | 1.34730i | 0.739050 | + | 0.673651i | \(0.235275\pi\) | ||||
−0.739050 | + | 0.673651i | \(0.764725\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.823399 | 0.147887 | 0.0739434 | − | 0.997262i | \(-0.476442\pi\) | ||||
0.0739434 | + | 0.997262i | \(0.476442\pi\) | |||||||
\(32\) | − | 5.13338i | − | 0.907463i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.80063 | 0.823301 | ||||||||
\(35\) | 8.66648 | 1.46490 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 7.67446i | − | 1.26167i | −0.775915 | − | 0.630837i | \(-0.782712\pi\) | ||
0.775915 | − | 0.630837i | \(-0.217288\pi\) | |||||||
\(38\) | −3.31755 | −0.538177 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −17.1039 | −2.70437 | ||||||||
\(41\) | 0.294392 | 0.0459763 | 0.0229881 | − | 0.999736i | \(-0.492682\pi\) | ||||
0.0229881 | + | 0.999736i | \(0.492682\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.0550168i | 0.00838999i | 0.999991 | + | 0.00419499i | \(0.00133531\pi\) | ||||
−0.999991 | + | 0.00419499i | \(0.998665\pi\) | |||||||
\(44\) | 16.1119i | 2.42896i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.0629807i | 0.00928600i | ||||||||
\(47\) | 8.78581 | 1.28154 | 0.640771 | − | 0.767732i | \(-0.278615\pi\) | ||||
0.640771 | + | 0.767732i | \(0.278615\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.97584 | −0.425121 | ||||||||
\(50\) | 6.42464i | 0.908582i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 29.7551i | − | 4.12629i | ||||||
\(53\) | 8.76528 | 1.20400 | 0.602002 | − | 0.798495i | \(-0.294370\pi\) | ||||
0.602002 | + | 0.798495i | \(0.294370\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.92644 | 1.33848 | ||||||||
\(56\) | 19.6880 | 2.63093 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 18.4318 | 2.42022 | ||||||||
\(59\) | 13.4742 | 1.75419 | 0.877095 | − | 0.480317i | \(-0.159478\pi\) | ||||
0.877095 | + | 0.480317i | \(0.159478\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.35821 | 0.942122 | 0.471061 | − | 0.882101i | \(-0.343871\pi\) | ||||
0.471061 | + | 0.882101i | \(0.343871\pi\) | |||||||
\(62\) | − | 2.09177i | − | 0.265656i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.815284 | 0.101910 | ||||||||
\(65\) | −18.3319 | −2.27379 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.45145 | 0.177323 | 0.0886616 | − | 0.996062i | \(-0.471741\pi\) | ||||
0.0886616 | + | 0.996062i | \(0.471741\pi\) | |||||||
\(68\) | − | 8.41619i | − | 1.02061i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | − | 22.0165i | − | 2.63147i | ||||||
\(71\) | 15.4302i | 1.83123i | 0.402053 | + | 0.915616i | \(0.368297\pi\) | ||||
−0.402053 | + | 0.915616i | \(0.631703\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 0.0953278i | − | 0.0111573i | −0.999984 | − | 0.00557864i | \(-0.998224\pi\) | ||
0.999984 | − | 0.00557864i | \(-0.00177574\pi\) | |||||||
\(74\) | −19.4963 | −2.26640 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.81613i | 0.667156i | ||||||||
\(77\) | −11.4262 | −1.30213 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 12.3605i | − | 1.39067i | −0.718688 | − | 0.695333i | \(-0.755257\pi\) | ||
0.718688 | − | 0.695333i | \(-0.244743\pi\) | |||||||
\(80\) | 19.0100i | 2.12538i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 0.747878i | − | 0.0825893i | ||||||
\(83\) | 9.34663i | 1.02593i | 0.858411 | + | 0.512963i | \(0.171452\pi\) | ||||
−0.858411 | + | 0.512963i | \(0.828548\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.18515 | −0.562409 | ||||||||
\(86\) | 0.139766 | 0.0150713 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 22.5504 | 2.40388 | ||||||||
\(89\) | 3.09409 | 0.327973 | 0.163987 | − | 0.986463i | \(-0.447565\pi\) | ||||
0.163987 | + | 0.986463i | \(0.447565\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 21.1016 | 2.21204 | ||||||||
\(92\) | 0.110414 | 0.0115115 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 22.3196i | − | 2.30209i | ||||||
\(95\) | 3.58328 | 0.367636 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 12.1734i | − | 1.23602i | −0.786169 | − | 0.618011i | \(-0.787939\pi\) | ||
0.786169 | − | 0.618011i | \(-0.212061\pi\) | |||||||
\(98\) | 7.55988i | 0.763663i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 11.2633 | 1.12633 | ||||||||
\(101\) | − | 2.31914i | − | 0.230764i | −0.993321 | − | 0.115382i | \(-0.963191\pi\) | ||
0.993321 | − | 0.115382i | \(-0.0368091\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 3.76412i | − | 0.370890i | −0.982655 | − | 0.185445i | \(-0.940627\pi\) | ||
0.982655 | − | 0.185445i | \(-0.0593726\pi\) | |||||||
\(104\) | −41.6454 | −4.08367 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 22.2675i | − | 2.16281i | ||||||
\(107\) | −9.64916 | −0.932820 | −0.466410 | − | 0.884569i | \(-0.654453\pi\) | ||||
−0.466410 | + | 0.884569i | \(0.654453\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −18.4710 | −1.76920 | −0.884602 | − | 0.466347i | \(-0.845570\pi\) | ||||
−0.884602 | + | 0.466347i | \(0.845570\pi\) | |||||||
\(110\) | − | 25.2173i | − | 2.40437i | ||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − | 21.8821i | − | 2.06767i | ||||||
\(113\) | − | 10.1240i | − | 0.952385i | −0.879341 | − | 0.476192i | \(-0.842017\pi\) | ||
0.879341 | − | 0.476192i | \(-0.157983\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 0.0680254i | − | 0.00634340i | ||||||
\(116\) | − | 32.3136i | − | 3.00025i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 34.2300i | − | 3.15113i | ||||||
\(119\) | 5.96854 | 0.547135 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.08734 | −0.189758 | ||||||||
\(122\) | − | 18.6929i | − | 1.69238i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.66718 | −0.329322 | ||||||||
\(125\) | 6.78024i | 0.606443i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.13936 | −0.544780 | −0.272390 | − | 0.962187i | \(-0.587814\pi\) | ||||
−0.272390 | + | 0.962187i | \(0.587814\pi\) | |||||||
\(128\) | − | 12.3379i | − | 1.09053i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 46.5707i | 4.08452i | ||||||||
\(131\) | 12.1961 | 1.06558 | 0.532788 | − | 0.846248i | \(-0.321144\pi\) | ||||
0.532788 | + | 0.846248i | \(0.321144\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.12465 | −0.357653 | ||||||||
\(134\) | − | 3.68729i | − | 0.318533i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −11.7793 | −1.01007 | ||||||||
\(137\) | −3.45116 | −0.294852 | −0.147426 | − | 0.989073i | \(-0.547099\pi\) | ||||
−0.147426 | + | 0.989073i | \(0.547099\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.8269i | 1.08797i | 0.839096 | + | 0.543984i | \(0.183085\pi\) | ||||
−0.839096 | + | 0.543984i | \(0.816915\pi\) | |||||||
\(140\) | −38.5980 | −3.26212 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 39.1992 | 3.28952 | ||||||||
\(143\) | 24.1694 | 2.02114 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −19.9082 | −1.65329 | ||||||||
\(146\) | −0.242172 | −0.0200423 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 34.1798i | 2.80956i | ||||||||
\(149\) | 7.37438 | 0.604133 | 0.302067 | − | 0.953287i | \(-0.402324\pi\) | ||||
0.302067 | + | 0.953287i | \(0.402324\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 8.29877i | − | 0.675345i | −0.941264 | − | 0.337672i | \(-0.890360\pi\) | ||
0.941264 | − | 0.337672i | \(-0.109640\pi\) | |||||||
\(152\) | 8.14029 | 0.660265 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 29.0272i | 2.33908i | ||||||||
\(155\) | 2.25932i | 0.181473i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.6696 | 1.41019 | 0.705096 | − | 0.709112i | \(-0.250904\pi\) | ||||
0.705096 | + | 0.709112i | \(0.250904\pi\) | |||||||
\(158\) | −31.4008 | −2.49811 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 14.0855 | 1.11355 | ||||||||
\(161\) | 0.0783029i | 0.00617113i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.26672 | 0.334195 | 0.167098 | − | 0.985940i | \(-0.446560\pi\) | ||||
0.167098 | + | 0.985940i | \(0.446560\pi\) | |||||||
\(164\) | −1.31114 | −0.102383 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 23.7443 | 1.84292 | ||||||||
\(167\) | 10.9531 | 0.847575 | 0.423787 | − | 0.905762i | \(-0.360700\pi\) | ||||
0.423787 | + | 0.905762i | \(0.360700\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −31.6354 | −2.43349 | ||||||||
\(170\) | 13.1724i | 1.01028i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 0.245029i | − | 0.0186833i | ||||||
\(173\) | 4.46558 | 0.339512 | 0.169756 | − | 0.985486i | \(-0.445702\pi\) | ||||
0.169756 | + | 0.985486i | \(0.445702\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.98765i | 0.603810i | ||||||||
\(176\) | − | 25.0634i | − | 1.88923i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 7.86029i | − | 0.589153i | ||||||
\(179\) | −21.5478 | −1.61056 | −0.805281 | − | 0.592894i | \(-0.797985\pi\) | ||||
−0.805281 | + | 0.592894i | \(0.797985\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 21.0683i | − | 1.56599i | −0.622026 | − | 0.782997i | \(-0.713690\pi\) | ||
0.622026 | − | 0.782997i | \(-0.286310\pi\) | |||||||
\(182\) | − | 53.6067i | − | 3.97359i | ||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 0.154536i | − | 0.0113926i | ||||||
\(185\) | 21.0579 | 1.54821 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.83627 | 0.499918 | ||||||||
\(188\) | −39.1295 | −2.85381 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | − | 9.10301i | − | 0.660402i | ||||||
\(191\) | 23.3758 | 1.69141 | 0.845706 | − | 0.533649i | \(-0.179180\pi\) | ||||
0.845706 | + | 0.533649i | \(0.179180\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.59111 | −0.546420 | −0.273210 | − | 0.961954i | \(-0.588085\pi\) | ||||
−0.273210 | + | 0.961954i | \(0.588085\pi\) | |||||||
\(194\) | −30.9255 | −2.22032 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 13.2535 | 0.946682 | ||||||||
\(197\) | 13.5652i | 0.966478i | 0.875488 | + | 0.483239i | \(0.160540\pi\) | ||||
−0.875488 | + | 0.483239i | \(0.839460\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.5598i | 0.890344i | 0.895445 | + | 0.445172i | \(0.146857\pi\) | ||||
−0.895445 | + | 0.445172i | \(0.853143\pi\) | |||||||
\(200\) | − | 15.7642i | − | 1.11470i | ||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −5.89159 | −0.414531 | ||||||||
\(203\) | 22.9160 | 1.60839 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.807781i | 0.0564179i | ||||||||
\(206\) | −9.56243 | −0.666246 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 46.2865i | 3.20939i | ||||||||
\(209\) | −4.72431 | −0.326787 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.3629 | 1.12647 | 0.563235 | − | 0.826297i | \(-0.309557\pi\) | ||||
0.563235 | + | 0.826297i | \(0.309557\pi\) | |||||||
\(212\) | −39.0380 | −2.68114 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 24.5129i | 1.67567i | ||||||||
\(215\) | −0.150961 | −0.0102954 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 2.60067i | − | 0.176545i | ||||||
\(218\) | 46.9241i | 3.17810i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −44.2095 | −2.98060 | ||||||||
\(221\) | −12.6251 | −0.849253 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.0222i | 0.738102i | 0.929409 | + | 0.369051i | \(0.120317\pi\) | ||||
−0.929409 | + | 0.369051i | \(0.879683\pi\) | |||||||
\(224\) | −16.2136 | −1.08331 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −25.7191 | −1.71081 | ||||||||
\(227\) | −2.22510 | −0.147685 | −0.0738425 | − | 0.997270i | \(-0.523526\pi\) | ||||
−0.0738425 | + | 0.997270i | \(0.523526\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.83565i | 0.583876i | 0.956437 | + | 0.291938i | \(0.0943002\pi\) | ||||
−0.956437 | + | 0.291938i | \(0.905700\pi\) | |||||||
\(230\) | −0.172813 | −0.0113949 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −45.2264 | −2.96926 | ||||||||
\(233\) | 19.6243 | 1.28563 | 0.642816 | − | 0.766021i | \(-0.277766\pi\) | ||||
0.642816 | + | 0.766021i | \(0.277766\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 24.1074i | 1.57259i | ||||||||
\(236\) | −60.0101 | −3.90633 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − | 15.1626i | − | 0.982844i | ||||||
\(239\) | 13.0981 | − | 8.21211i | 0.847248 | − | 0.531197i | ||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.96331 | 0.448546 | 0.224273 | − | 0.974526i | \(-0.427999\pi\) | ||||
0.224273 | + | 0.974526i | \(0.427999\pi\) | |||||||
\(242\) | 5.30271i | 0.340871i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −32.7713 | −2.09797 | ||||||||
\(245\) | − | 8.16541i | − | 0.521669i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.72473 | 0.555141 | ||||||||
\(248\) | 5.13261i | 0.325921i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 17.2246 | 1.08938 | ||||||||
\(251\) | 7.70445i | 0.486300i | 0.969989 | + | 0.243150i | \(0.0781808\pi\) | ||||
−0.969989 | + | 0.243150i | \(0.921819\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.0896868i | 0.00563856i | ||||||||
\(254\) | 15.5965i | 0.978612i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −29.7129 | −1.85706 | ||||||||
\(257\) | 22.0120i | 1.37307i | 0.727097 | + | 0.686534i | \(0.240869\pi\) | ||||
−0.727097 | + | 0.686534i | \(0.759131\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −24.2395 | −1.50617 | ||||||||
\(260\) | 81.6450 | 5.06341 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 30.9831i | − | 1.91414i | ||||||
\(263\) | − | 4.18120i | − | 0.257824i | −0.991656 | − | 0.128912i | \(-0.958852\pi\) | ||
0.991656 | − | 0.128912i | \(-0.0411484\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 24.0510i | 1.47744i | ||||||||
\(266\) | 10.4783i | 0.642467i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −6.46435 | −0.394873 | ||||||||
\(269\) | 2.73513i | 0.166764i | 0.996518 | + | 0.0833818i | \(0.0265721\pi\) | ||||
−0.996518 | + | 0.0833818i | \(0.973428\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −30.6712 | −1.86314 | −0.931571 | − | 0.363560i | \(-0.881561\pi\) | ||||
−0.931571 | + | 0.363560i | \(0.881561\pi\) | |||||||
\(272\) | 13.0921i | 0.793823i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8.76737i | 0.529656i | ||||||||
\(275\) | 9.14892i | 0.551701i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 27.5314i | 1.65420i | 0.562053 | + | 0.827101i | \(0.310012\pi\) | ||||
−0.562053 | + | 0.827101i | \(0.689988\pi\) | |||||||
\(278\) | 32.5858 | 1.95437 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 54.0220i | 3.22843i | ||||||||
\(281\) | −30.9835 | −1.84832 | −0.924161 | − | 0.382002i | \(-0.875235\pi\) | ||||
−0.924161 | + | 0.382002i | \(0.875235\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.9257 | 0.827798 | 0.413899 | − | 0.910323i | \(-0.364167\pi\) | ||||
0.413899 | + | 0.910323i | \(0.364167\pi\) | |||||||
\(284\) | − | 68.7218i | − | 4.07789i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 61.4002i | − | 3.63067i | ||||||
\(287\) | − | 0.929824i | − | 0.0548858i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.4290 | 0.789943 | ||||||||
\(290\) | 50.5751i | 2.96987i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.424562i | 0.0248456i | ||||||||
\(293\) | 16.2221i | 0.947707i | 0.880604 | + | 0.473853i | \(0.157137\pi\) | ||||
−0.880604 | + | 0.473853i | \(0.842863\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 36.9718i | 2.15258i | ||||||||
\(296\) | 47.8383 | 2.78054 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 18.7340i | − | 1.08523i | ||||||
\(299\) | − | 0.165631i | − | 0.00957871i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.173768 | 0.0100158 | ||||||||
\(302\) | −21.0823 | −1.21315 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 9.04746i | − | 0.518907i | ||||||
\(305\) | 20.1902i | 1.15609i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.3345 | 0.932258 | 0.466129 | − | 0.884717i | \(-0.345648\pi\) | ||||
0.466129 | + | 0.884717i | \(0.345648\pi\) | |||||||
\(308\) | 50.8888 | 2.89966 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 5.73961 | 0.325988 | ||||||||
\(311\) | 5.20846i | 0.295345i | 0.989036 | + | 0.147672i | \(0.0471781\pi\) | ||||
−0.989036 | + | 0.147672i | \(0.952822\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 0.279682i | − | 0.0158086i | −0.999969 | − | 0.00790429i | \(-0.997484\pi\) | ||
0.999969 | − | 0.00790429i | \(-0.00251604\pi\) | |||||||
\(314\) | − | 44.8882i | − | 2.53319i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 55.0501i | 3.09681i | ||||||||
\(317\) | 26.8614 | 1.50869 | 0.754344 | − | 0.656479i | \(-0.227955\pi\) | ||||
0.754344 | + | 0.656479i | \(0.227955\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 26.2476 | 1.46958 | ||||||||
\(320\) | 2.23706i | 0.125055i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.198922 | 0.0110855 | ||||||||
\(323\) | 2.46778 | 0.137311 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 16.8960i | − | 0.937222i | ||||||
\(326\) | − | 10.8392i | − | 0.600330i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.83507i | 0.101325i | ||||||||
\(329\) | − | 27.7496i | − | 1.52989i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 17.3353i | − | 0.952834i | −0.879219 | − | 0.476417i | \(-0.841935\pi\) | ||
0.879219 | − | 0.476417i | \(-0.158065\pi\) | |||||||
\(332\) | − | 41.6272i | − | 2.28459i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 27.8254i | − | 1.52254i | ||||||
\(335\) | 3.98264i | 0.217595i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.8455 | 0.863161 | 0.431580 | − | 0.902074i | \(-0.357956\pi\) | ||||
0.431580 | + | 0.902074i | \(0.357956\pi\) | |||||||
\(338\) | 80.3671i | 4.37139i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 23.0932 | 1.25240 | ||||||||
\(341\) | − | 2.97876i | − | 0.161309i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 12.7101i | − | 0.686282i | ||||||
\(344\) | −0.342944 | −0.0184903 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 11.3444i | − | 0.609881i | ||||||
\(347\) | 15.3686i | 0.825030i | 0.910951 | + | 0.412515i | \(0.135350\pi\) | ||||
−0.910951 | + | 0.412515i | \(0.864650\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.3056 | 1.03341 | 0.516703 | − | 0.856165i | \(-0.327159\pi\) | ||||
0.516703 | + | 0.856165i | \(0.327159\pi\) | |||||||
\(350\) | 20.2920 | 1.08465 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −18.5707 | −0.989824 | ||||||||
\(353\) | −29.6340 | −1.57726 | −0.788629 | − | 0.614870i | \(-0.789208\pi\) | ||||
−0.788629 | + | 0.614870i | \(0.789208\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −42.3390 | −2.24712 | ||||||||
\(356\) | −13.7802 | −0.730349 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 54.7405i | 2.89312i | ||||||||
\(359\) | 22.9649i | 1.21204i | 0.795450 | + | 0.606020i | \(0.207235\pi\) | ||||
−0.795450 | + | 0.606020i | \(0.792765\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.2946 | 0.910242 | ||||||||
\(362\) | −53.5222 | −2.81306 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −93.9802 | −4.92590 | ||||||||
\(365\) | 0.261570 | 0.0136912 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 22.7643 | 1.18828 | 0.594142 | − | 0.804360i | \(-0.297492\pi\) | ||||
0.594142 | + | 0.804360i | \(0.297492\pi\) | |||||||
\(368\) | −0.171758 | −0.00895352 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 53.4959i | − | 2.78112i | ||||||
\(371\) | − | 27.6848i | − | 1.43732i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −23.3244 | −1.20769 | −0.603847 | − | 0.797100i | \(-0.706366\pi\) | ||||
−0.603847 | + | 0.797100i | \(0.706366\pi\) | |||||||
\(374\) | − | 17.3670i | − | 0.898024i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 54.7658i | 2.82433i | ||||||||
\(377\) | −48.4734 | −2.49651 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.9477i | 1.53831i | 0.639064 | + | 0.769154i | \(0.279322\pi\) | ||||
−0.639064 | + | 0.769154i | \(0.720678\pi\) | |||||||
\(380\) | −15.9589 | −0.818673 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 59.3842i | − | 3.03836i | ||||||
\(383\) | − | 26.8157i | − | 1.37022i | −0.728440 | − | 0.685110i | \(-0.759754\pi\) | ||
0.728440 | − | 0.685110i | \(-0.240246\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 31.3522i | − | 1.59786i | ||||||
\(386\) | 19.2846i | 0.981559i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 54.2168i | 2.75244i | ||||||||
\(389\) | − | 10.4488i | − | 0.529774i | −0.964279 | − | 0.264887i | \(-0.914665\pi\) | ||
0.964279 | − | 0.264887i | \(-0.0853346\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 0.0468486i | − | 0.00236923i | ||||||
\(392\) | − | 18.5497i | − | 0.936903i | ||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 34.4612 | 1.73613 | ||||||||
\(395\) | 33.9160 | 1.70650 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.1691i | 0.610751i | 0.952232 | + | 0.305375i | \(0.0987820\pi\) | ||||
−0.952232 | + | 0.305375i | \(0.901218\pi\) | |||||||
\(398\) | 31.9072 | 1.59936 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −17.5210 | −0.876050 | ||||||||
\(401\) | − | 4.50204i | − | 0.224821i | −0.993662 | − | 0.112411i | \(-0.964143\pi\) | ||
0.993662 | − | 0.112411i | \(-0.0358572\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.50110i | 0.274030i | ||||||||
\(404\) | 10.3288i | 0.513877i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | − | 58.2162i | − | 2.88922i | ||||||
\(407\) | −27.7635 | −1.37618 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.18270 | 0.0584808 | 0.0292404 | − | 0.999572i | \(-0.490691\pi\) | ||||
0.0292404 | + | 0.999572i | \(0.490691\pi\) | |||||||
\(410\) | 2.05210 | 0.101346 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 16.7643i | 0.825918i | ||||||||
\(413\) | − | 42.5576i | − | 2.09412i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −25.6462 | −1.25892 | ||||||||
\(416\) | 34.2960 | 1.68150 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 12.0017i | 0.587022i | ||||||||
\(419\) | − | 4.13425i | − | 0.201971i | −0.994888 | − | 0.100986i | \(-0.967800\pi\) | ||
0.994888 | − | 0.100986i | \(-0.0321996\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 35.7666 | 1.74316 | 0.871579 | − | 0.490256i | \(-0.163097\pi\) | ||||
0.871579 | + | 0.490256i | \(0.163097\pi\) | |||||||
\(422\) | − | 41.5686i | − | 2.02353i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 54.6379i | 2.65345i | ||||||||
\(425\) | − | 4.77901i | − | 0.231816i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 23.2406i | − | 1.12469i | ||||||
\(428\) | 42.9746 | 2.07725 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.383503i | 0.0184941i | ||||||||
\(431\) | − | 4.38847i | − | 0.211385i | −0.994399 | − | 0.105693i | \(-0.966294\pi\) | ||
0.994399 | − | 0.105693i | \(-0.0337059\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 33.5767i | 1.61359i | 0.590829 | + | 0.806797i | \(0.298801\pi\) | ||||
−0.590829 | + | 0.806797i | \(0.701199\pi\) | |||||||
\(434\) | −6.60678 | −0.317135 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 82.2646 | 3.93976 | ||||||||
\(437\) | 0.0323754i | 0.00154873i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.12131 | 0.0535172 | 0.0267586 | − | 0.999642i | \(-0.491481\pi\) | ||||
0.0267586 | + | 0.999642i | \(0.491481\pi\) | |||||||
\(440\) | 61.8759i | 2.94982i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 32.0729i | 1.52555i | ||||||||
\(443\) | − | 34.6898i | − | 1.64816i | −0.566472 | − | 0.824081i | \(-0.691692\pi\) | ||
0.566472 | − | 0.824081i | \(-0.308308\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.48988i | 0.402459i | ||||||||
\(446\) | 28.0010 | 1.32589 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − | 2.57504i | − | 0.121659i | ||||||
\(449\) | −27.6575 | −1.30524 | −0.652619 | − | 0.757686i | \(-0.726330\pi\) | ||||
−0.652619 | + | 0.757686i | \(0.726330\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 1.06500i | − | 0.0501491i | ||||||
\(452\) | 45.0893i | 2.12082i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 5.65267i | 0.265293i | ||||||||
\(455\) | 57.9005i | 2.71442i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −32.7132 | −1.53026 | −0.765130 | − | 0.643876i | \(-0.777325\pi\) | ||||
−0.765130 | + | 0.643876i | \(0.777325\pi\) | |||||||
\(458\) | 22.4462 | 1.04884 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.302965i | 0.0141258i | ||||||||
\(461\) | −19.8347 | −0.923796 | −0.461898 | − | 0.886933i | \(-0.652831\pi\) | ||||
−0.461898 | + | 0.886933i | \(0.652831\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 40.8649i | − | 1.89915i | −0.313539 | − | 0.949575i | \(-0.601515\pi\) | ||
0.313539 | − | 0.949575i | \(-0.398485\pi\) | |||||||
\(464\) | 50.2665i | 2.33356i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | − | 49.8539i | − | 2.30944i | ||||||
\(467\) | −26.7199 | −1.23645 | −0.618224 | − | 0.786002i | \(-0.712148\pi\) | ||||
−0.618224 | + | 0.786002i | \(0.712148\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 4.58435i | − | 0.211686i | ||||||
\(470\) | 61.2427 | 2.82492 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 83.9906i | 3.86598i | ||||||||
\(473\) | 0.199031 | 0.00915147 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.30260i | 0.151534i | ||||||||
\(476\) | −26.5822 | −1.21839 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −20.8622 | − | 33.2747i | −0.954214 | − | 1.52195i | ||||
\(479\) | 9.06080i | 0.413998i | 0.978341 | + | 0.206999i | \(0.0663698\pi\) | ||||
−0.978341 | + | 0.206999i | \(0.933630\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 51.2729 | 2.33784 | ||||||||
\(482\) | − | 17.6897i | − | 0.805744i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9.29641 | 0.422564 | ||||||||
\(485\) | 33.4026 | 1.51673 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −33.1167 | −1.50066 | −0.750331 | − | 0.661062i | \(-0.770106\pi\) | ||||
−0.750331 | + | 0.661062i | \(0.770106\pi\) | |||||||
\(488\) | 45.8669i | 2.07630i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −20.7435 | −0.937097 | ||||||||
\(491\) | −12.5893 | −0.568149 | −0.284075 | − | 0.958802i | \(-0.591686\pi\) | ||||
−0.284075 | + | 0.958802i | \(0.591686\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −13.7106 | −0.617496 | ||||||||
\(494\) | − | 22.1644i | − | 0.997225i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.70459 | 0.256144 | ||||||||
\(497\) | 48.7357 | 2.18610 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.3577i | 0.821804i | 0.911679 | + | 0.410902i | \(0.134786\pi\) | ||||
−0.911679 | + | 0.410902i | \(0.865214\pi\) | |||||||
\(500\) | − | 30.1972i | − | 1.35046i | ||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 19.5725 | 0.873563 | ||||||||
\(503\) | 26.7645i | 1.19337i | 0.802475 | + | 0.596685i | \(0.203516\pi\) | ||||
−0.802475 | + | 0.596685i | \(0.796484\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.36350 | 0.283172 | ||||||||
\(506\) | 0.227842 | 0.0101288 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 27.3429 | 1.21315 | ||||||||
\(509\) | − | 32.2824i | − | 1.43089i | −0.698668 | − | 0.715447i | \(-0.746223\pi\) | ||
0.698668 | − | 0.715447i | \(-0.253777\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.301089 | −0.0133194 | ||||||||
\(512\) | 50.8072i | 2.24538i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 55.9195 | 2.46651 | ||||||||
\(515\) | 10.3284 | 0.455122 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 31.7839i | − | 1.39786i | ||||||
\(518\) | 61.5783i | 2.70559i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | − | 114.271i | − | 5.01111i | ||||||
\(521\) | 18.3071 | 0.802049 | 0.401024 | − | 0.916067i | \(-0.368654\pi\) | ||||
0.401024 | + | 0.916067i | \(0.368654\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −24.0246 | −1.05052 | −0.525262 | − | 0.850941i | \(-0.676033\pi\) | ||||
−0.525262 | + | 0.850941i | \(0.676033\pi\) | |||||||
\(524\) | −54.3178 | −2.37288 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −10.6220 | −0.463140 | ||||||||
\(527\) | 1.55598i | 0.0677795i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9994 | −0.999973 | ||||||||
\(530\) | 61.0996 | 2.65400 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 18.3700 | 0.796440 | ||||||||
\(533\) | 1.96682i | 0.0851926i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 26.4763i | − | 1.14467i | ||||||
\(536\) | 9.04754i | 0.390794i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 6.94836 | 0.299565 | ||||||||
\(539\) | 10.7655i | 0.463705i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.5660i | 0.454269i | 0.973863 | + | 0.227135i | \(0.0729358\pi\) | ||||
−0.973863 | + | 0.227135i | \(0.927064\pi\) | |||||||
\(542\) | 77.9175i | 3.34684i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 9.70057 | 0.415908 | ||||||||
\(545\) | − | 50.6826i | − | 2.17101i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.0915418i | 0.00391405i | 0.999998 | + | 0.00195702i | \(0.000622940\pi\) | ||||
−0.999998 | + | 0.00195702i | \(0.999377\pi\) | |||||||
\(548\) | 15.3704 | 0.656593 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 23.2421 | 0.991045 | ||||||||
\(551\) | 9.47494 | 0.403646 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −39.0401 | −1.66015 | ||||||||
\(554\) | 69.9412 | 2.97152 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 57.1275i | − | 2.42275i | ||||||
\(557\) | 11.2511 | 0.476725 | 0.238362 | − | 0.971176i | \(-0.423389\pi\) | ||||
0.238362 | + | 0.971176i | \(0.423389\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.367566 | −0.0155464 | ||||||||
\(560\) | 60.0423 | 2.53725 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 78.7110i | 3.32022i | ||||||||
\(563\) | 7.07737i | 0.298276i | 0.988816 | + | 0.149138i | \(0.0476498\pi\) | ||||
−0.988816 | + | 0.149138i | \(0.952350\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 27.7792 | 1.16868 | ||||||||
\(566\) | − | 35.3771i | − | 1.48701i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −96.1835 | −4.03577 | ||||||||
\(569\) | 42.7649i | 1.79280i | 0.443249 | + | 0.896399i | \(0.353826\pi\) | ||||
−0.443249 | + | 0.896399i | \(0.646174\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.41437 | 0.0591893 | 0.0295947 | − | 0.999562i | \(-0.490578\pi\) | ||||
0.0295947 | + | 0.999562i | \(0.490578\pi\) | |||||||
\(572\) | −107.643 | −4.50080 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.36214 | −0.0985938 | ||||||||
\(575\) | 0.0626971 | 0.00261465 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −27.9262 | −1.16258 | −0.581292 | − | 0.813695i | \(-0.697453\pi\) | ||||
−0.581292 | + | 0.813695i | \(0.697453\pi\) | |||||||
\(578\) | − | 34.1153i | − | 1.41901i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 88.6653 | 3.68163 | ||||||||
\(581\) | 29.5209 | 1.22473 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 31.7097i | − | 1.31328i | ||||||
\(584\) | 0.594220 | 0.0245890 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 41.2109 | 1.70241 | ||||||||
\(587\) | − | 26.2194i | − | 1.08219i | −0.840961 | − | 0.541095i | \(-0.818010\pi\) | ||
0.840961 | − | 0.541095i | \(-0.181990\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 1.07528i | − | 0.0443062i | ||||||
\(590\) | 93.9237 | 3.86678 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 53.1695i | − | 2.18525i | ||||||
\(593\) | −24.5699 | −1.00896 | −0.504482 | − | 0.863422i | \(-0.668317\pi\) | ||||
−0.504482 | + | 0.863422i | \(0.668317\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 16.3771i | 0.671394i | ||||||||
\(596\) | −32.8434 | −1.34532 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.420773 | −0.0172067 | ||||||||
\(599\) | − | 23.0112i | − | 0.940211i | −0.882610 | − | 0.470105i | \(-0.844216\pi\) | ||
0.882610 | − | 0.470105i | \(-0.155784\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 1.69938i | − | 0.0693192i | −0.999399 | − | 0.0346596i | \(-0.988965\pi\) | ||
0.999399 | − | 0.0346596i | \(-0.0110347\pi\) | |||||||
\(602\) | − | 0.441444i | − | 0.0179919i | ||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 36.9603i | 1.50389i | ||||||||
\(605\) | − | 5.72745i | − | 0.232854i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 27.3501i | 1.11011i | 0.831814 | + | 0.555054i | \(0.187302\pi\) | ||||
−0.831814 | + | 0.555054i | \(0.812698\pi\) | |||||||
\(608\) | −6.70372 | −0.271872 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 51.2914 | 2.07673 | ||||||||
\(611\) | 58.6978i | 2.37466i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 34.5836 | 1.39682 | 0.698409 | − | 0.715699i | \(-0.253892\pi\) | ||||
0.698409 | + | 0.715699i | \(0.253892\pi\) | |||||||
\(614\) | − | 41.4964i | − | 1.67466i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 71.2243i | − | 2.86971i | ||||||
\(617\) | −8.76076 | −0.352695 | −0.176347 | − | 0.984328i | \(-0.556428\pi\) | ||||
−0.176347 | + | 0.984328i | \(0.556428\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 44.1885i | − | 1.77609i | −0.459760 | − | 0.888043i | \(-0.652065\pi\) | ||
0.459760 | − | 0.888043i | \(-0.347935\pi\) | |||||||
\(620\) | − | 10.0624i | − | 0.404114i | ||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 13.2317 | 0.530541 | ||||||||
\(623\) | − | 9.77256i | − | 0.391529i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.2492 | −1.24997 | ||||||||
\(626\) | −0.710510 | −0.0283977 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −78.6955 | −3.14029 | ||||||||
\(629\) | 14.5025 | 0.578251 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.39134 | −0.254435 | −0.127218 | − | 0.991875i | \(-0.540605\pi\) | ||||
−0.127218 | + | 0.991875i | \(0.540605\pi\) | |||||||
\(632\) | 77.0484 | 3.06482 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 68.2392i | − | 2.71012i | ||||||
\(635\) | − | 16.8458i | − | 0.668504i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 19.8815i | − | 0.787735i | ||||||
\(638\) | − | 66.6798i | − | 2.63988i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 33.8540 | 1.33820 | ||||||||
\(641\) | − | 10.3794i | − | 0.409963i | −0.978766 | − | 0.204982i | \(-0.934287\pi\) | ||
0.978766 | − | 0.204982i | \(-0.0657134\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −23.6406 | −0.932293 | −0.466146 | − | 0.884708i | \(-0.654358\pi\) | ||||
−0.466146 | + | 0.884708i | \(0.654358\pi\) | |||||||
\(644\) | − | 0.348738i | − | 0.0137422i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | − | 6.26918i | − | 0.246657i | ||||||
\(647\) | 34.6941i | 1.36397i | 0.731367 | + | 0.681984i | \(0.238882\pi\) | ||||
−0.731367 | + | 0.681984i | \(0.761118\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 48.7448i | − | 1.91340i | ||||||
\(650\) | −42.9229 | −1.68357 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −19.0027 | −0.744205 | ||||||||
\(653\) | −43.4851 | −1.70170 | −0.850852 | − | 0.525405i | \(-0.823914\pi\) | ||||
−0.850852 | + | 0.525405i | \(0.823914\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 33.4648i | 1.30758i | ||||||||
\(656\) | 2.03958 | 0.0796322 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −70.4955 | −2.74820 | ||||||||
\(659\) | 8.01415 | 0.312187 | 0.156093 | − | 0.987742i | \(-0.450110\pi\) | ||||
0.156093 | + | 0.987742i | \(0.450110\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 46.3416 | 1.80248 | 0.901239 | − | 0.433322i | \(-0.142659\pi\) | ||||
0.901239 | + | 0.433322i | \(0.142659\pi\) | |||||||
\(662\) | −44.0389 | −1.71162 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −58.2616 | −2.26099 | ||||||||
\(665\) | − | 11.3176i | − | 0.438878i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 0.179873i | − | 0.00696473i | ||||||
\(668\) | −48.7818 | −1.88743 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 10.1176 | 0.390875 | ||||||||
\(671\) | − | 26.6194i | − | 1.02763i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 46.6089i | 1.79664i | 0.439343 | + | 0.898320i | \(0.355211\pi\) | ||||
−0.439343 | + | 0.898320i | \(0.644789\pi\) | |||||||
\(674\) | − | 40.2542i | − | 1.55053i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 140.895 | 5.41903 | ||||||||
\(677\) | −10.5146 | −0.404110 | −0.202055 | − | 0.979374i | \(-0.564762\pi\) | ||||
−0.202055 | + | 0.979374i | \(0.564762\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −38.4492 | −1.47554 | ||||||||
\(680\) | − | 32.3213i | − | 1.23947i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −7.56729 | −0.289767 | ||||||||
\(683\) | 37.6116 | 1.43917 | 0.719584 | − | 0.694405i | \(-0.244332\pi\) | ||||
0.719584 | + | 0.694405i | \(0.244332\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 9.46962i | − | 0.361816i | ||||||
\(686\) | −32.2890 | −1.23280 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.381162i | 0.0145317i | ||||||||
\(689\) | 58.5606i | 2.23098i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.9382 | −0.720442 | −0.360221 | − | 0.932867i | \(-0.617299\pi\) | ||||
−0.360221 | + | 0.932867i | \(0.617299\pi\) | |||||||
\(692\) | −19.8884 | −0.756044 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 39.0426 | 1.48204 | ||||||||
\(695\) | −35.1958 | −1.33505 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.556313i | 0.0210719i | ||||||||
\(698\) | − | 49.0443i | − | 1.85635i | ||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | − | 35.5747i | − | 1.34460i | ||||||
\(701\) | 7.01381 | 0.264908 | 0.132454 | − | 0.991189i | \(-0.457714\pi\) | ||||
0.132454 | + | 0.991189i | \(0.457714\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.0221 | −0.377992 | ||||||||
\(704\) | − | 2.94941i | − | 0.111160i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 75.2826i | 2.83330i | ||||||||
\(707\) | −7.32492 | −0.275482 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 9.61006i | − | 0.360913i | −0.983583 | − | 0.180457i | \(-0.942242\pi\) | ||
0.983583 | − | 0.180457i | \(-0.0577575\pi\) | |||||||
\(710\) | 107.559i | 4.03660i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 19.2869i | 0.722805i | ||||||||
\(713\) | −0.0204133 | −0.000764484 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 66.3183i | 2.48016i | ||||||||
\(716\) | 95.9678 | 3.58649 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 58.3403 | 2.17724 | ||||||||
\(719\) | 4.04578i | 0.150882i | 0.997150 | + | 0.0754411i | \(0.0240365\pi\) | ||||
−0.997150 | + | 0.0754411i | \(0.975964\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11.8888 | −0.442762 | ||||||||
\(722\) | − | 43.9355i | − | 1.63511i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 93.8320i | 3.48724i | ||||||||
\(725\) | − | 18.3488i | − | 0.681458i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19.6221 | −0.727742 | −0.363871 | − | 0.931449i | \(-0.618545\pi\) | ||||
−0.363871 | + | 0.931449i | \(0.618545\pi\) | |||||||
\(728\) | 131.535i | 4.87502i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | − | 0.664496i | − | 0.0245941i | ||||||
\(731\) | −0.103965 | −0.00384530 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.1672 | 0.375533 | 0.187766 | − | 0.982214i | \(-0.439875\pi\) | ||||
0.187766 | + | 0.982214i | \(0.439875\pi\) | |||||||
\(734\) | − | 57.8306i | − | 2.13457i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.127264i | 0.00469103i | ||||||||
\(737\) | − | 5.25084i | − | 0.193417i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14.9520 | −0.550017 | −0.275009 | − | 0.961442i | \(-0.588681\pi\) | ||||
−0.275009 | + | 0.961442i | \(0.588681\pi\) | |||||||
\(740\) | −93.7859 | −3.44764 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −70.3308 | −2.58192 | ||||||||
\(743\) | 9.88641 | 0.362697 | 0.181349 | − | 0.983419i | \(-0.441954\pi\) | ||||
0.181349 | + | 0.983419i | \(0.441954\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 20.2346i | 0.741337i | ||||||||
\(746\) | 59.2538i | 2.16944i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −30.4468 | −1.11324 | ||||||||
\(749\) | 30.4765i | 1.11359i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.07548 | −0.294678 | −0.147339 | − | 0.989086i | \(-0.547071\pi\) | ||||
−0.147339 | + | 0.989086i | \(0.547071\pi\) | |||||||
\(752\) | 60.8690 | 2.21967 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 123.143i | 4.48459i | ||||||||
\(755\) | 22.7710 | 0.828721 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.17985 | 0.115573 | 0.0577867 | − | 0.998329i | \(-0.481596\pi\) | ||||
0.0577867 | + | 0.998329i | \(0.481596\pi\) | |||||||
\(758\) | 76.0795 | 2.76333 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 22.3361i | 0.810217i | ||||||||
\(761\) | 49.7358i | 1.80292i | 0.432860 | + | 0.901461i | \(0.357504\pi\) | ||||
−0.432860 | + | 0.901461i | \(0.642496\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 58.3399i | 2.11205i | ||||||||
\(764\) | −104.109 | −3.76653 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −68.1231 | −2.46139 | ||||||||
\(767\) | 90.0207i | 3.25046i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 1.24815i | − | 0.0450095i | −0.999747 | − | 0.0225048i | \(-0.992836\pi\) | ||
0.999747 | − | 0.0225048i | \(-0.00716409\pi\) | |||||||
\(770\) | −79.6477 | −2.87030 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 33.8086 | 1.21680 | ||||||||
\(773\) | −35.7398 | −1.28547 | −0.642736 | − | 0.766088i | \(-0.722201\pi\) | ||||
−0.642736 | + | 0.766088i | \(0.722201\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.08235 | −0.0748004 | ||||||||
\(776\) | 75.8822 | 2.72401 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −26.5442 | −0.951657 | ||||||||
\(779\) | − | 0.384449i | − | 0.0137743i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 55.8211 | 1.99744 | ||||||||
\(782\) | −0.119015 | −0.00425596 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −20.6170 | −0.736320 | ||||||||
\(785\) | 48.4837i | 1.73046i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 12.4044i | − | 0.442169i | −0.975255 | − | 0.221085i | \(-0.929040\pi\) | ||
0.975255 | − | 0.221085i | \(-0.0709597\pi\) | |||||||
\(788\) | − | 60.4153i | − | 2.15221i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − | 86.1606i | − | 3.06546i | ||||||
\(791\) | −31.9762 | −1.13694 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 49.1600i | 1.74572i | ||||||||
\(794\) | 30.9146 | 1.09712 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 55.9379i | − | 1.98267i | ||||||
\(797\) | 9.21427i | 0.326386i | 0.986594 | + | 0.163193i | \(0.0521794\pi\) | ||||
−0.986594 | + | 0.163193i | \(0.947821\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.6026i | 0.587357i | ||||||||
\(800\) | 12.9822i | 0.458990i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −11.4371 | −0.403857 | ||||||||
\(803\) | −0.344862 | −0.0121699 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.214855 | −0.00757265 | ||||||||
\(806\) | 13.9751 | 0.492251 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 14.4562 | 0.508569 | ||||||||
\(809\) | 4.93657 | 0.173561 | 0.0867804 | − | 0.996227i | \(-0.472342\pi\) | ||||
0.0867804 | + | 0.996227i | \(0.472342\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 7.67772i | − | 0.269601i | −0.990873 | − | 0.134801i | \(-0.956961\pi\) | ||
0.990873 | − | 0.134801i | \(-0.0430394\pi\) | |||||||
\(812\) | −102.061 | −3.58165 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 70.5307i | 2.47210i | ||||||||
\(815\) | 11.7074i | 0.410094i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.0718469 | 0.00251360 | ||||||||
\(818\) | − | 3.00455i | − | 0.105052i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − | 3.59762i | − | 0.125634i | ||||||
\(821\) | 28.3626 | 0.989861 | 0.494930 | − | 0.868933i | \(-0.335194\pi\) | ||||
0.494930 | + | 0.868933i | \(0.335194\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 13.2138i | − | 0.460605i | −0.973119 | − | 0.230302i | \(-0.926029\pi\) | ||
0.973119 | − | 0.230302i | \(-0.0739715\pi\) | |||||||
\(824\) | 23.4634 | 0.817387 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −108.114 | −3.76177 | ||||||||
\(827\) | − | 39.3101i | − | 1.36695i | −0.729976 | − | 0.683473i | \(-0.760469\pi\) | ||
0.729976 | − | 0.683473i | \(-0.239531\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 37.2496i | − | 1.29373i | −0.762604 | − | 0.646866i | \(-0.776079\pi\) | ||
0.762604 | − | 0.646866i | \(-0.223921\pi\) | |||||||
\(830\) | 65.1520i | 2.26146i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5.44689i | 0.188837i | ||||||||
\(833\) | − | 5.62346i | − | 0.194841i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 30.0541i | 1.04007i | ||||||||
\(836\) | 21.0407 | 0.727707 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −10.5027 | −0.362810 | ||||||||
\(839\) | − | 47.9046i | − | 1.65385i | −0.562313 | − | 0.826925i | \(-0.690088\pi\) | ||
0.562313 | − | 0.826925i | \(-0.309912\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.6415 | −0.815223 | ||||||||
\(842\) | − | 90.8620i | − | 3.13131i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −72.8757 | −2.50849 | ||||||||
\(845\) | − | 86.8043i | − | 2.98616i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.59277i | 0.226530i | ||||||||
\(848\) | 60.7268 | 2.08537 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −12.1407 | −0.416421 | ||||||||
\(851\) | 0.190262i | 0.00652208i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19.6700 | −0.673487 | −0.336743 | − | 0.941596i | \(-0.609325\pi\) | ||||
−0.336743 | + | 0.941596i | \(0.609325\pi\) | |||||||
\(854\) | −59.0407 | −2.02033 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | − | 60.1475i | − | 2.05580i | ||||||
\(857\) | −9.99242 | −0.341334 | −0.170667 | − | 0.985329i | \(-0.554592\pi\) | ||||
−0.170667 | + | 0.985329i | \(0.554592\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.5166 | 0.563541 | 0.281770 | − | 0.959482i | \(-0.409078\pi\) | ||||
0.281770 | + | 0.959482i | \(0.409078\pi\) | |||||||
\(860\) | 0.672334 | 0.0229264 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −11.1485 | −0.379721 | ||||||||
\(863\) | 16.8671 | 0.574164 | 0.287082 | − | 0.957906i | \(-0.407315\pi\) | ||||
0.287082 | + | 0.957906i | \(0.407315\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.2531i | 0.416618i | ||||||||
\(866\) | 85.2988 | 2.89857 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 11.5826i | 0.393140i | ||||||||
\(869\) | −44.7159 | −1.51688 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.69711i | 0.328574i | ||||||||
\(872\) | − | 115.138i | − | 3.89907i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.0822470 | 0.00278205 | ||||||||
\(875\) | 21.4151 | 0.723962 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15.7423 | −0.531579 | −0.265790 | − | 0.964031i | \(-0.585633\pi\) | ||||
−0.265790 | + | 0.964031i | \(0.585633\pi\) | |||||||
\(878\) | − | 2.84859i | − | 0.0961353i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 68.7714 | 2.31828 | ||||||||
\(881\) | −24.3002 | −0.818695 | −0.409348 | − | 0.912379i | \(-0.634244\pi\) | ||||
−0.409348 | + | 0.912379i | \(0.634244\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −36.8222 | −1.23917 | −0.619583 | − | 0.784931i | \(-0.712698\pi\) | ||||
−0.619583 | + | 0.784931i | \(0.712698\pi\) | |||||||
\(884\) | 56.2283 | 1.89116 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −88.1265 | −2.96067 | ||||||||
\(887\) | − | 4.70714i | − | 0.158050i | −0.996873 | − | 0.0790252i | \(-0.974819\pi\) | ||
0.996873 | − | 0.0790252i | \(-0.0251807\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 19.3909i | 0.650349i | ||||||||
\(890\) | 21.5678 | 0.722955 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 49.0897i | − | 1.64364i | ||||||
\(893\) | − | 11.4735i | − | 0.383945i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 59.1251i | − | 1.97633i | ||||||
\(896\) | −38.9688 | −1.30186 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 70.2615i | 2.34466i | ||||||||
\(899\) | 5.97412i | 0.199248i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.5638i | 0.551819i | ||||||||
\(902\) | −2.70555 | −0.0900851 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 63.1073 | 2.09892 | ||||||||
\(905\) | 57.8092 | 1.92164 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 50.7684i | 1.68574i | 0.538118 | + | 0.842869i | \(0.319135\pi\) | ||||
−0.538118 | + | 0.842869i | \(0.680865\pi\) | |||||||
\(908\) | 9.90994 | 0.328873 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 147.091 | 4.87603 | ||||||||
\(911\) | 28.6351 | 0.948722 | 0.474361 | − | 0.880330i | \(-0.342679\pi\) | ||||
0.474361 | + | 0.880330i | \(0.342679\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 33.8128 | 1.11904 | ||||||||
\(914\) | 83.1052i | 2.74887i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 39.3514i | − | 1.30021i | ||||||
\(917\) | − | 38.5208i | − | 1.27207i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10.5541 | 0.348146 | 0.174073 | − | 0.984733i | \(-0.444307\pi\) | ||||
0.174073 | + | 0.984733i | \(0.444307\pi\) | |||||||
\(920\) | 0.424032 | 0.0139799 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 50.3885i | 1.65946i | ||||||||
\(923\) | −103.089 | −3.39322 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 19.4085i | 0.638148i | ||||||||
\(926\) | −103.814 | −3.41153 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 37.2450 | 1.22263 | ||||||||
\(929\) | 16.5948 | 0.544457 | 0.272228 | − | 0.962233i | \(-0.412239\pi\) | ||||
0.272228 | + | 0.962233i | \(0.412239\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.88618i | 0.127364i | ||||||||
\(932\) | −87.4010 | −2.86291 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 67.8796i | 2.22109i | ||||||||
\(935\) | 18.7580i | 0.613453i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 51.6131 | 1.68613 | 0.843063 | − | 0.537815i | \(-0.180750\pi\) | ||||
0.843063 | + | 0.537815i | \(0.180750\pi\) | |||||||
\(938\) | −11.6461 | −0.380260 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | − | 107.367i | − | 3.50193i | ||||||
\(941\) | 47.3870 | 1.54477 | 0.772386 | − | 0.635154i | \(-0.219063\pi\) | ||||
0.772386 | + | 0.635154i | \(0.219063\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.00729842 | −0.000237669 | ||||||||
\(944\) | 93.3506 | 3.03830 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | − | 0.505622i | − | 0.0164392i | ||||||
\(947\) | 49.7804 | 1.61765 | 0.808823 | − | 0.588052i | \(-0.200105\pi\) | ||||
0.808823 | + | 0.588052i | \(0.200105\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.636883 | 0.0206741 | ||||||||
\(950\) | 8.38999 | 0.272207 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 37.2045i | 1.20581i | ||||||||
\(953\) | −7.13021 | −0.230970 | −0.115485 | − | 0.993309i | \(-0.536842\pi\) | ||||
−0.115485 | + | 0.993309i | \(0.536842\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 64.1407i | 2.07555i | ||||||||
\(956\) | −58.3353 | + | 36.5744i | −1.88670 | + | 1.18290i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 23.0182 | 0.743684 | ||||||||
\(959\) | 10.9003i | 0.351990i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.3220 | −0.978130 | ||||||||
\(962\) | − | 130.254i | − | 4.19957i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −31.0126 | −0.998847 | ||||||||
\(965\) | − | 20.8292i | − | 0.670517i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −29.2478 | −0.940545 | −0.470272 | − | 0.882521i | \(-0.655844\pi\) | ||||
−0.470272 | + | 0.882521i | \(0.655844\pi\) | |||||||
\(968\) | − | 13.0113i | − | 0.418199i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | − | 84.8565i | − | 2.72458i | ||||||
\(971\) | 21.0708i | 0.676193i | 0.941111 | + | 0.338096i | \(0.109783\pi\) | ||||
−0.941111 | + | 0.338096i | \(0.890217\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 40.5134 | 1.29880 | ||||||||
\(974\) | 84.1302i | 2.69571i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 50.9784 | 1.63178 | ||||||||
\(977\) | −36.7623 | −1.17613 | −0.588065 | − | 0.808814i | \(-0.700110\pi\) | ||||
−0.588065 | + | 0.808814i | \(0.700110\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 11.1933i | − | 0.357740i | ||||||
\(980\) | 36.3664i | 1.16168i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 31.9822i | 1.02059i | ||||||||
\(983\) | − | 37.1739i | − | 1.18566i | −0.805327 | − | 0.592831i | \(-0.798010\pi\) | ||
0.805327 | − | 0.592831i | \(-0.201990\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −37.2214 | −1.18597 | ||||||||
\(986\) | 34.8307i | 1.10924i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −38.8574 | −1.23622 | ||||||||
\(989\) | − | 0.00136395i | − | 4.33711e-5i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.00579448i | 0.000184068i | 1.00000 | 9.20339e-5i | \(2.92953e-5\pi\) | |||||
−1.00000 | 9.20339e-5i | \(0.999971\pi\) | ||||||||
\(992\) | − | 4.22682i | − | 0.134202i | ||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | − | 123.809i | − | 3.92698i | ||||||
\(995\) | −34.4629 | −1.09255 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 13.0063i | − | 0.411913i | −0.978561 | − | 0.205956i | \(-0.933969\pi\) | ||
0.978561 | − | 0.205956i | \(-0.0660305\pi\) | |||||||
\(998\) | 46.6362 | 1.47624 | ||||||||
\(999\) | 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 | 2151.2.b.a.2150.5 | ✓ | 80 | |
3.2 | odd | 2 | inner | 2151.2.b.a.2150.75 | yes | 80 | |
239.238 | odd | 2 | inner | 2151.2.b.a.2150.6 | yes | 80 | |
717.716 | even | 2 | inner | 2151.2.b.a.2150.76 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2151.2.b.a.2150.5 | ✓ | 80 | 1.1 | even | 1 | trivial | |
2151.2.b.a.2150.6 | yes | 80 | 239.238 | odd | 2 | inner | |
2151.2.b.a.2150.75 | yes | 80 | 3.2 | odd | 2 | inner | |
2151.2.b.a.2150.76 | yes | 80 | 717.716 | even | 2 | inner |