Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3024,2,Mod(289,3024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3024, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3024.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3024.t (of order \(3\), degree \(2\), not 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: | \(24.1467615712\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{3})\) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 289.7 | ||
Character | \(\chi\) | \(=\) | 3024.289 |
Dual form | 3024.2.t.l.1873.7 |
$q$-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 \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1135\) | \(2593\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.58188 | 0.707436 | 0.353718 | − | 0.935352i | \(-0.384917\pi\) | ||||
0.353718 | + | 0.935352i | \(0.384917\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.80922 | + | 1.93047i | 0.683822 | + | 0.729649i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.17139 | 1.55923 | 0.779616 | − | 0.626258i | \(-0.215414\pi\) | ||||
0.779616 | + | 0.626258i | \(0.215414\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.681985 | − | 1.18123i | −0.189149 | − | 0.327615i | 0.755818 | − | 0.654782i | \(-0.227239\pi\) |
−0.944967 | + | 0.327167i | \(0.893906\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.30781 | + | 3.99724i | 0.559726 | + | 0.969473i | 0.997519 | + | 0.0703975i | \(0.0224268\pi\) |
−0.437794 | + | 0.899076i | \(0.644240\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.0321742 | + | 0.0557274i | −0.00738128 | + | 0.0127847i | −0.869692 | − | 0.493594i | \(-0.835683\pi\) |
0.862311 | + | 0.506379i | \(0.169016\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.74395 | 1.40621 | 0.703105 | − | 0.711086i | \(-0.251796\pi\) | ||||
0.703105 | + | 0.711086i | \(0.251796\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.49767 | −0.499534 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.70787 | + | 8.15427i | −0.874229 | + | 1.51421i | −0.0166475 | + | 0.999861i | \(0.505299\pi\) |
−0.857582 | + | 0.514348i | \(0.828034\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.33139 | + | 2.30604i | −0.239125 | + | 0.414177i | −0.960463 | − | 0.278406i | \(-0.910194\pi\) |
0.721339 | + | 0.692583i | \(0.243527\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.86196 | + | 3.05376i | 0.483760 | + | 0.516180i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.880766 | − | 1.52553i | 0.144797 | − | 0.250796i | −0.784500 | − | 0.620129i | \(-0.787080\pi\) |
0.929297 | + | 0.369333i | \(0.120414\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.858924 | + | 1.48770i | 0.134141 | + | 0.232340i | 0.925269 | − | 0.379311i | \(-0.123839\pi\) |
−0.791128 | + | 0.611651i | \(0.790506\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.12012 | − | 8.86831i | 0.780811 | − | 1.35240i | −0.150658 | − | 0.988586i | \(-0.548139\pi\) |
0.931470 | − | 0.363819i | \(-0.118527\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.60417 | − | 4.51056i | −0.379857 | − | 0.657932i | 0.611184 | − | 0.791489i | \(-0.290694\pi\) |
−0.991041 | + | 0.133556i | \(0.957360\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.453429 | + | 6.98530i | −0.0647756 | + | 0.997900i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.479996 | + | 0.831377i | 0.0659325 | + | 0.114198i | 0.897107 | − | 0.441813i | \(-0.145664\pi\) |
−0.831175 | + | 0.556011i | \(0.812331\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.18049 | 1.10306 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.66676 | − | 8.08307i | 0.607561 | − | 1.05233i | −0.384080 | − | 0.923300i | \(-0.625481\pi\) |
0.991641 | − | 0.129027i | \(-0.0411852\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.19512 | − | 12.4623i | −0.921241 | − | 1.59564i | −0.797498 | − | 0.603321i | \(-0.793844\pi\) |
−0.123742 | − | 0.992314i | \(-0.539490\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.07882 | − | 1.86856i | −0.133811 | − | 0.231767i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.24903 | + | 10.8236i | −0.763441 | + | 1.32232i | 0.177626 | + | 0.984098i | \(0.443158\pi\) |
−0.941067 | + | 0.338220i | \(0.890175\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.49160 | −0.533055 | −0.266527 | − | 0.963827i | \(-0.585876\pi\) | ||||
−0.266527 | + | 0.963827i | \(0.585876\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.941655 | − | 1.63099i | −0.110212 | − | 0.190893i | 0.805643 | − | 0.592401i | \(-0.201820\pi\) |
−0.915856 | + | 0.401507i | \(0.868486\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9.35619 | + | 9.98321i | 1.06624 | + | 1.13769i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.26752 | + | 5.65951i | 0.367625 | + | 0.636745i | 0.989194 | − | 0.146615i | \(-0.0468377\pi\) |
−0.621569 | + | 0.783360i | \(0.713504\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.08661 | + | 8.81026i | −0.558328 | + | 0.967052i | 0.439309 | + | 0.898336i | \(0.355223\pi\) |
−0.997636 | + | 0.0687156i | \(0.978110\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.65066 | + | 6.32314i | 0.395970 | + | 0.685840i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.12369 | − | 7.14243i | 0.437110 | − | 0.757096i | −0.560355 | − | 0.828252i | \(-0.689335\pi\) |
0.997465 | + | 0.0711559i | \(0.0226688\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.04647 | − | 3.45366i | 0.109700 | − | 0.362042i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.0508957 | + | 0.0881539i | −0.00522178 | + | 0.00904440i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.26638 | + | 12.5857i | −0.737789 | + | 1.27789i | 0.215700 | + | 0.976460i | \(0.430797\pi\) |
−0.953489 | + | 0.301428i | \(0.902537\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.24620 | −0.621520 | −0.310760 | − | 0.950488i | \(-0.600584\pi\) | ||||
−0.310760 | + | 0.950488i | \(0.600584\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.77762 | 0.569286 | 0.284643 | − | 0.958634i | \(-0.408125\pi\) | ||||
0.284643 | + | 0.958634i | \(0.408125\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.251126 | + | 0.434963i | −0.0242773 | + | 0.0420494i | −0.877909 | − | 0.478828i | \(-0.841062\pi\) |
0.853632 | + | 0.520877i | \(0.174395\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.37218 | − | 4.10874i | −0.227214 | − | 0.393546i | 0.729767 | − | 0.683696i | \(-0.239628\pi\) |
−0.956981 | + | 0.290149i | \(0.906295\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.11328 | + | 1.92825i | 0.104728 | + | 0.181395i | 0.913627 | − | 0.406553i | \(-0.133269\pi\) |
−0.808899 | + | 0.587948i | \(0.799936\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.6681 | 0.994804 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.54121 | + | 11.6870i | −0.324623 | + | 1.07135i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 15.7432 | 1.43120 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.8604 | −1.06082 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.6057 | 1.65099 | 0.825494 | − | 0.564410i | \(-0.190896\pi\) | ||||
0.825494 | + | 0.564410i | \(0.190896\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.5404 | 1.18303 | 0.591515 | − | 0.806294i | \(-0.298530\pi\) | ||||
0.591515 | + | 0.806294i | \(0.298530\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.165791 | + | 0.0387119i | −0.0143759 | + | 0.00335675i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.7420 | −1.17406 | −0.587029 | − | 0.809566i | \(-0.699702\pi\) | ||||
−0.587029 | + | 0.809566i | \(0.699702\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.79328 | − | 11.7663i | −0.576198 | − | 0.998005i | −0.995910 | − | 0.0903476i | \(-0.971202\pi\) |
0.419712 | − | 0.907657i | \(-0.362131\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.52681 | − | 6.10861i | −0.294927 | − | 0.510828i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.44726 | + | 12.8990i | −0.618461 | + | 1.07121i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.96066 | −0.488317 | −0.244158 | − | 0.969735i | \(-0.578512\pi\) | ||||
−0.244158 | + | 0.969735i | \(0.578512\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.54142 | −0.695091 | −0.347546 | − | 0.937663i | \(-0.612985\pi\) | ||||
−0.347546 | + | 0.937663i | \(0.612985\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.10610 | + | 3.64786i | −0.169166 | + | 0.293004i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.31996 | − | 2.28623i | 0.105344 | − | 0.182461i | −0.808535 | − | 0.588449i | \(-0.799739\pi\) |
0.913879 | + | 0.405987i | \(0.133072\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12.2013 | + | 13.0190i | 0.961597 | + | 1.02604i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.87875 | − | 15.3785i | 0.695438 | − | 1.20453i | −0.274595 | − | 0.961560i | \(-0.588544\pi\) |
0.970033 | − | 0.242973i | \(-0.0781228\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.98937 | + | 6.90979i | 0.308706 | + | 0.534695i | 0.978080 | − | 0.208231i | \(-0.0667706\pi\) |
−0.669373 | + | 0.742926i | \(0.733437\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.56979 | − | 9.64716i | 0.428446 | − | 0.742090i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.83170 | + | 6.63670i | 0.291319 | + | 0.504579i | 0.974122 | − | 0.226023i | \(-0.0725726\pi\) |
−0.682803 | + | 0.730603i | \(0.739239\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.51884 | − | 4.82168i | −0.341592 | − | 0.364485i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.7864 | + | 20.4147i | 0.880958 | + | 1.52586i | 0.850277 | + | 0.526335i | \(0.176434\pi\) |
0.0306808 | + | 0.999529i | \(0.490232\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.3700 | 1.29110 | 0.645551 | − | 0.763717i | \(-0.276628\pi\) | ||||
0.645551 | + | 0.763717i | \(0.276628\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.39326 | − | 2.41320i | 0.102435 | − | 0.177422i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.9346 | + | 20.6713i | 0.872742 | + | 1.51163i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.42330 | − | 4.19728i | −0.175344 | − | 0.303704i | 0.764936 | − | 0.644106i | \(-0.222770\pi\) |
−0.940280 | + | 0.340402i | \(0.889437\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.32091 | − | 12.6802i | 0.526970 | − | 0.912739i | −0.472536 | − | 0.881312i | \(-0.656661\pi\) |
0.999506 | − | 0.0314278i | \(-0.0100054\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 19.1996 | 1.36791 | 0.683957 | − | 0.729522i | \(-0.260257\pi\) | ||||
0.683957 | + | 0.729522i | \(0.260257\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.50796 | − | 11.2721i | −0.461337 | − | 0.799060i | 0.537691 | − | 0.843142i | \(-0.319297\pi\) |
−0.999028 | + | 0.0440825i | \(0.985964\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −24.2591 | + | 5.66448i | −1.70266 | + | 0.397569i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.35871 | + | 2.35336i | 0.0948965 | + | 0.164366i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.166385 | + | 0.288188i | −0.0115091 | + | 0.0199344i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.43389 | + | 12.8759i | 0.511770 | + | 0.886412i | 0.999907 | + | 0.0136450i | \(0.00434348\pi\) |
−0.488137 | + | 0.872767i | \(0.662323\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.09940 | − | 14.0286i | 0.552374 | − | 0.956740i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.86052 | + | 1.60192i | −0.465722 | + | 0.108746i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.14778 | − | 5.45212i | 0.211743 | − | 0.366749i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.2085 | + | 19.4136i | −0.750574 | + | 1.30003i | 0.196971 | + | 0.980409i | \(0.436890\pi\) |
−0.947545 | + | 0.319623i | \(0.896444\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.89450 | 0.258487 | 0.129243 | − | 0.991613i | \(-0.458745\pi\) | ||||
0.129243 | + | 0.991613i | \(0.458745\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.38717 | −0.0916669 | −0.0458334 | − | 0.998949i | \(-0.514594\pi\) | ||||
−0.0458334 | + | 0.998949i | \(0.514594\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.99057 | + | 15.5721i | −0.588992 | + | 1.02016i | 0.405373 | + | 0.914151i | \(0.367142\pi\) |
−0.994365 | + | 0.106013i | \(0.966192\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.11947 | − | 7.13514i | −0.268725 | − | 0.465445i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.68043 | − | 4.64264i | −0.173382 | − | 0.300307i | 0.766218 | − | 0.642581i | \(-0.222136\pi\) |
−0.939600 | + | 0.342274i | \(0.888803\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.416592 | 0.0268351 | 0.0134175 | − | 0.999910i | \(-0.495729\pi\) | ||||
0.0134175 | + | 0.999910i | \(0.495729\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.717269 | + | 11.0499i | −0.0458246 | + | 0.705951i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.0877694 | 0.00558464 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 22.5606 | 1.42401 | 0.712006 | − | 0.702173i | \(-0.247787\pi\) | ||||
0.712006 | + | 0.702173i | \(0.247787\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 34.8756 | 2.19261 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 11.0461 | 0.689039 | 0.344520 | − | 0.938779i | \(-0.388042\pi\) | ||||
0.344520 | + | 0.938779i | \(0.388042\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.53850 | − | 1.05973i | 0.282008 | − | 0.0658486i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −25.4620 | −1.57006 | −0.785028 | − | 0.619460i | \(-0.787352\pi\) | ||||
−0.785028 | + | 0.619460i | \(0.787352\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.759294 | + | 1.31514i | 0.0466430 | + | 0.0807881i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.78957 | − | 4.83168i | −0.170083 | − | 0.294593i | 0.768366 | − | 0.640011i | \(-0.221070\pi\) |
−0.938449 | + | 0.345419i | \(0.887737\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.46645 | − | 2.53997i | 0.0890806 | − | 0.154292i | −0.818042 | − | 0.575158i | \(-0.804940\pi\) |
0.907123 | + | 0.420866i | \(0.138274\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −12.9164 | −0.778889 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.0917 | 1.32736 | 0.663680 | − | 0.748016i | \(-0.268993\pi\) | ||||
0.663680 | + | 0.748016i | \(0.268993\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.81009 | − | 4.86721i | 0.167636 | − | 0.290354i | −0.769952 | − | 0.638101i | \(-0.779720\pi\) |
0.937588 | + | 0.347748i | \(0.113053\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.6502 | − | 18.4466i | 0.633086 | − | 1.09654i | −0.353831 | − | 0.935309i | \(-0.615121\pi\) |
0.986917 | − | 0.161228i | \(-0.0515454\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.31798 | + | 4.34971i | −0.0777977 | + | 0.256755i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.15195 | + | 3.72729i | −0.126585 | + | 0.219252i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −14.1128 | − | 24.4440i | −0.824477 | − | 1.42804i | −0.902319 | − | 0.431070i | \(-0.858136\pi\) |
0.0778418 | − | 0.996966i | \(-0.475197\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.38224 | − | 12.7864i | 0.429811 | − | 0.744454i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.59927 | − | 7.96617i | −0.265983 | − | 0.460696i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 26.3834 | − | 6.16050i | 1.52072 | − | 0.355086i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −11.3818 | − | 19.7138i | −0.651719 | − | 1.12881i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.41329 | 0.137734 | 0.0688669 | − | 0.997626i | \(-0.478062\pi\) | ||||
0.0688669 | + | 0.997626i | \(0.478062\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.76840 | + | 8.25911i | −0.270391 | + | 0.468331i | −0.968962 | − | 0.247210i | \(-0.920486\pi\) |
0.698571 | + | 0.715541i | \(0.253820\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.3010 | − | 28.2341i | −0.921386 | − | 1.59589i | −0.797273 | − | 0.603619i | \(-0.793725\pi\) |
−0.124112 | − | 0.992268i | \(-0.539608\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.54977 | − | 2.68428i | −0.0870438 | − | 0.150764i | 0.819216 | − | 0.573484i | \(-0.194409\pi\) |
−0.906260 | + | 0.422720i | \(0.861075\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −24.3462 | + | 42.1689i | −1.36313 | + | 2.36100i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.297008 | −0.0165260 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.70337 | + | 2.95033i | 0.0944862 | + | 0.163655i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.99597 | − | 13.1879i | 0.220305 | − | 0.727071i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.83825 | − | 3.18394i | −0.101039 | − | 0.175005i | 0.811074 | − | 0.584944i | \(-0.198883\pi\) |
−0.912113 | + | 0.409939i | \(0.865550\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −9.88519 | + | 17.1216i | −0.540086 | + | 0.935456i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.15866 | + | 10.6671i | 0.335483 | + | 0.581074i | 0.983578 | − | 0.180486i | \(-0.0577670\pi\) |
−0.648094 | + | 0.761560i | \(0.724434\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.88514 | + | 11.9254i | −0.372851 | + | 0.645797i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.3053 | + | 11.7626i | −0.772412 | + | 0.635122i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8.85078 | − | 15.3300i | 0.475135 | − | 0.822958i | −0.524460 | − | 0.851435i | \(-0.675733\pi\) |
0.999594 | + | 0.0284778i | \(0.00906598\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.562639 | − | 0.974519i | 0.0301174 | − | 0.0521648i | −0.850574 | − | 0.525856i | \(-0.823745\pi\) |
0.880691 | + | 0.473691i | \(0.157079\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.9625 | 0.583475 | 0.291738 | − | 0.956498i | \(-0.405767\pi\) | ||||
0.291738 | + | 0.956498i | \(0.405767\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.10515 | −0.377102 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −13.4733 | + | 23.3364i | −0.711092 | + | 1.23165i | 0.253356 | + | 0.967373i | \(0.418466\pi\) |
−0.964448 | + | 0.264274i | \(0.914868\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.49793 | + | 16.4509i | 0.499891 | + | 0.865837i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.48958 | − | 2.58003i | −0.0779682 | − | 0.135045i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −34.8273 | −1.81797 | −0.908986 | − | 0.416826i | \(-0.863142\pi\) | ||||
−0.908986 | + | 0.416826i | \(0.863142\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.736530 | + | 2.43076i | −0.0382387 | + | 0.126199i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −23.1585 | −1.19910 | −0.599551 | − | 0.800336i | \(-0.704654\pi\) | ||||
−0.599551 | + | 0.800336i | \(0.704654\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12.8428 | 0.661437 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.7259 | −1.16735 | −0.583676 | − | 0.811987i | \(-0.698386\pi\) | ||||
−0.583676 | + | 0.811987i | \(0.698386\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 23.2041 | 1.18567 | 0.592837 | − | 0.805322i | \(-0.298008\pi\) | ||||
0.592837 | + | 0.805322i | \(0.298008\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 14.8003 | + | 15.7922i | 0.754294 | + | 0.804844i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.13474 | 0.463149 | 0.231575 | − | 0.972817i | \(-0.425612\pi\) | ||||
0.231575 | + | 0.972817i | \(0.425612\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15.5637 | + | 26.9572i | 0.787092 | + | 1.36328i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.16881 | + | 8.95265i | 0.260071 | + | 0.450456i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −19.2126 | + | 33.2773i | −0.964255 | + | 1.67014i | −0.252652 | + | 0.967557i | \(0.581303\pi\) |
−0.711603 | + | 0.702582i | \(0.752031\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.94696 | −0.147164 | −0.0735821 | − | 0.997289i | \(-0.523443\pi\) | ||||
−0.0735821 | + | 0.997289i | \(0.523443\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.63196 | 0.180921 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.55478 | − | 7.88912i | 0.225772 | − | 0.391049i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.30296 | + | 5.72089i | −0.163321 | + | 0.282880i | −0.936058 | − | 0.351847i | \(-0.885554\pi\) |
0.772737 | + | 0.634726i | \(0.218887\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 24.0473 | − | 5.61503i | 1.18329 | − | 0.276297i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.04638 | + | 13.9367i | −0.394981 | + | 0.684127i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.381961 | − | 0.661576i | −0.0186600 | − | 0.0323201i | 0.856545 | − | 0.516073i | \(-0.172607\pi\) |
−0.875205 | + | 0.483753i | \(0.839273\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.48798 | + | 4.30931i | −0.121257 | + | 0.210023i | −0.920264 | − | 0.391299i | \(-0.872026\pi\) |
0.799007 | + | 0.601322i | \(0.205359\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.76414 | − | 9.98378i | −0.279602 | − | 0.484285i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.0406 | − | 36.4371i | 0.534290 | − | 1.76331i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.01856 | − | 6.96035i | −0.193567 | − | 0.335268i | 0.752863 | − | 0.658178i | \(-0.228672\pi\) |
−0.946430 | + | 0.322909i | \(0.895339\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.8006 | −0.519043 | −0.259522 | − | 0.965737i | \(-0.583565\pi\) | ||||
−0.259522 | + | 0.965737i | \(0.583565\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.216981 | + | 0.375823i | −0.0103796 | + | 0.0179780i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.0597 | − | 17.4239i | −0.480122 | − | 0.831596i | 0.519618 | − | 0.854399i | \(-0.326074\pi\) |
−0.999740 | + | 0.0228028i | \(0.992741\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.60623 | + | 7.97822i | 0.218848 | + | 0.379057i | 0.954456 | − | 0.298351i | \(-0.0964366\pi\) |
−0.735608 | + | 0.677408i | \(0.763103\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.52316 | − | 11.2984i | 0.309227 | − | 0.535597i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 22.4840 | 1.06109 | 0.530544 | − | 0.847658i | \(-0.321988\pi\) | ||||
0.530544 | + | 0.847658i | \(0.321988\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.44183 | + | 7.69347i | 0.209158 | + | 0.362271i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.65539 | − | 5.46327i | 0.0776058 | − | 0.256122i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.39776 | − | 16.2774i | −0.439609 | − | 0.761425i | 0.558050 | − | 0.829807i | \(-0.311550\pi\) |
−0.997659 | + | 0.0683823i | \(0.978216\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.3773 | + | 17.9739i | −0.483317 | + | 0.837129i | −0.999816 | − | 0.0191582i | \(-0.993901\pi\) |
0.516500 | + | 0.856287i | \(0.327235\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.0414 | − | 17.3922i | −0.466663 | − | 0.808284i | 0.532612 | − | 0.846360i | \(-0.321211\pi\) |
−0.999275 | + | 0.0380753i | \(0.987877\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14.6015 | − | 25.2905i | 0.675676 | − | 1.17030i | −0.300595 | − | 0.953752i | \(-0.597185\pi\) |
0.976271 | − | 0.216553i | \(-0.0694813\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −32.2006 | + | 7.51880i | −1.48689 | + | 0.347186i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 26.4781 | − | 45.8615i | 1.21747 | − | 2.10871i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.0803606 | − | 0.139189i | 0.00368720 | − | 0.00638642i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −40.0654 | −1.83064 | −0.915319 | − | 0.402731i | \(-0.868061\pi\) | ||||
−0.915319 | + | 0.402731i | \(0.868061\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.40268 | −0.109553 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −11.4945 | + | 19.9091i | −0.521939 | + | 0.904024i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.32801 | − | 16.1566i | −0.422692 | − | 0.732125i | 0.573509 | − | 0.819199i | \(-0.305582\pi\) |
−0.996202 | + | 0.0870742i | \(0.972248\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.285132 | − | 0.493864i | −0.0128678 | − | 0.0222878i | 0.859520 | − | 0.511102i | \(-0.170763\pi\) |
−0.872388 | + | 0.488815i | \(0.837429\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −43.4594 | −1.95731 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8.12630 | − | 8.67090i | −0.364514 | − | 0.388943i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.928593 | 0.0415695 | 0.0207848 | − | 0.999784i | \(-0.493384\pi\) | ||||
0.0207848 | + | 0.999784i | \(0.493384\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.27170 | −0.145878 | −0.0729389 | − | 0.997336i | \(-0.523238\pi\) | ||||
−0.0729389 | + | 0.997336i | \(0.523238\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.88071 | −0.439686 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8.96781 | −0.397491 | −0.198746 | − | 0.980051i | \(-0.563687\pi\) | ||||
−0.198746 | + | 0.980051i | \(0.563687\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.44492 | − | 4.76867i | 0.0639196 | − | 0.210953i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9.13948 | 0.402734 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.4672 | − | 23.3258i | −0.592286 | − | 1.02587i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.37649 | + | 9.31235i | 0.235548 | + | 0.407982i | 0.959432 | − | 0.281940i | \(-0.0909781\pi\) |
−0.723884 | + | 0.689922i | \(0.757645\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.2796 | − | 28.1970i | 0.711856 | − | 1.23297i | −0.252304 | − | 0.967648i | \(-0.581188\pi\) |
0.964160 | − | 0.265322i | \(-0.0854784\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −12.2904 | −0.535377 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.4808 | 0.977427 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.17155 | − | 2.02918i | 0.0507453 | − | 0.0878935i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.397250 | + | 0.688057i | −0.0171746 | + | 0.0297473i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.34486 | + | 36.1237i | −0.101000 | + | 1.55596i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.46359 | + | 5.99911i | −0.148911 | + | 0.257922i | −0.930825 | − | 0.365464i | \(-0.880910\pi\) |
0.781914 | + | 0.623386i | \(0.214244\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.75250 | − | 6.49952i | −0.160739 | − | 0.278409i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.8974 | − | 27.5351i | 0.679725 | − | 1.17732i | −0.295339 | − | 0.955392i | \(-0.595433\pi\) |
0.975064 | − | 0.221925i | \(-0.0712340\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.302944 | − | 0.524715i | −0.0129059 | − | 0.0223536i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.01385 | + | 16.5472i | −0.213211 | + | 0.703657i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −14.1679 | − | 24.5395i | −0.600314 | − | 1.03977i | −0.992773 | − | 0.120005i | \(-0.961709\pi\) |
0.392460 | − | 0.919769i | \(-0.371624\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −13.9674 | −0.590758 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 22.3270 | − | 38.6715i | 0.940972 | − | 1.62981i | 0.177350 | − | 0.984148i | \(-0.443248\pi\) |
0.763622 | − | 0.645664i | \(-0.223419\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.76106 | + | 3.05025i | 0.0740885 | + | 0.128325i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −10.6102 | − | 18.3775i | −0.444804 | − | 0.770423i | 0.553235 | − | 0.833025i | \(-0.313393\pi\) |
−0.998039 | + | 0.0626026i | \(0.980060\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.94786 | − | 10.3020i | 0.248910 | − | 0.431125i | −0.714313 | − | 0.699826i | \(-0.753261\pi\) |
0.963224 | + | 0.268701i | \(0.0865943\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −16.8442 | −0.702450 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19.3490 | − | 33.5135i | −0.805511 | − | 1.39519i | −0.915946 | − | 0.401302i | \(-0.868558\pi\) |
0.110435 | − | 0.993883i | \(-0.464776\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −26.2107 | + | 6.12018i | −1.08741 | + | 0.253908i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.48224 | + | 4.29937i | 0.102804 | + | 0.178062i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.92138 | − | 17.1843i | 0.409499 | − | 0.709274i | −0.585334 | − | 0.810792i | \(-0.699037\pi\) |
0.994834 | + | 0.101518i | \(0.0323701\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.0856730 | − | 0.148390i | −0.00353010 | − | 0.00611431i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −10.9566 | + | 18.9774i | −0.449933 | + | 0.779307i | −0.998381 | − | 0.0568775i | \(-0.981886\pi\) |
0.548448 | + | 0.836185i | \(0.315219\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.60176 | + | 18.4875i | −0.229650 | + | 0.757912i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −16.5223 | + | 28.6174i | −0.675081 | + | 1.16928i | 0.301364 | + | 0.953509i | \(0.402558\pi\) |
−0.976445 | + | 0.215766i | \(0.930775\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.4951 | − | 19.9100i | 0.468893 | − | 0.812147i | −0.530475 | − | 0.847701i | \(-0.677986\pi\) |
0.999368 | + | 0.0355541i | \(0.0113196\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 24.9038 | 1.01248 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −27.6564 | −1.12254 | −0.561269 | − | 0.827634i | \(-0.689686\pi\) | ||||
−0.561269 | + | 0.827634i | \(0.689686\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.55201 | + | 6.15226i | −0.143699 | + | 0.248894i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15.7684 | − | 27.3116i | −0.636879 | − | 1.10311i | −0.986114 | − | 0.166072i | \(-0.946892\pi\) |
0.349235 | − | 0.937035i | \(-0.386442\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10.7513 | + | 18.6217i | 0.432830 | + | 0.749683i | 0.997116 | − | 0.0758961i | \(-0.0241817\pi\) |
−0.564286 | + | 0.825580i | \(0.690848\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −28.2522 | −1.13555 | −0.567776 | − | 0.823183i | \(-0.692196\pi\) | ||||
−0.567776 | + | 0.823183i | \(0.692196\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 21.2489 | − | 4.96160i | 0.851320 | − | 0.198782i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.27330 | −0.250932 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.13056 | 0.324187 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.12550 | 0.363281 | 0.181640 | − | 0.983365i | \(-0.441859\pi\) | ||||
0.181640 | + | 0.983365i | \(0.441859\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 29.4319 | 1.16797 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.56050 | − | 4.22826i | 0.339179 | − | 0.167530i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −32.8978 | −1.29939 | −0.649693 | − | 0.760197i | \(-0.725103\pi\) | ||||
−0.649693 | + | 0.760197i | \(0.725103\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.1276 | − | 17.5415i | −0.399392 | − | 0.691767i | 0.594259 | − | 0.804274i | \(-0.297445\pi\) |
−0.993651 | + | 0.112506i | \(0.964112\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.67441 | − | 9.82837i | −0.223084 | − | 0.386393i | 0.732659 | − | 0.680596i | \(-0.238279\pi\) |
−0.955743 | + | 0.294203i | \(0.904946\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 24.1336 | − | 41.8007i | 0.947328 | − | 1.64082i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.58036 | −0.140110 | −0.0700552 | − | 0.997543i | \(-0.522318\pi\) | ||||
−0.0700552 | + | 0.997543i | \(0.522318\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 21.4192 | 0.836918 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.13582 | − | 15.8237i | 0.355881 | − | 0.616404i | −0.631387 | − | 0.775468i | \(-0.717514\pi\) |
0.987268 | + | 0.159064i | \(0.0508475\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.11696 | + | 1.93462i | −0.0434446 | + | 0.0752482i | −0.886930 | − | 0.461904i | \(-0.847167\pi\) |
0.843485 | + | 0.537152i | \(0.180500\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.262260 | + | 0.0612374i | −0.0101700 | + | 0.00237468i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −31.7496 | + | 54.9919i | −1.22935 | + | 2.12930i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −37.2087 | − | 64.4474i | −1.43643 | − | 2.48797i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.4804 | + | 21.6166i | −0.481083 | + | 0.833260i | −0.999764 | − | 0.0217074i | \(-0.993090\pi\) |
0.518681 | + | 0.854968i | \(0.326423\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.90633 | − | 17.1583i | −0.380731 | − | 0.659446i | 0.610436 | − | 0.792066i | \(-0.290994\pi\) |
−0.991167 | + | 0.132620i | \(0.957661\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −37.4429 | + | 8.74287i | −1.43693 | + | 0.335521i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.72871 | + | 9.92242i | 0.219203 | + | 0.379671i | 0.954565 | − | 0.298004i | \(-0.0963209\pi\) |
−0.735361 | + | 0.677675i | \(0.762988\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −21.7381 | −0.830571 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.654700 | − | 1.13397i | 0.0249421 | − | 0.0432010i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.2552 | + | 35.0831i | 0.770545 | + | 1.33462i | 0.937265 | + | 0.348619i | \(0.113349\pi\) |
−0.166719 | + | 0.986004i | \(0.553317\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −10.7461 | − | 18.6128i | −0.407624 | − | 0.706025i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.96446 | + | 6.86665i | −0.150165 | + | 0.260093i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 29.5416 | 1.11577 | 0.557885 | − | 0.829918i | \(-0.311613\pi\) | ||||
0.557885 | + | 0.829918i | \(0.311613\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.0566760 | + | 0.0981657i | 0.00213758 | + | 0.00370239i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −11.3008 | − | 12.0581i | −0.425009 | − | 0.453492i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.7407 | + | 32.4599i | 0.703822 | + | 1.21906i | 0.967115 | + | 0.254340i | \(0.0818581\pi\) |
−0.263293 | + | 0.964716i | \(0.584809\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.97883 | + | 15.5518i | −0.336260 | + | 0.582419i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.57897 | − | 9.66306i | −0.208642 | − | 0.361378i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.35418 | − | 11.0058i | 0.236971 | − | 0.410445i | −0.722873 | − | 0.690981i | \(-0.757179\pi\) |
0.959844 | + | 0.280536i | \(0.0905121\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.4530 | + | 11.1535i | 0.389290 | + | 0.415379i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 11.7587 | − | 20.3667i | 0.436707 | − | 0.756399i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19.9463 | + | 34.5480i | −0.739768 | + | 1.28132i | 0.212832 | + | 0.977089i | \(0.431731\pi\) |
−0.952600 | + | 0.304227i | \(0.901602\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 47.2650 | 1.74816 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −44.8182 | −1.65540 | −0.827699 | − | 0.561172i | \(-0.810350\pi\) | ||||
−0.827699 | + | 0.561172i | \(0.810350\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −32.3162 | + | 55.9732i | −1.19038 | + | 2.06180i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.64954 | + | 11.5173i | 0.244607 | + | 0.423672i | 0.962021 | − | 0.272975i | \(-0.0880076\pi\) |
−0.717414 | + | 0.696647i | \(0.754674\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.15562 | + | 3.73365i | 0.0790822 | + | 0.136974i | 0.902854 | − | 0.429947i | \(-0.141468\pi\) |
−0.823772 | + | 0.566921i | \(0.808134\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.42903 | −0.345453 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.29402 | + | 0.302153i | −0.0472826 | + | 0.0110404i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 43.5303 | 1.58844 | 0.794221 | − | 0.607629i | \(-0.207879\pi\) | ||||
0.794221 | + | 0.607629i | \(0.207879\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −13.5115 | −0.491733 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34.6790 | 1.26043 | 0.630215 | − | 0.776420i | \(-0.282967\pi\) | ||||
0.630215 | + | 0.776420i | \(0.282967\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.51946 | 0.127580 | 0.0637902 | − | 0.997963i | \(-0.479681\pi\) | ||||
0.0637902 | + | 0.997963i | \(0.479681\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.64000 | − | 12.0131i | 0.131777 | − | 0.434902i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −12.7307 | −0.459677 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −19.5075 | − | 33.7879i | −0.703457 | − | 1.21842i | −0.967245 | − | 0.253843i | \(-0.918305\pi\) |
0.263788 | − | 0.964581i | \(-0.415028\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −23.2169 | − | 40.2128i | −0.835054 | − | 1.44636i | −0.893987 | − | 0.448094i | \(-0.852103\pi\) |
0.0589329 | − | 0.998262i | \(-0.481230\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.32538 | − | 5.75972i | 0.119451 | − | 0.206895i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.110541 | −0.00396054 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −23.2278 | −0.831156 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.08801 | − | 3.61654i | 0.0745242 | − | 0.129080i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23.7212 | − | 41.0863i | 0.845569 | − | 1.46457i | −0.0395575 | − | 0.999217i | \(-0.512595\pi\) |
0.885126 | − | 0.465351i | \(-0.154072\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.70827 | + | 5.63778i | −0.0607390 | + | 0.200456i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.81393 | + | 16.9982i | −0.348503 | + | 0.603625i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −7.69773 | − | 13.3329i | −0.272668 | − | 0.472274i | 0.696876 | − | 0.717191i | \(-0.254573\pi\) |
−0.969544 | + | 0.244917i | \(0.921239\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.0198 | − | 20.8190i | 0.425232 | − | 0.736523i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.86966 | − | 8.43450i | −0.171847 | − | 0.297647i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 19.3009 | + | 20.5944i | 0.680269 | + | 0.725858i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 15.0433 | + | 26.0557i | 0.528893 | + | 0.916069i | 0.999432 | + | 0.0336903i | \(0.0107260\pi\) |
−0.470539 | + | 0.882379i | \(0.655941\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.2821 | 0.396170 | 0.198085 | − | 0.980185i | \(-0.436528\pi\) | ||||
0.198085 | + | 0.980185i | \(0.436528\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 14.0451 | − | 24.3268i | 0.491978 | − | 0.852130i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.329472 | + | 0.570662i | 0.0115268 | + | 0.0199650i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.62633 | + | 2.81688i | 0.0567593 | + | 0.0983099i | 0.893009 | − | 0.450039i | \(-0.148590\pi\) |
−0.836250 | + | 0.548349i | \(0.815257\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.29842 | − | 12.6412i | 0.254407 | − | 0.440645i | −0.710327 | − | 0.703871i | \(-0.751453\pi\) |
0.964734 | + | 0.263226i | \(0.0847865\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 42.7500 | 1.48656 | 0.743282 | − | 0.668978i | \(-0.233268\pi\) | ||||
0.743282 | + | 0.668978i | \(0.233268\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17.6799 | − | 30.6225i | −0.614049 | − | 1.06356i | −0.990551 | − | 0.137148i | \(-0.956207\pi\) |
0.376502 | − | 0.926416i | \(-0.377127\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −28.9683 | + | 14.3083i | −1.00369 | + | 0.495752i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.31068 | + | 10.9304i | 0.218390 | + | 0.378263i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15.0886 | − | 26.1343i | 0.520917 | − | 0.902255i | −0.478787 | − | 0.877931i | \(-0.658923\pi\) |
0.999704 | − | 0.0243242i | \(-0.00774340\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −29.8280 | − | 51.6637i | −1.02855 | − | 1.78151i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8.81072 | − | 15.2606i | 0.303098 | − | 0.524981i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 28.4830 | + | 30.3918i | 0.978688 | + | 1.04428i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.93984 | − | 10.2881i | 0.203615 | − | 0.352672i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −20.4789 | + | 35.4705i | −0.701184 | + | 1.21449i | 0.266867 | + | 0.963733i | \(0.414011\pi\) |
−0.968051 | + | 0.250753i | \(0.919322\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −30.4566 | −1.04038 | −0.520190 | − | 0.854051i | \(-0.674139\pi\) | ||||
−0.520190 | + | 0.854051i | \(0.674139\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.18935 | −0.108819 | −0.0544096 | − | 0.998519i | \(-0.517328\pi\) | ||||
−0.0544096 | + | 0.998519i | \(0.517328\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 11.5498 | − | 20.0049i | 0.393161 | − | 0.680975i | −0.599703 | − | 0.800222i | \(-0.704715\pi\) |
0.992865 | + | 0.119247i | \(0.0380481\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.06128 | + | 10.4984i | 0.206090 | + | 0.356958i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 16.8976 | + | 29.2675i | 0.573212 | + | 0.992833i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17.0470 | 0.577615 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −21.4581 | − | 22.8961i | −0.725415 | − | 0.774030i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.28938 | −0.111074 | −0.0555372 | − | 0.998457i | \(-0.517687\pi\) | ||||
−0.0555372 | + | 0.998457i | \(0.517687\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −51.4835 | −1.73452 | −0.867262 | − | 0.497852i | \(-0.834122\pi\) | ||||
−0.867262 | + | 0.497852i | \(0.834122\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.359433 | −0.0120959 | −0.00604794 | − | 0.999982i | \(-0.501925\pi\) | ||||
−0.00604794 | + | 0.999982i | \(0.501925\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11.6000 | 0.389488 | 0.194744 | − | 0.980854i | \(-0.437612\pi\) | ||||
0.194744 | + | 0.980854i | \(0.437612\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 33.6618 | + | 35.9177i | 1.12898 | + | 1.20464i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.335149 | 0.0112153 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 18.6446 | + | 32.2935i | 0.623222 | + | 1.07945i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −12.5360 | − | 21.7130i | −0.418100 | − | 0.724170i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.21548 | + | 3.83732i | −0.0738082 | + | 0.127840i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 27.4772 | 0.913373 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −24.5791 | −0.816135 | −0.408067 | − | 0.912952i | \(-0.633797\pi\) | ||||
−0.408067 | + | 0.912952i | \(0.633797\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −20.1678 | + | 34.9317i | −0.668190 | + | 1.15734i | 0.310219 | + | 0.950665i | \(0.399598\pi\) |
−0.978410 | + | 0.206675i | \(0.933736\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −26.3048 | + | 45.5613i | −0.870562 | + | 1.50786i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 24.4976 | + | 26.1393i | 0.808981 | + | 0.863197i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10.8377 | + | 18.7714i | −0.357501 | + | 0.619210i | −0.987543 | − | 0.157351i | \(-0.949705\pi\) |
0.630041 | + | 0.776562i | \(0.283038\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.06320 | + | 5.30562i | 0.100827 | + | 0.174637i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.19986 | + | 3.81028i | −0.0723311 | + | 0.125281i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.96409 | − | 6.86601i | −0.130058 | − | 0.225266i | 0.793641 | − | 0.608386i | \(-0.208183\pi\) |
−0.923699 | + | 0.383120i | \(0.874850\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.374684 | − | 0.250015i | −0.0122798 | − | 0.00819392i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 18.8790 | + | 32.6994i | 0.617409 | + | 1.06938i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.84549 | 0.190964 | 0.0954819 | − | 0.995431i | \(-0.469561\pi\) | ||||
0.0954819 | + | 0.995431i | \(0.469561\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −19.5046 | + | 33.7829i | −0.635831 | + | 1.10129i | 0.350508 | + | 0.936560i | \(0.386009\pi\) |
−0.986339 | + | 0.164731i | \(0.947324\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.79254 | + | 10.0330i | 0.188631 | + | 0.326719i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.52185 | + | 6.10003i | 0.114445 | + | 0.198224i | 0.917558 | − | 0.397603i | \(-0.130158\pi\) |
−0.803113 | + | 0.595827i | \(0.796824\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.28439 | + | 2.22463i | −0.0416930 | + | 0.0722145i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −28.2379 | −0.914716 | −0.457358 | − | 0.889283i | \(-0.651204\pi\) | ||||
−0.457358 | + | 0.889283i | \(0.651204\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.83336 | − | 6.63957i | −0.124044 | − | 0.214851i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −24.8623 | − | 26.5285i | −0.802846 | − | 0.856650i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.9548 | + | 20.7063i | 0.385639 | + | 0.667946i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 11.5808 | − | 20.0585i | 0.372798 | − | 0.645705i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.430925 | + | 0.746384i | 0.0138576 | + | 0.0240021i | 0.872871 | − | 0.487951i | \(-0.162256\pi\) |
−0.859013 | + | 0.511953i | \(0.828922\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19.6403 | + | 34.0181i | −0.630288 | + | 1.09169i | 0.357204 | + | 0.934026i | \(0.383730\pi\) |
−0.987493 | + | 0.157665i | \(0.949603\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10.4239 | − | 34.4021i | 0.334176 | − | 1.10288i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −17.2739 | + | 29.9193i | −0.552641 | + | 0.957202i | 0.445442 | + | 0.895311i | \(0.353047\pi\) |
−0.998083 | + | 0.0618913i | \(0.980287\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 21.3252 | − | 36.9363i | 0.681555 | − | 1.18049i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −20.0193 | −0.638516 | −0.319258 | − | 0.947668i | \(-0.603434\pi\) | ||||
−0.319258 | + | 0.947668i | \(0.603434\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 30.3714 | 0.967712 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 34.5298 | − | 59.8074i | 1.09798 | − | 1.90177i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.27853 | − | 3.94653i | −0.0723799 | − | 0.125366i | 0.827564 | − | 0.561371i | \(-0.189726\pi\) |
−0.899944 | + | 0.436006i | \(0.856393\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −10.2948 | − | 17.8311i | −0.326367 | − | 0.565284i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21.7323 | 0.688270 | 0.344135 | − | 0.938920i | \(-0.388172\pi\) | ||||
0.344135 | + | 0.938920i | \(0.388172\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 3024.2.t.l.289.7 | 22 | ||
3.2 | odd | 2 | 1008.2.t.k.961.8 | 22 | |||
4.3 | odd | 2 | 1512.2.t.d.289.7 | 22 | |||
7.4 | even | 3 | 3024.2.q.k.2881.5 | 22 | |||
9.4 | even | 3 | 3024.2.q.k.2305.5 | 22 | |||
9.5 | odd | 6 | 1008.2.q.k.625.1 | 22 | |||
12.11 | even | 2 | 504.2.t.d.457.4 | yes | 22 | ||
21.11 | odd | 6 | 1008.2.q.k.529.1 | 22 | |||
28.11 | odd | 6 | 1512.2.q.c.1369.5 | 22 | |||
36.23 | even | 6 | 504.2.q.d.121.11 | yes | 22 | ||
36.31 | odd | 6 | 1512.2.q.c.793.5 | 22 | |||
63.4 | even | 3 | inner | 3024.2.t.l.1873.7 | 22 | ||
63.32 | odd | 6 | 1008.2.t.k.193.8 | 22 | |||
84.11 | even | 6 | 504.2.q.d.25.11 | ✓ | 22 | ||
252.67 | odd | 6 | 1512.2.t.d.361.7 | 22 | |||
252.95 | even | 6 | 504.2.t.d.193.4 | yes | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.q.d.25.11 | ✓ | 22 | 84.11 | even | 6 | ||
504.2.q.d.121.11 | yes | 22 | 36.23 | even | 6 | ||
504.2.t.d.193.4 | yes | 22 | 252.95 | even | 6 | ||
504.2.t.d.457.4 | yes | 22 | 12.11 | even | 2 | ||
1008.2.q.k.529.1 | 22 | 21.11 | odd | 6 | |||
1008.2.q.k.625.1 | 22 | 9.5 | odd | 6 | |||
1008.2.t.k.193.8 | 22 | 63.32 | odd | 6 | |||
1008.2.t.k.961.8 | 22 | 3.2 | odd | 2 | |||
1512.2.q.c.793.5 | 22 | 36.31 | odd | 6 | |||
1512.2.q.c.1369.5 | 22 | 28.11 | odd | 6 | |||
1512.2.t.d.289.7 | 22 | 4.3 | odd | 2 | |||
1512.2.t.d.361.7 | 22 | 252.67 | odd | 6 | |||
3024.2.q.k.2305.5 | 22 | 9.4 | even | 3 | |||
3024.2.q.k.2881.5 | 22 | 7.4 | even | 3 | |||
3024.2.t.l.289.7 | 22 | 1.1 | even | 1 | trivial | ||
3024.2.t.l.1873.7 | 22 | 63.4 | even | 3 | inner |