Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [572,2,Mod(441,572)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(572, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("572.441");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 572 = 2^{2} \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 572.f (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.56744299562\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 21x^{6} + 136x^{4} + 309x^{2} + 225 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 441.2 | ||
Root | \(-3.32727i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 572.441 |
Dual form | 572.2.f.c.441.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/572\mathbb{Z}\right)^\times\).
\(n\) | \(287\) | \(353\) | \(365\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.32727 | −1.92100 | −0.960499 | − | 0.278284i | \(-0.910234\pi\) | ||||
−0.960499 | + | 0.278284i | \(0.910234\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.74343i | 1.22690i | 0.789734 | + | 0.613450i | \(0.210219\pi\) | ||||
−0.789734 | + | 0.613450i | \(0.789781\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 4.32727i | − | 1.63555i | −0.575536 | − | 0.817776i | \(-0.695207\pi\) | ||
0.575536 | − | 0.817776i | \(-0.304793\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 8.07070 | 2.69023 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 1.00000i | − | 0.301511i | ||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.60281 | − | 0.140622i | −0.999239 | − | 0.0390016i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 9.12812i | − | 2.35687i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.28124 | 0.553283 | 0.276642 | − | 0.960973i | \(-0.410779\pi\) | ||||
0.276642 | + | 0.960973i | \(0.410779\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.78945i | 1.32819i | 0.747648 | + | 0.664096i | \(0.231183\pi\) | ||||
−0.747648 | + | 0.664096i | \(0.768817\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 14.3980i | 3.14189i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.58384 | 0.330252 | 0.165126 | − | 0.986272i | \(-0.447197\pi\) | ||||
0.165126 | + | 0.986272i | \(0.447197\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.52641 | −0.505282 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −16.8716 | −3.24693 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.44892 | −0.269057 | −0.134528 | − | 0.990910i | \(-0.542952\pi\) | ||||
−0.134528 | + | 0.990910i | \(0.542952\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.74343i | 1.57037i | 0.619264 | + | 0.785183i | \(0.287431\pi\) | ||||
−0.619264 | + | 0.785183i | \(0.712569\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.32727i | 0.579203i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 11.8716 | 2.00666 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.39796i | 1.21622i | 0.793854 | + | 0.608109i | \(0.208072\pi\) | ||||
−0.793854 | + | 0.608109i | \(0.791928\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 11.9875 | + | 0.467888i | 1.91954 | + | 0.0749220i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.33867i | 0.677586i | 0.940861 | + | 0.338793i | \(0.110019\pi\) | ||||
−0.940861 | + | 0.338793i | \(0.889981\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.44892 | −0.525955 | −0.262977 | − | 0.964802i | \(-0.584704\pi\) | ||||
−0.262977 | + | 0.964802i | \(0.584704\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 22.1414i | 3.30064i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.65453i | 0.387203i | 0.981080 | + | 0.193602i | \(0.0620169\pi\) | ||||
−0.981080 | + | 0.193602i | \(0.937983\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −11.7252 | −1.67503 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.59031 | −1.06286 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.8009 | 1.62097 | 0.810486 | − | 0.585758i | \(-0.199203\pi\) | ||||
0.810486 | + | 0.585758i | \(0.199203\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.74343 | 0.369924 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 19.2630i | − | 2.55145i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.986729i | 0.128461i | 0.997935 | + | 0.0642306i | \(0.0204593\pi\) | ||||
−0.997935 | + | 0.0642306i | \(0.979541\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.44892 | −0.697662 | −0.348831 | − | 0.937186i | \(-0.613421\pi\) | ||||
−0.348831 | + | 0.937186i | \(0.613421\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 34.9240i | − | 4.40002i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.385788 | − | 9.88405i | 0.0478511 | − | 1.22597i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 0.180941i | − | 0.0221055i | −0.999939 | − | 0.0110527i | \(-0.996482\pi\) | ||
0.999939 | − | 0.0110527i | \(-0.00351826\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.26984 | −0.634414 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15.1281i | 1.79538i | 0.440630 | + | 0.897689i | \(0.354755\pi\) | ||||
−0.440630 | + | 0.897689i | \(0.645245\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.72523i | 0.787128i | 0.919297 | + | 0.393564i | \(0.128758\pi\) | ||||
−0.919297 | + | 0.393564i | \(0.871242\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 8.40604 | 0.970646 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.32727 | −0.493138 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.6659 | 1.42503 | 0.712515 | − | 0.701657i | \(-0.247556\pi\) | ||||
0.712515 | + | 0.701657i | \(0.247556\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 31.9240 | 3.54712 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 11.5329i | − | 1.26590i | −0.774193 | − | 0.632949i | \(-0.781844\pi\) | ||
0.774193 | − | 0.632949i | \(-0.218156\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.25844i | 0.678823i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.82093 | 0.516857 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 6.56563i | − | 0.695956i | −0.937503 | − | 0.347978i | \(-0.886868\pi\) | ||
0.937503 | − | 0.347978i | \(-0.113132\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.608510 | + | 15.5903i | −0.0637892 | + | 1.63431i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 29.0917i | − | 3.01667i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −15.8830 | −1.62956 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.25657i | 0.533724i | 0.963735 | + | 0.266862i | \(0.0859868\pi\) | ||||
−0.963735 | + | 0.266862i | \(0.914013\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 8.07070i | − | 0.811135i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.00000 | −0.597022 | −0.298511 | − | 0.954406i | \(-0.596490\pi\) | ||||
−0.298511 | + | 0.954406i | \(0.596490\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.61991 | −0.258148 | −0.129074 | − | 0.991635i | \(-0.541200\pi\) | ||||
−0.129074 | + | 0.991635i | \(0.541200\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −39.4998 | −3.85479 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.93578 | 0.283812 | 0.141906 | − | 0.989880i | \(-0.454677\pi\) | ||||
0.141906 | + | 0.989880i | \(0.454677\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 0.865080i | − | 0.0828596i | −0.999141 | − | 0.0414298i | \(-0.986809\pi\) | ||
0.999141 | − | 0.0414298i | \(-0.0131913\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 24.6150i | − | 2.33635i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.46866 | −0.702592 | −0.351296 | − | 0.936264i | \(-0.614259\pi\) | ||||
−0.351296 | + | 0.936264i | \(0.614259\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.34514i | 0.405187i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −29.0772 | − | 1.13492i | −2.68819 | − | 0.104923i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 9.87155i | − | 0.904924i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 14.4359i | − | 1.30164i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.78612i | 0.606969i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.4112 | −1.27879 | −0.639395 | − | 0.768878i | \(-0.720815\pi\) | ||||
−0.639395 | + | 0.768878i | \(0.720815\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 11.4755 | 1.01036 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.7959 | 0.943244 | 0.471622 | − | 0.881801i | \(-0.343669\pi\) | ||||
0.471622 | + | 0.881801i | \(0.343669\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 25.0525 | 2.17233 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 46.2859i | − | 3.98366i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 16.0753i | 1.37341i | 0.726938 | + | 0.686703i | \(0.240943\pi\) | ||||
−0.726938 | + | 0.686703i | \(0.759057\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.87155 | 0.328381 | 0.164190 | − | 0.986429i | \(-0.447499\pi\) | ||||
0.164190 | + | 0.986429i | \(0.447499\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 8.83233i | − | 0.743816i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.140622 | + | 3.60281i | −0.0117594 | + | 0.301282i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 3.97500i | − | 0.330106i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 39.0129 | 3.21773 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 9.49494i | − | 0.777855i | −0.921268 | − | 0.388928i | \(-0.872846\pi\) | ||
0.921268 | − | 0.388928i | \(-0.127154\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.0506i | 1.22480i | 0.790547 | + | 0.612401i | \(0.209796\pi\) | ||||
−0.790547 | + | 0.612401i | \(0.790204\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 18.4112 | 1.48846 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −23.9870 | −1.92668 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.4554 | 1.07386 | 0.536928 | − | 0.843628i | \(-0.319585\pi\) | ||||
0.536928 | + | 0.843628i | \(0.319585\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −39.2646 | −3.11388 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 6.85368i | − | 0.540145i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.56249i | 0.200710i | 0.994952 | + | 0.100355i | \(0.0319978\pi\) | ||||
−0.994952 | + | 0.100355i | \(0.968002\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −9.12812 | −0.710623 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.1855i | 0.788181i | 0.919072 | + | 0.394091i | \(0.128940\pi\) | ||||
−0.919072 | + | 0.394091i | \(0.871060\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.9605 | + | 1.01327i | 0.996958 | + | 0.0779439i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 46.7249i | 3.57314i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 19.0278 | 1.44666 | 0.723329 | − | 0.690503i | \(-0.242611\pi\) | ||||
0.723329 | + | 0.690503i | \(0.242611\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.9324i | 0.826415i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 3.28311i | − | 0.246774i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.45078 | 0.631641 | 0.315821 | − | 0.948819i | \(-0.397720\pi\) | ||||
0.315821 | + | 0.948819i | \(0.397720\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.1068 | 1.12288 | 0.561439 | − | 0.827518i | \(-0.310248\pi\) | ||||
0.561439 | + | 0.827518i | \(0.310248\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 18.1300 | 1.34021 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −20.2958 | −1.49218 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 2.28124i | − | 0.166821i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 73.0077i | 5.31053i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.8898 | −0.860312 | −0.430156 | − | 0.902754i | \(-0.641542\pi\) | ||||
−0.430156 | + | 0.902754i | \(0.641542\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 9.22510i | − | 0.664037i | −0.943273 | − | 0.332018i | \(-0.892270\pi\) | ||
0.943273 | − | 0.332018i | \(-0.107730\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.28362 | + | 32.8869i | −0.0919218 | + | 2.35508i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 17.9422i | − | 1.27833i | −0.769069 | − | 0.639166i | \(-0.779280\pi\) | ||
0.769069 | − | 0.639166i | \(-0.220720\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.70881 | 0.121135 | 0.0605673 | − | 0.998164i | \(-0.480709\pi\) | ||||
0.0605673 | + | 0.998164i | \(0.480709\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.602039i | 0.0424645i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.26984i | 0.440057i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.9028 | −0.831330 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 12.7827 | 0.888456 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.78945 | 0.400465 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.04935 | −0.554140 | −0.277070 | − | 0.960850i | \(-0.589363\pi\) | ||||
−0.277070 | + | 0.960850i | \(0.589363\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 50.3353i | − | 3.44892i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 9.46186i | − | 0.645293i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 37.8351 | 2.56842 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 22.3766i | − | 1.51207i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.21889 | − | 0.320794i | −0.552862 | − | 0.0215789i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.1775i | 1.41815i | 0.705134 | + | 0.709074i | \(0.250887\pi\) | ||||
−0.705134 | + | 0.709074i | \(0.749113\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −20.3899 | −1.35933 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.3026i | 1.08204i | 0.841009 | + | 0.541020i | \(0.181962\pi\) | ||||
−0.841009 | + | 0.541020i | \(0.818038\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.76997i | 0.183045i | 0.995803 | + | 0.0915224i | \(0.0291733\pi\) | ||||
−0.995803 | + | 0.0915224i | \(0.970827\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 14.3980 | 0.947316 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.0920 | 0.792176 | 0.396088 | − | 0.918213i | \(-0.370368\pi\) | ||||
0.396088 | + | 0.918213i | \(0.370368\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.28252 | −0.475059 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −42.1429 | −2.73748 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 2.22195i | − | 0.143726i | −0.997415 | − | 0.0718631i | \(-0.977106\pi\) | ||
0.997415 | − | 0.0718631i | \(-0.0228945\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 3.68414i | − | 0.237316i | −0.992935 | − | 0.118658i | \(-0.962141\pi\) | ||
0.992935 | − | 0.118658i | \(-0.0378593\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −55.6051 | −3.56707 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 32.1673i | − | 2.05510i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.814126 | − | 20.8583i | 0.0518016 | − | 1.32718i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 38.3730i | 2.43179i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.3405 | −0.968286 | −0.484143 | − | 0.874989i | \(-0.660869\pi\) | ||||
−0.484143 | + | 0.874989i | \(0.660869\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 1.58384i | − | 0.0995749i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 20.8235i | − | 1.30402i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.57083 | 0.472255 | 0.236128 | − | 0.971722i | \(-0.424122\pi\) | ||||
0.236128 | + | 0.971722i | \(0.424122\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 32.0129 | 1.98919 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −11.6938 | −0.723825 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −21.1806 | −1.30605 | −0.653026 | − | 0.757335i | \(-0.726501\pi\) | ||||
−0.653026 | + | 0.757335i | \(0.726501\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 32.3748i | 1.98877i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 21.8456i | 1.33693i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.69928 | −0.103607 | −0.0518033 | − | 0.998657i | \(-0.516497\pi\) | ||||
−0.0518033 | + | 0.998657i | \(0.516497\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 21.5804i | − | 1.31091i | −0.755233 | − | 0.655457i | \(-0.772476\pi\) | ||
0.755233 | − | 0.655457i | \(-0.227524\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.02467 | − | 51.8731i | 0.122539 | − | 3.13950i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.52641i | 0.152348i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.2562 | −0.616238 | −0.308119 | − | 0.951348i | \(-0.599699\pi\) | ||||
−0.308119 | + | 0.951348i | \(0.599699\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 70.5656i | 4.22465i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 19.0216i | − | 1.13473i | −0.823465 | − | 0.567367i | \(-0.807962\pi\) | ||
0.823465 | − | 0.567367i | \(-0.192038\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −30.2448 | −1.79787 | −0.898934 | − | 0.438083i | \(-0.855658\pi\) | ||||
−0.898934 | + | 0.438083i | \(0.855658\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 52.8468 | 3.13037 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 18.7746 | 1.10823 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.7959 | −0.693878 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 17.4900i | − | 1.02528i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 12.4881i | − | 0.729565i | −0.931093 | − | 0.364782i | \(-0.881143\pi\) | ||
0.931093 | − | 0.364782i | \(-0.118857\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.70702 | −0.157609 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 16.8716i | 0.978987i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.70625 | − | 0.222723i | −0.330001 | − | 0.0128804i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 14.9244i | 0.860226i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 19.9636 | 1.14688 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 14.9487i | − | 0.855961i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 15.4603i | − | 0.882367i | −0.897417 | − | 0.441184i | \(-0.854559\pi\) | ||
0.897417 | − | 0.441184i | \(-0.145441\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.71715 | 0.495901 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −27.6989 | −1.57066 | −0.785332 | − | 0.619075i | \(-0.787508\pi\) | ||||
−0.785332 | + | 0.619075i | \(0.787508\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.5841 | −0.937389 | −0.468694 | − | 0.883360i | \(-0.655275\pi\) | ||||
−0.468694 | + | 0.883360i | \(0.655275\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 95.8117 | 5.39838 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.4372i | 0.586211i | 0.956080 | + | 0.293105i | \(0.0946887\pi\) | ||||
−0.956080 | + | 0.293105i | \(0.905311\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.44892i | 0.0811237i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.76811 | −0.545202 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.2072i | 0.734866i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.10217 | + | 0.355270i | 0.504898 | + | 0.0197068i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.87835i | 0.159173i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 11.4869 | 0.633291 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 1.07877i | − | 0.0592946i | −0.999560 | − | 0.0296473i | \(-0.990562\pi\) | ||
0.999560 | − | 0.0296473i | \(-0.00943842\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 59.7067i | 3.27191i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.496399 | 0.0271212 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.1300 | −1.09655 | −0.548275 | − | 0.836298i | \(-0.684715\pi\) | ||||
−0.548275 | + | 0.836298i | \(0.684715\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 24.8502 | 1.34968 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.74343 | 0.473483 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.4473i | 1.10405i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 14.4574i | − | 0.778362i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.4489 | 0.721976 | 0.360988 | − | 0.932571i | \(-0.382440\pi\) | ||||
0.360988 | + | 0.932571i | \(0.382440\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.5822i | 1.26233i | 0.775649 | + | 0.631164i | \(0.217422\pi\) | ||||
−0.775649 | + | 0.631164i | \(0.782578\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 60.7850 | + | 2.37252i | 3.24446 | + | 0.126636i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 33.9240i | − | 1.80559i | −0.430066 | − | 0.902797i | \(-0.641510\pi\) | ||
0.430066 | − | 0.902797i | \(-0.358490\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −41.5029 | −2.20275 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 32.8453i | 1.73836i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.273169i | 0.0144173i | 0.999974 | + | 0.00720866i | \(0.00229461\pi\) | ||||
−0.999974 | + | 0.00720866i | \(0.997705\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.5177 | −0.764092 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.32727 | 0.174636 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −18.4502 | −0.965727 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −15.4915 | −0.808648 | −0.404324 | − | 0.914616i | \(-0.632493\pi\) | ||||
−0.404324 | + | 0.914616i | \(0.632493\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 35.0161i | 1.82286i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 51.0654i | − | 2.65119i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.6052 | −0.549115 | −0.274558 | − | 0.961571i | \(-0.588531\pi\) | ||||
−0.274558 | + | 0.961571i | \(0.588531\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 22.5792i | − | 1.16599i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.22016 | + | 0.203750i | 0.268852 | + | 0.0104936i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 21.6542i | − | 1.11230i | −0.831081 | − | 0.556151i | \(-0.812278\pi\) | ||
0.831081 | − | 0.556151i | \(-0.187722\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 47.9500 | 2.45655 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 10.5001i | − | 0.536532i | −0.963345 | − | 0.268266i | \(-0.913549\pi\) | ||
0.963345 | − | 0.268266i | \(-0.0864506\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 11.8716i | − | 0.605030i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −27.8351 | −1.41494 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9.98180 | −0.506097 | −0.253049 | − | 0.967454i | \(-0.581433\pi\) | ||||
−0.253049 | + | 0.967454i | \(0.581433\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.61312 | 0.182723 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −35.9209 | −1.81197 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 34.7481i | 1.74837i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.4603i | 0.775931i | 0.921674 | + | 0.387966i | \(0.126822\pi\) | ||||
−0.921674 | + | 0.387966i | \(0.873178\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −83.3563 | −4.17303 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.02281i | 0.200889i | 0.994943 | + | 0.100445i | \(0.0320266\pi\) | ||||
−0.994943 | + | 0.100445i | \(0.967973\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.22952 | − | 31.5009i | 0.0612468 | − | 1.56917i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 87.5814i | 4.35195i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.39796 | 0.366703 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 4.41123i | − | 0.218121i | −0.994035 | − | 0.109061i | \(-0.965216\pi\) | ||
0.994035 | − | 0.109061i | \(-0.0347843\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 53.4868i | − | 2.63831i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.26984 | 0.210105 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 31.6397 | 1.55313 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −12.8817 | −0.630819 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 26.2482 | 1.28231 | 0.641153 | − | 0.767413i | \(-0.278456\pi\) | ||||
0.641153 | + | 0.767413i | \(0.278456\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.2828i | 0.696100i | 0.937476 | + | 0.348050i | \(0.113156\pi\) | ||||
−0.937476 | + | 0.348050i | \(0.886844\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 21.4239i | 1.04167i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.76336 | −0.279564 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 23.5789i | 1.14106i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.467888 | − | 11.9875i | 0.0225898 | − | 0.578762i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.86822i | 0.282662i | 0.989962 | + | 0.141331i | \(0.0451382\pi\) | ||||
−0.989962 | + | 0.141331i | \(0.954862\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −29.2216 | −1.40430 | −0.702151 | − | 0.712028i | \(-0.747777\pi\) | ||||
−0.702151 | + | 0.712028i | \(0.747777\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 13.2259i | 0.634132i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9.16954i | 0.438638i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 35.0408 | 1.67240 | 0.836202 | − | 0.548421i | \(-0.184771\pi\) | ||||
0.836202 | + | 0.548421i | \(0.184771\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −94.6307 | −4.50623 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 25.5740 | 1.21506 | 0.607528 | − | 0.794298i | \(-0.292161\pi\) | ||||
0.607528 | + | 0.794298i | \(0.292161\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 18.0124 | 0.853867 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 31.5922i | 1.49426i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 30.2958i | − | 1.42975i | −0.699254 | − | 0.714873i | \(-0.746484\pi\) | ||
0.699254 | − | 0.714873i | \(-0.253516\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.33867 | 0.204300 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 50.0774i | − | 2.35284i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −42.7709 | − | 1.66941i | −2.00513 | − | 0.0782629i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 27.8929i | 1.30477i | 0.757886 | + | 0.652387i | \(0.226232\pi\) | ||||
−0.757886 | + | 0.652387i | \(0.773768\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −38.4881 | −1.79647 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19.3782i | 0.902534i | 0.892389 | + | 0.451267i | \(0.149028\pi\) | ||||
−0.892389 | + | 0.451267i | \(0.850972\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 23.6542i | − | 1.09930i | −0.835394 | − | 0.549652i | \(-0.814760\pi\) | ||
0.835394 | − | 0.549652i | \(-0.185240\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 79.8111 | 3.70115 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.34514 | −0.293618 | −0.146809 | − | 0.989165i | \(-0.546900\pi\) | ||||
−0.146809 | + | 0.989165i | \(0.546900\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.782980 | −0.0361546 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −44.7696 | −2.06288 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.44892i | 0.158581i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 14.6265i | − | 0.671111i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 95.2411 | 4.36079 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 25.5918i | 1.16932i | 0.811278 | + | 0.584661i | \(0.198772\pi\) | ||||
−0.811278 | + | 0.584661i | \(0.801228\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.04032 | − | 26.6534i | 0.0474344 | − | 1.21529i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 22.8040i | 1.03762i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −14.4210 | −0.654825 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 21.2202i | 0.961577i | 0.876836 | + | 0.480789i | \(0.159650\pi\) | ||||
−0.876836 | + | 0.480789i | \(0.840350\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 8.52608i | − | 0.385563i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 32.6811 | 1.47488 | 0.737438 | − | 0.675415i | \(-0.236035\pi\) | ||||
0.737438 | + | 0.675415i | \(0.236035\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.30533 | −0.148865 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 22.1414 | 0.995182 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 65.4634 | 2.93643 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.7466i | 0.660147i | 0.943955 | + | 0.330074i | \(0.107074\pi\) | ||||
−0.943955 | + | 0.330074i | \(0.892926\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 33.8900i | − | 1.51409i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 34.7731 | 1.55046 | 0.775228 | − | 0.631681i | \(-0.217635\pi\) | ||||
0.775228 | + | 0.631681i | \(0.217635\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 16.4606i | − | 0.732486i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −43.1229 | − | 3.37142i | −1.91515 | − | 0.149730i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 24.4637i | − | 1.08434i | −0.840270 | − | 0.542168i | \(-0.817604\pi\) | ||
0.840270 | − | 0.542168i | \(-0.182396\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 29.1018 | 1.28739 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 97.6770i | − | 4.31255i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 7.18755i | − | 0.316721i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.65453 | 0.116746 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −63.3106 | −2.77903 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.70881 | 0.381540 | 0.190770 | − | 0.981635i | \(-0.438902\pi\) | ||||
0.190770 | + | 0.981635i | \(0.438902\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −33.1531 | −1.44968 | −0.724841 | − | 0.688916i | \(-0.758087\pi\) | ||||
−0.724841 | + | 0.688916i | \(0.758087\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 36.3752i | − | 1.58754i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 19.9459i | 0.868857i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.4915 | −0.890933 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.96359i | 0.345591i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.610114 | − | 15.6314i | 0.0264270 | − | 0.677071i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.05410i | 0.348209i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −28.1180 | −1.21338 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 11.7252i | 0.505041i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 30.3782i | 1.30606i | 0.757333 | + | 0.653029i | \(0.226502\pi\) | ||||
−0.757333 | + | 0.653029i | \(0.773498\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −50.2643 | −2.15705 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.37329 | 0.101660 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.89809 | −0.423212 | −0.211606 | − | 0.977355i | \(-0.567869\pi\) | ||||
−0.211606 | + | 0.977355i | \(0.567869\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −43.9765 | −1.87687 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 8.38842i | − | 0.357359i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 54.8089i | − | 2.33071i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 67.5295 | 2.86647 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 19.0197i | − | 0.805892i | −0.915224 | − | 0.402946i | \(-0.867986\pi\) | ||
0.915224 | − | 0.402946i | \(-0.132014\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.4258 | + | 0.484995i | 0.525554 | + | 0.0205131i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.59031i | 0.320463i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 38.5239 | 1.62359 | 0.811794 | − | 0.583944i | \(-0.198491\pi\) | ||||
0.811794 | + | 0.583944i | \(0.198491\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 20.4897i | − | 0.862010i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 138.144i | − | 5.80149i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18.8323 | 0.789492 | 0.394746 | − | 0.918790i | \(-0.370833\pi\) | ||||
0.394746 | + | 0.918790i | \(0.370833\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24.2334 | 1.01414 | 0.507069 | − | 0.861906i | \(-0.330729\pi\) | ||||
0.507069 | + | 0.861906i | \(0.330729\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 39.5604 | 1.65266 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.00142 | −0.166871 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 31.4473i | − | 1.30917i | −0.755989 | − | 0.654584i | \(-0.772844\pi\) | ||
0.755989 | − | 0.654584i | \(-0.227156\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 30.6943i | 1.27561i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −49.9058 | −2.07044 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 11.8009i | − | 0.488742i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.11357 | − | 79.7712i | 0.128730 | − | 3.29813i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 42.8880i | − | 1.77018i | −0.465424 | − | 0.885088i | \(-0.654098\pi\) | ||
0.465424 | − | 0.885088i | \(-0.345902\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −50.6197 | −2.08575 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 59.6986i | 2.45567i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.10678i | 0.332905i | 0.986049 | + | 0.166453i | \(0.0532313\pi\) | ||||
−0.986049 | + | 0.166453i | \(0.946769\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 27.0819 | 1.11025 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.68568 | −0.232699 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 14.4554 | 0.590631 | 0.295316 | − | 0.955400i | \(-0.404575\pi\) | ||||
0.295316 | + | 0.955400i | \(0.404575\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 29.7203 | 1.21232 | 0.606158 | − | 0.795344i | \(-0.292710\pi\) | ||||
0.606158 | + | 0.795344i | \(0.292710\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 1.46032i | − | 0.0594688i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 2.74343i | − | 0.111536i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.67094 | 0.392532 | 0.196266 | − | 0.980551i | \(-0.437118\pi\) | ||||
0.196266 | + | 0.980551i | \(0.437118\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 20.8614i | − | 0.845348i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.373286 | − | 9.56377i | 0.0151015 | − | 0.386909i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 1.72395i | − | 0.0696297i | −0.999394 | − | 0.0348149i | \(-0.988916\pi\) | ||
0.999394 | − | 0.0348149i | \(-0.0110842\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 39.6039 | 1.59698 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.0886i | 0.446409i | 0.974772 | + | 0.223205i | \(0.0716518\pi\) | ||||
−0.974772 | + | 0.223205i | \(0.928348\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 26.6577i | − | 1.07146i | −0.844389 | − | 0.535731i | \(-0.820036\pi\) | ||
0.844389 | − | 0.535731i | \(-0.179964\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −26.7218 | −1.07231 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −28.4112 | −1.13827 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.2493 | −1.24997 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −19.2630 | −0.769292 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 16.8766i | 0.672913i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 0.371683i | − | 0.0147965i | −0.999973 | − | 0.00739823i | \(-0.997645\pi\) | ||
0.999973 | − | 0.00739823i | \(-0.00235495\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 26.7823 | 1.06450 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 39.5362i | − | 1.56895i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 42.2437 | + | 1.64883i | 1.67376 | + | 0.0653290i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 122.094i | 4.82998i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 19.3671 | 0.764954 | 0.382477 | − | 0.923965i | \(-0.375071\pi\) | ||||
0.382477 | + | 0.923965i | \(0.375071\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.4242i | 0.489964i | 0.969528 | + | 0.244982i | \(0.0787821\pi\) | ||||
−0.969528 | + | 0.244982i | \(0.921218\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 31.4821i | 1.23961i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.10678 | 0.122140 | 0.0610700 | − | 0.998133i | \(-0.480549\pi\) | ||||
0.0610700 | + | 0.998133i | \(0.480549\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.986729 | 0.0387325 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −125.888 | −4.93392 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8.47732 | 0.331743 | 0.165872 | − | 0.986147i | \(-0.446956\pi\) | ||||
0.165872 | + | 0.986147i | \(0.446956\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 29.6179i | 1.15727i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 54.2773i | 2.11756i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14.3239 | −0.557981 | −0.278991 | − | 0.960294i | \(-0.590000\pi\) | ||||
−0.278991 | + | 0.960294i | \(0.590000\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 32.8620i | 1.27818i | 0.769130 | + | 0.639092i | \(0.220690\pi\) | ||||
−0.769130 | + | 0.639092i | \(0.779310\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 27.3464 | + | 1.06737i | 1.06205 | + | 0.0414531i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 68.7298i | 2.66523i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.29484 | −0.0888567 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 70.4631i | − | 2.72426i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.44892i | 0.210353i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22.6561 | −0.873327 | −0.436664 | − | 0.899625i | \(-0.643840\pi\) | ||||
−0.436664 | + | 0.899625i | \(0.643840\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 42.6245 | 1.64062 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −30.7694 | −1.18256 | −0.591282 | − | 0.806465i | \(-0.701378\pi\) | ||||
−0.591282 | + | 0.806465i | \(0.701378\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 22.7466 | 0.872933 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 54.2430i | − | 2.07860i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 49.0886i | 1.87832i | 0.343477 | + | 0.939161i | \(0.388395\pi\) | ||||
−0.343477 | + | 0.939161i | \(0.611605\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −44.1015 | −1.68503 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 9.21643i | − | 0.351629i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −42.5162 | − | 1.65946i | −1.61974 | − | 0.0632205i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 25.6542i | − | 0.975932i | −0.872863 | − | 0.487966i | \(-0.837739\pi\) | ||
0.872863 | − | 0.487966i | \(-0.162261\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −34.9240 | −1.32665 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 10.6213i | 0.402890i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.89757i | 0.374897i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −40.2334 | −1.52177 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16.0784 | 0.607274 | 0.303637 | − | 0.952788i | \(-0.401799\pi\) | ||||
0.303637 | + | 0.952788i | \(0.401799\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −42.8301 | −1.61537 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 24.2309 | 0.912588 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 25.9636i | 0.976461i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 33.2066i | − | 1.24710i | −0.781784 | − | 0.623549i | \(-0.785690\pi\) | ||
0.781784 | − | 0.623549i | \(-0.214310\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 102.223 | 3.83366 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 13.8482i | 0.518617i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.88405 | − | 0.385788i | −0.369643 | − | 0.0144276i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7.39303i | 0.276098i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −20.4508 | −0.762685 | −0.381343 | − | 0.924434i | \(-0.624538\pi\) | ||||
−0.381343 | + | 0.924434i | \(0.624538\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.3371i | 0.422214i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 12.2581i | 0.455884i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.66055 | 0.135950 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 37.5968 | 1.39439 | 0.697194 | − | 0.716883i | \(-0.254432\pi\) | ||||
0.697194 | + | 0.716883i | \(0.254432\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 89.2409 | 3.30522 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.86782 | −0.291002 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 25.9305i | 0.957765i | 0.877879 | + | 0.478883i | \(0.158958\pi\) | ||||
−0.877879 | + | 0.478883i | \(0.841042\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 107.029i | 3.94783i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.180941 | −0.00666505 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.1760i | 0.521473i | 0.965410 | + | 0.260736i | \(0.0839654\pi\) | ||||
−0.965410 | + | 0.260736i | \(0.916035\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.70881 | + | 69.4010i | −0.0995108 | + | 2.54951i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 39.1328i | 1.43564i | 0.696227 | + | 0.717822i | \(0.254861\pi\) | ||||
−0.696227 | + | 0.717822i | \(0.745139\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 26.0487 | 0.954350 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 93.0784i | − | 3.40556i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 12.7039i | − | 0.464190i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.4585 | 0.454618 | 0.227309 | − | 0.973823i | \(-0.427007\pi\) | ||||
0.227309 | + | 0.973823i | \(0.427007\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 51.0420 | 1.86008 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −41.2903 | −1.50271 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 35.1460 | 1.27740 | 0.638701 | − | 0.769455i | \(-0.279472\pi\) | ||||
0.638701 | + | 0.769455i | \(0.279472\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.26984i | 0.191283i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 41.7626i | − | 1.51389i | −0.653477 | − | 0.756946i | \(-0.726690\pi\) | ||
0.653477 | − | 0.756946i | \(-0.273310\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.74343 | −0.135521 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 50.5099i | 1.82619i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.138756 | − | 3.55500i | 0.00501020 | − | 0.128363i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 33.8407i | 1.22033i | 0.792276 | + | 0.610163i | \(0.208896\pi\) | ||||
−0.792276 | + | 0.610163i | \(0.791104\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −25.1902 | −0.907201 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 13.3584i | − | 0.480469i | −0.970715 | − | 0.240234i | \(-0.922776\pi\) | ||
0.970715 | − | 0.240234i | \(-0.0772243\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 22.0895i | − | 0.793478i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −106.516 | −3.82122 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −25.1185 | −0.899964 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.1281 | 0.541327 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 24.4454 | 0.873609 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 36.9139i | 1.31751i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 45.4424i | − | 1.61985i | −0.586536 | − | 0.809923i | \(-0.699509\pi\) | ||
0.586536 | − | 0.809923i | \(-0.300491\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 70.4735 | 2.50892 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 32.3189i | 1.14913i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 19.6314 | + | 0.766239i | 0.697131 | + | 0.0272100i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 107.720i | − | 3.82042i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −56.1445 | −1.98874 | −0.994371 | − | 0.105957i | \(-0.966209\pi\) | ||||
−0.994371 | + | 0.105957i | \(0.966209\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.05563i | 0.214233i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 52.9892i | − | 1.87228i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.72523 | 0.237328 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 18.8026 | 0.662704 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.65394 | 0.199028 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8.75323 | 0.307747 | 0.153874 | − | 0.988091i | \(-0.450825\pi\) | ||||
0.153874 | + | 0.988091i | \(0.450825\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 12.5850i | − | 0.441921i | −0.975283 | − | 0.220960i | \(-0.929081\pi\) | ||
0.975283 | − | 0.220960i | \(-0.0709191\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 71.8036i | 2.51826i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.03001 | −0.246251 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 19.9673i | − | 0.698568i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.91110 | + | 125.825i | −0.171608 | + | 4.39667i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 1.41251i | − | 0.0492969i | −0.999696 | − | 0.0246484i | \(-0.992153\pi\) | ||
0.999696 | − | 0.0246484i | \(-0.00784664\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.30413 | 0.184890 | 0.0924452 | − | 0.995718i | \(-0.470532\pi\) | ||||
0.0924452 | + | 0.995718i | \(0.470532\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 8.40604i | − | 0.292661i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 28.2994i | 0.984066i | 0.870577 | + | 0.492033i | \(0.163746\pi\) | ||||
−0.870577 | + | 0.492033i | \(0.836254\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.61319 | −0.299148 | −0.149574 | − | 0.988750i | \(-0.547790\pi\) | ||||
−0.149574 | + | 0.988750i | \(0.547790\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 34.1252 | 1.18379 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −26.7481 | −0.926767 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −27.9433 | −0.967019 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 147.515i | − | 5.09887i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 27.3745i | 0.945073i | 0.881311 | + | 0.472536i | \(0.156661\pi\) | ||||
−0.881311 | + | 0.472536i | \(0.843339\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.9006 | −0.927608 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 63.2899i | 2.17982i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.77984 | + | 35.5561i | −0.0956293 | + | 1.22317i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.32727i | 0.148687i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 100.633 | 3.45370 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.7172i | 0.401659i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 39.2940i | 1.34540i | 0.739915 | + | 0.672700i | \(0.234866\pi\) | ||||
−0.739915 | + | 0.672700i | \(0.765134\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −128.187 | −4.38389 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −32.9601 | −1.12590 | −0.562948 | − | 0.826492i | \(-0.690333\pi\) | ||||
−0.562948 | + | 0.826492i | \(0.690333\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.21241 | 0.177845 | 0.0889227 | − | 0.996039i | \(-0.471658\pi\) | ||||
0.0889227 | + | 0.996039i | \(0.471658\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −62.4680 | −2.12890 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 26.8614i | − | 0.914373i | −0.889371 | − | 0.457187i | \(-0.848857\pi\) | ||
0.889371 | − | 0.457187i | \(-0.151143\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 52.2015i | 1.77490i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 39.2482 | 1.33294 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 12.6659i | − | 0.429662i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.0254443 | + | 0.651896i | −0.000862149 | + | 0.0220886i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 42.4242i | 1.43584i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 29.3654 | 0.992730 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 5.04288i | − | 0.170286i | −0.996369 | − | 0.0851430i | \(-0.972865\pi\) | ||
0.996369 | − | 0.0851430i | \(-0.0271347\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 41.5513i | 1.40149i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.12666 | −0.105340 | −0.0526699 | − | 0.998612i | \(-0.516773\pi\) | ||||
−0.0526699 | + | 0.998612i | \(0.516773\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 35.8602 | 1.20679 | 0.603396 | − | 0.797441i | \(-0.293814\pi\) | ||||
0.603396 | + | 0.797441i | \(0.293814\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 9.00699 | 0.302767 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 36.0572 | 1.21068 | 0.605341 | − | 0.795966i | \(-0.293037\pi\) | ||||
0.605341 | + | 0.795966i | \(0.293037\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 62.3612i | 2.09153i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 31.9240i | − | 1.06950i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −15.3683 | −0.514280 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 23.1841i | 0.774960i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 18.9862 | + | 0.741057i | 0.633932 | + | 0.0247432i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 12.6685i | − | 0.422518i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 26.9206 | 0.896857 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 49.6573i | − | 1.65249i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 41.4444i | 1.37766i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.35007 | −0.210851 | −0.105425 | − | 0.994427i | \(-0.533620\pi\) | ||||
−0.105425 | + | 0.994427i | \(0.533620\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −48.4242 | −1.60613 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 19.7382 | 0.653957 | 0.326978 | − | 0.945032i | \(-0.393970\pi\) | ||||
0.326978 | + | 0.945032i | \(0.393970\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.5329 | −0.381683 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 49.7384i | 1.64430i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 46.7168i | − | 1.54273i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.90950 | 0.194936 | 0.0974682 | − | 0.995239i | \(-0.468926\pi\) | ||||
0.0974682 | + | 0.995239i | \(0.468926\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 51.4406i | 1.69503i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.12735 | − | 54.5037i | 0.0700226 | − | 1.79401i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 18.6903i | − | 0.614533i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −21.1445 | −0.694478 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 12.4502i | − | 0.408478i | −0.978921 | − | 0.204239i | \(-0.934528\pi\) | ||
0.978921 | − | 0.204239i | \(-0.0654719\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 67.8826i | − | 2.22476i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 92.1618 | 3.01724 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.25844 | 0.204673 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 43.5289 | 1.42203 | 0.711014 | − | 0.703178i | \(-0.248236\pi\) | ||||
0.711014 | + | 0.703178i | \(0.248236\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 55.1797 | 1.80072 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 28.4896i | − | 0.928734i | −0.885643 | − | 0.464367i | \(-0.846282\pi\) | ||
0.885643 | − | 0.464367i | \(-0.153718\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.87174i | 0.223775i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −200.291 | −6.51548 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 18.4773i | 0.600432i | 0.953871 | + | 0.300216i | \(0.0970588\pi\) | ||||
−0.953871 | + | 0.300216i | \(0.902941\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.945717 | − | 24.2297i | 0.0306993 | − | 0.786529i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 34.7273i | − | 1.12611i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 26.6384 | 0.862902 | 0.431451 | − | 0.902136i | \(-0.358002\pi\) | ||||
0.431451 | + | 0.902136i | \(0.358002\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 32.6187i | − | 1.05552i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 4.82093i | − | 0.155838i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 69.5621 | 2.24628 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −45.4476 | −1.46605 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 23.6938 | 0.763521 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 25.3084 | 0.814706 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 38.4455i | − | 1.23632i | −0.786050 | − | 0.618162i | \(-0.787877\pi\) | ||
0.786050 | − | 0.618162i | \(-0.212123\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 43.9437i | − | 1.41168i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14.1887 | −0.455337 | −0.227668 | − | 0.973739i | \(-0.573110\pi\) | ||||
−0.227668 | + | 0.973739i | \(0.573110\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 16.7532i | − | 0.537084i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −30.2853 | − | 1.18208i | −0.969907 | − | 0.0378567i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 20.7298i | 0.663206i | 0.943419 | + | 0.331603i | \(0.107589\pi\) | ||||
−0.943419 | + | 0.331603i | \(0.892411\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.56563 | −0.209839 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 6.98180i | − | 0.222912i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 15.7333i | 0.501814i | 0.968011 | + | 0.250907i | \(0.0807289\pi\) | ||||
−0.968011 | + | 0.250907i | \(0.919271\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 49.2233 | 1.56838 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −38.2198 | −1.21655 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.46251 | −0.173698 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.1754 | 0.545595 | 0.272798 | − | 0.962071i | \(-0.412051\pi\) | ||||
0.272798 | + | 0.962071i | \(0.412051\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.58936i | 0.113905i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.68801i | 0.148620i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.6511 | −0.559015 | −0.279507 | − | 0.960144i | \(-0.590171\pi\) | ||||
−0.279507 | + | 0.960144i | \(0.590171\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 124.815i | − | 3.94897i |
(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 | 572.2.f.c.441.2 | yes | 8 | |
3.2 | odd | 2 | 5148.2.e.c.1585.3 | 8 | |||
4.3 | odd | 2 | 2288.2.j.i.1585.8 | 8 | |||
13.5 | odd | 4 | 7436.2.a.p.1.1 | 4 | |||
13.8 | odd | 4 | 7436.2.a.o.1.1 | 4 | |||
13.12 | even | 2 | inner | 572.2.f.c.441.1 | ✓ | 8 | |
39.38 | odd | 2 | 5148.2.e.c.1585.6 | 8 | |||
52.51 | odd | 2 | 2288.2.j.i.1585.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
572.2.f.c.441.1 | ✓ | 8 | 13.12 | even | 2 | inner | |
572.2.f.c.441.2 | yes | 8 | 1.1 | even | 1 | trivial | |
2288.2.j.i.1585.7 | 8 | 52.51 | odd | 2 | |||
2288.2.j.i.1585.8 | 8 | 4.3 | odd | 2 | |||
5148.2.e.c.1585.3 | 8 | 3.2 | odd | 2 | |||
5148.2.e.c.1585.6 | 8 | 39.38 | odd | 2 | |||
7436.2.a.o.1.1 | 4 | 13.8 | odd | 4 | |||
7436.2.a.p.1.1 | 4 | 13.5 | odd | 4 |