Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [600,3,Mod(449,600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(600, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("600.449");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 600 = 2^{3} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 600.c (of order \(2\), degree \(1\), 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: | \(16.3488158616\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 138x^{12} + 3393x^{8} + 15208x^{4} + 1296 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{37}]\) |
Coefficient ring index: | \( 2^{26}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 120) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 449.8 | ||
Root | \(0.383916 - 0.383916i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 600.449 |
Dual form | 600.3.c.d.449.7 |
$q$-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 \(\left(\mathbb{Z}/600\mathbb{Z}\right)^\times\).
\(n\) | \(151\) | \(301\) | \(401\) | \(577\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | −0.323191 | + | 2.98254i | −0.107730 | + | 0.994180i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 4.72640i | − | 0.675201i | −0.941290 | − | 0.337600i | \(-0.890385\pi\) | ||
0.941290 | − | 0.337600i | \(-0.109615\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −8.79110 | − | 1.92786i | −0.976788 | − | 0.214207i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 4.76442i | − | 0.433129i | −0.976268 | − | 0.216565i | \(-0.930515\pi\) | ||
0.976268 | − | 0.216565i | \(-0.0694852\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.06692i | − | 0.0820707i | −0.999158 | − | 0.0410354i | \(-0.986934\pi\) | ||
0.999158 | − | 0.0410354i | \(-0.0130656\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 26.7847 | 1.57557 | 0.787785 | − | 0.615950i | \(-0.211228\pi\) | ||||
0.787785 | + | 0.615950i | \(0.211228\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.12938 | 0.427862 | 0.213931 | − | 0.976849i | \(-0.431373\pi\) | ||||
0.213931 | + | 0.976849i | \(0.431373\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 14.0967 | + | 1.52753i | 0.671271 | + | 0.0727395i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 40.0468 | 1.74117 | 0.870583 | − | 0.492021i | \(-0.163742\pi\) | ||||
0.870583 | + | 0.492021i | \(0.163742\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 8.59112 | − | 25.5967i | 0.318190 | − | 0.948027i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 20.8744i | − | 0.719807i | −0.932990 | − | 0.359903i | \(-0.882810\pi\) | ||
0.932990 | − | 0.359903i | \(-0.117190\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −33.7860 | −1.08987 | −0.544936 | − | 0.838478i | \(-0.683446\pi\) | ||||
−0.544936 | + | 0.838478i | \(0.683446\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 14.2101 | + | 1.53982i | 0.430608 | + | 0.0466611i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 60.4351i | 1.63338i | 0.577075 | + | 0.816691i | \(0.304194\pi\) | ||||
−0.577075 | + | 0.816691i | \(0.695806\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.18213 | + | 0.344819i | 0.0815931 | + | 0.00884150i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 59.2611i | 1.44539i | 0.691166 | + | 0.722696i | \(0.257097\pi\) | ||||
−0.691166 | + | 0.722696i | \(0.742903\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 56.4424i | − | 1.31261i | −0.754494 | − | 0.656307i | \(-0.772117\pi\) | ||
0.754494 | − | 0.656307i | \(-0.227883\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.68942 | −0.206158 | −0.103079 | − | 0.994673i | \(-0.532869\pi\) | ||||
−0.103079 | + | 0.994673i | \(0.532869\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 26.6611 | 0.544104 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.65657 | + | 79.8864i | −0.169737 | + | 1.56640i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 93.1378 | 1.75732 | 0.878659 | − | 0.477451i | \(-0.158439\pi\) | ||||
0.878659 | + | 0.477451i | \(0.158439\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.62734 | + | 24.2462i | −0.0460937 | + | 0.425372i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 17.4907i | − | 0.296453i | −0.988953 | − | 0.148227i | \(-0.952643\pi\) | ||
0.988953 | − | 0.148227i | \(-0.0473565\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 57.7400 | 0.946558 | 0.473279 | − | 0.880913i | \(-0.343070\pi\) | ||||
0.473279 | + | 0.880913i | \(0.343070\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −9.11184 | + | 41.5503i | −0.144632 | + | 0.659528i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 101.531i | − | 1.51539i | −0.652609 | − | 0.757695i | \(-0.726325\pi\) | ||
0.652609 | − | 0.757695i | \(-0.273675\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −12.9428 | + | 119.441i | −0.187576 | + | 1.73103i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 90.1745i | 1.27006i | 0.772486 | + | 0.635032i | \(0.219013\pi\) | ||||
−0.772486 | + | 0.635032i | \(0.780987\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 40.0700i | 0.548904i | 0.961601 | + | 0.274452i | \(0.0884965\pi\) | ||||
−0.961601 | + | 0.274452i | \(0.911504\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −22.5186 | −0.292449 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −65.3727 | −0.827502 | −0.413751 | − | 0.910390i | \(-0.635782\pi\) | ||||
−0.413751 | + | 0.910390i | \(0.635782\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 73.5667 | + | 33.8960i | 0.908231 | + | 0.418469i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 117.888 | 1.42033 | 0.710166 | − | 0.704034i | \(-0.248620\pi\) | ||||
0.710166 | + | 0.704034i | \(0.248620\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 62.2587 | + | 6.74641i | 0.715618 | + | 0.0775450i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 119.679i | − | 1.34471i | −0.740228 | − | 0.672356i | \(-0.765282\pi\) | ||
0.740228 | − | 0.672356i | \(-0.234718\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.04269 | −0.0554142 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 10.9193 | − | 100.768i | 0.117412 | − | 1.08353i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.2522i | 0.157239i | 0.996905 | + | 0.0786196i | \(0.0250513\pi\) | ||||
−0.996905 | + | 0.0786196i | \(0.974949\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −9.18513 | + | 41.8845i | −0.0927791 | + | 0.423075i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 72.0047i | − | 0.712918i | −0.934311 | − | 0.356459i | \(-0.883984\pi\) | ||
0.934311 | − | 0.356459i | \(-0.116016\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 110.950i | 1.07718i | 0.842567 | + | 0.538591i | \(0.181043\pi\) | ||||
−0.842567 | + | 0.538591i | \(0.818957\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −30.6020 | −0.286000 | −0.143000 | − | 0.989723i | \(-0.545675\pi\) | ||||
−0.143000 | + | 0.989723i | \(0.545675\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.3694 | 0.159353 | 0.0796763 | − | 0.996821i | \(-0.474611\pi\) | ||||
0.0796763 | + | 0.996821i | \(0.474611\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −180.250 | − | 19.5321i | −1.62388 | − | 0.175965i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.71526 | −0.0417280 | −0.0208640 | − | 0.999782i | \(-0.506642\pi\) | ||||
−0.0208640 | + | 0.999782i | \(0.506642\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.05687 | + | 9.37939i | −0.0175801 | + | 0.0801657i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 126.595i | − | 1.06383i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 98.3003 | 0.812399 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −176.749 | − | 19.1526i | −1.43698 | − | 0.155712i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.39528i | 0.0109865i | 0.999985 | + | 0.00549325i | \(0.00174856\pi\) | ||||
−0.999985 | + | 0.00549325i | \(0.998251\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 168.342 | + | 18.2417i | 1.30498 | + | 0.141408i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 226.220i | − | 1.72687i | −0.504460 | − | 0.863435i | \(-0.668308\pi\) | ||
0.504460 | − | 0.863435i | \(-0.331692\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 38.4227i | − | 0.288893i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 76.2589 | 0.556634 | 0.278317 | − | 0.960489i | \(-0.410223\pi\) | ||||
0.278317 | + | 0.960489i | \(0.410223\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −127.660 | −0.918417 | −0.459208 | − | 0.888329i | \(-0.651867\pi\) | ||||
−0.459208 | + | 0.888329i | \(0.651867\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.13153 | − | 28.8991i | 0.0222094 | − | 0.204958i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.08325 | −0.0355472 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −8.61662 | + | 79.5178i | −0.0586165 | + | 0.540938i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 63.3790i | − | 0.425362i | −0.977122 | − | 0.212681i | \(-0.931780\pi\) | ||
0.977122 | − | 0.212681i | \(-0.0682195\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −115.233 | −0.763134 | −0.381567 | − | 0.924341i | \(-0.624615\pi\) | ||||
−0.381567 | + | 0.924341i | \(0.624615\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −235.467 | − | 51.6371i | −1.53900 | − | 0.337498i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.3695i | 0.117003i | 0.998287 | + | 0.0585017i | \(0.0186323\pi\) | ||||
−0.998287 | + | 0.0585017i | \(0.981368\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −30.1013 | + | 277.787i | −0.189316 | + | 1.74709i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 189.278i | − | 1.17564i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 163.693i | − | 1.00425i | −0.864794 | − | 0.502126i | \(-0.832551\pi\) | ||
0.864794 | − | 0.502126i | \(-0.167449\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 48.7025 | 0.291632 | 0.145816 | − | 0.989312i | \(-0.453419\pi\) | ||||
0.145816 | + | 0.989312i | \(0.453419\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 167.862 | 0.993264 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −71.4662 | − | 15.6723i | −0.417931 | − | 0.0916509i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −140.785 | −0.813787 | −0.406894 | − | 0.913476i | \(-0.633388\pi\) | ||||
−0.406894 | + | 0.913476i | \(0.633388\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 52.1669 | + | 5.65285i | 0.294728 | + | 0.0319370i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 11.1350i | − | 0.0622065i | −0.999516 | − | 0.0311033i | \(-0.990098\pi\) | ||
0.999516 | − | 0.0311033i | \(-0.00990207\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −150.235 | −0.830028 | −0.415014 | − | 0.909815i | \(-0.636223\pi\) | ||||
−0.415014 | + | 0.909815i | \(0.636223\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −18.6610 | + | 172.212i | −0.101973 | + | 0.941049i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 127.614i | − | 0.682425i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −120.981 | − | 40.6051i | −0.640108 | − | 0.214842i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 168.060i | − | 0.879895i | −0.898023 | − | 0.439948i | \(-0.854997\pi\) | ||
0.898023 | − | 0.439948i | \(-0.145003\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 312.926i | 1.62138i | 0.585479 | + | 0.810688i | \(0.300907\pi\) | ||||
−0.585479 | + | 0.810688i | \(0.699093\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −166.150 | −0.843400 | −0.421700 | − | 0.906735i | \(-0.638566\pi\) | ||||
−0.421700 | + | 0.906735i | \(0.638566\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 105.535 | 0.530327 | 0.265163 | − | 0.964204i | \(-0.414574\pi\) | ||||
0.265163 | + | 0.964204i | \(0.414574\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 302.821 | + | 32.8139i | 1.50657 | + | 0.163253i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −98.6608 | −0.486014 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −352.056 | − | 77.2046i | −1.70075 | − | 0.372969i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 38.7318i | − | 0.185320i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 283.373 | 1.34300 | 0.671500 | − | 0.741004i | \(-0.265650\pi\) | ||||
0.671500 | + | 0.741004i | \(0.265650\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −268.949 | − | 29.1436i | −1.26267 | − | 0.136824i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 159.686i | 0.735882i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −119.510 | − | 12.9503i | −0.545710 | − | 0.0591336i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 28.5771i | − | 0.129308i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 100.108i | − | 0.448915i | −0.974484 | − | 0.224458i | \(-0.927939\pi\) | ||
0.974484 | − | 0.224458i | \(-0.0720610\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −239.794 | −1.05636 | −0.528181 | − | 0.849132i | \(-0.677126\pi\) | ||||
−0.528181 | + | 0.849132i | \(0.677126\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −393.036 | −1.71632 | −0.858158 | − | 0.513386i | \(-0.828391\pi\) | ||||
−0.858158 | + | 0.513386i | \(0.828391\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7.27779 | − | 67.1626i | 0.0315056 | − | 0.290747i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 278.691 | 1.19610 | 0.598050 | − | 0.801459i | \(-0.295942\pi\) | ||||
0.598050 | + | 0.801459i | \(0.295942\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 21.1278 | − | 194.977i | 0.0891470 | − | 0.822686i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 196.594i | − | 0.822570i | −0.911507 | − | 0.411285i | \(-0.865080\pi\) | ||
0.911507 | − | 0.411285i | \(-0.134920\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −231.153 | −0.959139 | −0.479570 | − | 0.877504i | \(-0.659207\pi\) | ||||
−0.479570 | + | 0.877504i | \(0.659207\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −124.872 | + | 208.461i | −0.513877 | + | 0.857864i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 8.67340i | − | 0.0351150i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −38.1002 | + | 351.604i | −0.153013 | + | 1.41207i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 243.442i | 0.969887i | 0.874545 | + | 0.484944i | \(0.161160\pi\) | ||||
−0.874545 | + | 0.484944i | \(0.838840\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 190.800i | − | 0.754150i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −358.482 | −1.39487 | −0.697437 | − | 0.716646i | \(-0.745676\pi\) | ||||
−0.697437 | + | 0.716646i | \(0.745676\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 285.641 | 1.10286 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −40.2429 | + | 183.509i | −0.154187 | + | 0.703099i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −330.913 | −1.25823 | −0.629113 | − | 0.777314i | \(-0.716582\pi\) | ||||
−0.629113 | + | 0.777314i | \(0.716582\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 356.949 | + | 38.6793i | 1.33689 | + | 0.144866i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 97.0354i | 0.360727i | 0.983600 | + | 0.180363i | \(0.0577273\pi\) | ||||
−0.983600 | + | 0.180363i | \(0.942273\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 67.1851 | 0.247915 | 0.123958 | − | 0.992288i | \(-0.460441\pi\) | ||||
0.123958 | + | 0.992288i | \(0.460441\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.62975 | − | 15.0400i | 0.00596979 | − | 0.0550917i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 361.801i | 1.30614i | 0.757298 | + | 0.653070i | \(0.226519\pi\) | ||||
−0.757298 | + | 0.653070i | \(0.773481\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 297.016 | + | 65.1347i | 1.06457 | + | 0.233458i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 288.193i | − | 1.02560i | −0.858509 | − | 0.512798i | \(-0.828609\pi\) | ||
0.858509 | − | 0.512798i | \(-0.171391\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 272.474i | − | 0.962805i | −0.876500 | − | 0.481402i | \(-0.840128\pi\) | ||
0.876500 | − | 0.481402i | \(-0.159872\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 280.092 | 0.975930 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 428.420 | 1.48242 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −45.4903 | − | 4.92937i | −0.156324 | − | 0.0169394i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 70.5674 | 0.240845 | 0.120422 | − | 0.992723i | \(-0.461575\pi\) | ||||
0.120422 | + | 0.992723i | \(0.461575\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −121.954 | − | 40.9317i | −0.410618 | − | 0.137817i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 42.7267i | − | 0.142899i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −266.770 | −0.886278 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 214.757 | + | 23.2713i | 0.708769 | + | 0.0768028i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 124.274i | 0.404801i | 0.979303 | + | 0.202401i | \(0.0648744\pi\) | ||||
−0.979303 | + | 0.202401i | \(0.935126\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −330.912 | − | 35.8580i | −1.07091 | − | 0.116045i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 229.006i | 0.736353i | 0.929756 | + | 0.368176i | \(0.120018\pi\) | ||||
−0.929756 | + | 0.368176i | \(0.879982\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 465.490i | 1.48719i | 0.668631 | + | 0.743594i | \(0.266880\pi\) | ||||
−0.668631 | + | 0.743594i | \(0.733120\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 405.458 | 1.27905 | 0.639524 | − | 0.768771i | \(-0.279131\pi\) | ||||
0.639524 | + | 0.768771i | \(0.279131\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −99.4544 | −0.311769 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.89027 | − | 91.2716i | 0.0308108 | − | 0.284335i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 217.743 | 0.674127 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.61364 | + | 51.8051i | −0.0171671 | + | 0.158425i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 45.7961i | 0.139198i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 45.9271 | 0.138753 | 0.0693763 | − | 0.997591i | \(-0.477899\pi\) | ||||
0.0693763 | + | 0.997591i | \(0.477899\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 116.510 | − | 531.291i | 0.349881 | − | 1.59547i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 516.924i | − | 1.53390i | −0.641707 | − | 0.766950i | \(-0.721774\pi\) | ||
0.641707 | − | 0.766950i | \(-0.278226\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.52393 | − | 14.0635i | 0.00449537 | − | 0.0414852i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 160.971i | 0.472055i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 357.605i | − | 1.04258i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.39280 | −0.0155412 | −0.00777061 | − | 0.999970i | \(-0.502473\pi\) | ||||
−0.00777061 | + | 0.999970i | \(0.502473\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −284.894 | −0.816315 | −0.408157 | − | 0.912912i | \(-0.633829\pi\) | ||||
−0.408157 | + | 0.912912i | \(0.633829\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −27.3097 | − | 9.16603i | −0.0778053 | − | 0.0261141i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 73.2882 | 0.207615 | 0.103808 | − | 0.994597i | \(-0.466897\pi\) | ||||
0.103808 | + | 0.994597i | \(0.466897\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 377.576 | + | 40.9144i | 1.05763 | + | 0.114606i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 361.674i | − | 1.00745i | −0.863865 | − | 0.503724i | \(-0.831963\pi\) | ||
0.863865 | − | 0.503724i | \(-0.168037\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −294.913 | −0.816934 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −31.7697 | + | 293.185i | −0.0875200 | + | 0.807671i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 131.432i | 0.358124i | 0.983838 | + | 0.179062i | \(0.0573063\pi\) | ||||
−0.983838 | + | 0.179062i | \(0.942694\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 114.247 | − | 520.970i | 0.309612 | − | 1.41184i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 440.207i | − | 1.18654i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 211.216i | 0.566262i | 0.959081 | + | 0.283131i | \(0.0913731\pi\) | ||||
−0.959081 | + | 0.283131i | \(0.908627\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −22.2713 | −0.0590751 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −47.4989 | −0.125327 | −0.0626635 | − | 0.998035i | \(-0.519959\pi\) | ||||
−0.0626635 | + | 0.998035i | \(0.519959\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.16149 | − | 0.450943i | −0.0109226 | − | 0.00118358i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 517.991 | 1.35246 | 0.676228 | − | 0.736692i | \(-0.263613\pi\) | ||||
0.676228 | + | 0.736692i | \(0.263613\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −108.813 | + | 496.191i | −0.281171 | + | 1.28215i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 253.951i | − | 0.652830i | −0.945227 | − | 0.326415i | \(-0.894159\pi\) | ||
0.945227 | − | 0.326415i | \(-0.105841\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1072.64 | 2.74333 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 674.710 | + | 73.1122i | 1.71682 | + | 0.186036i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 527.905i | − | 1.32974i | −0.746961 | − | 0.664868i | \(-0.768488\pi\) | ||
0.746961 | − | 0.664868i | \(-0.231512\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 114.597 | + | 12.4179i | 0.287212 | + | 0.0311225i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 664.097i | 1.65610i | 0.560653 | + | 0.828051i | \(0.310550\pi\) | ||||
−0.560653 | + | 0.828051i | \(0.689450\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 36.0470i | 0.0894466i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 287.938 | 0.707465 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −79.2471 | −0.193758 | −0.0968791 | − | 0.995296i | \(-0.530886\pi\) | ||||
−0.0968791 | + | 0.995296i | \(0.530886\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −24.6462 | + | 227.445i | −0.0599664 | + | 0.553395i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −82.6683 | −0.200165 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 41.2585 | − | 380.751i | 0.0989413 | − | 0.913072i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 666.530i | 1.59076i | 0.606109 | + | 0.795381i | \(0.292729\pi\) | ||||
−0.606109 | + | 0.795381i | \(0.707271\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −306.220 | −0.727364 | −0.363682 | − | 0.931523i | \(-0.618480\pi\) | ||||
−0.363682 | + | 0.931523i | \(0.618480\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 85.1806 | + | 18.6798i | 0.201373 | + | 0.0441604i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 272.903i | − | 0.639116i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.64286 | − | 15.1610i | 0.00382951 | − | 0.0353403i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 254.551i | 0.590605i | 0.955404 | + | 0.295303i | \(0.0954205\pi\) | ||||
−0.955404 | + | 0.295303i | \(0.904579\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 442.391i | 1.02169i | 0.859673 | + | 0.510845i | \(0.170667\pi\) | ||||
−0.859673 | + | 0.510845i | \(0.829333\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 325.556 | 0.744979 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −561.568 | −1.27920 | −0.639599 | − | 0.768709i | \(-0.720899\pi\) | ||||
−0.639599 | + | 0.768709i | \(0.720899\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −234.380 | − | 51.3988i | −0.531475 | − | 0.116551i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 564.841 | 1.27504 | 0.637518 | − | 0.770436i | \(-0.279961\pi\) | ||||
0.637518 | + | 0.770436i | \(0.279961\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 189.030 | + | 20.4835i | 0.422887 | + | 0.0458244i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 512.215i | 1.14079i | 0.821370 | + | 0.570396i | \(0.193210\pi\) | ||||
−0.821370 | + | 0.570396i | \(0.806790\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 282.345 | 0.626041 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 37.2423 | − | 343.688i | 0.0822126 | − | 0.758692i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 52.5358i | − | 0.114958i | −0.998347 | − | 0.0574790i | \(-0.981694\pi\) | ||
0.998347 | − | 0.0574790i | \(-0.0183062\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 230.110 | − | 685.601i | 0.501330 | − | 1.49368i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 625.737i | 1.35735i | 0.734441 | + | 0.678673i | \(0.237445\pi\) | ||||
−0.734441 | + | 0.678673i | \(0.762555\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 49.8782i | − | 0.107728i | −0.998548 | − | 0.0538641i | \(-0.982846\pi\) | ||
0.998548 | − | 0.0538641i | \(-0.0171538\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 64.6312 | 0.138397 | 0.0691983 | − | 0.997603i | \(-0.477956\pi\) | ||||
0.0691983 | + | 0.997603i | \(0.477956\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −479.877 | −1.02319 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −54.7879 | − | 5.93686i | −0.116322 | − | 0.0126048i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −268.915 | −0.568532 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −818.783 | − | 179.557i | −1.71653 | − | 0.376429i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 872.673i | 1.82186i | 0.412556 | + | 0.910932i | \(0.364636\pi\) | ||||
−0.412556 | + | 0.910932i | \(0.635364\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 64.4794 | 0.134053 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 564.528 | + | 61.1727i | 1.16879 | + | 0.126652i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 883.613i | 1.81440i | 0.420698 | + | 0.907201i | \(0.361785\pi\) | ||||
−0.420698 | + | 0.907201i | \(0.638215\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 488.221 | + | 52.9041i | 0.998408 | + | 0.108188i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 596.247i | 1.21435i | 0.794567 | + | 0.607177i | \(0.207698\pi\) | ||||
−0.794567 | + | 0.607177i | \(0.792302\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 559.114i | − | 1.13411i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 426.201 | 0.857548 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 560.109 | 1.12246 | 0.561231 | − | 0.827659i | \(-0.310328\pi\) | ||||
0.561231 | + | 0.827659i | \(0.310328\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −15.7402 | + | 145.257i | −0.0314175 | + | 0.289934i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −505.038 | −1.00405 | −0.502026 | − | 0.864853i | \(-0.667412\pi\) | ||||
−0.502026 | + | 0.864853i | \(0.667412\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −54.2513 | + | 500.654i | −0.107005 | + | 0.987484i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 13.3027i | − | 0.0261350i | −0.999915 | − | 0.0130675i | \(-0.995840\pi\) | ||
0.999915 | − | 0.0130675i | \(-0.00415963\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 189.387 | 0.370620 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 69.8405 | − | 208.086i | 0.136141 | − | 0.405625i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 46.1645i | 0.0892930i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 45.5005 | − | 419.898i | 0.0876695 | − | 0.809051i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 267.898i | 0.514200i | 0.966385 | + | 0.257100i | \(0.0827670\pi\) | ||||
−0.966385 | + | 0.257100i | \(0.917233\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 176.493i | 0.337463i | 0.985662 | + | 0.168731i | \(0.0539671\pi\) | ||||
−0.985662 | + | 0.168731i | \(0.946033\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −904.949 | −1.71717 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1074.75 | 2.03166 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −33.7197 | + | 153.763i | −0.0635022 | + | 0.289572i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 63.2268 | 0.118624 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 33.2105 | + | 3.59872i | 0.0618445 | + | 0.00670152i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 127.025i | − | 0.235667i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −790.757 | −1.46166 | −0.730829 | − | 0.682561i | \(-0.760866\pi\) | ||||
−0.730829 | + | 0.682561i | \(0.760866\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 48.5546 | − | 448.082i | 0.0894191 | − | 0.825198i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 44.1668i | 0.0807436i | 0.999185 | + | 0.0403718i | \(0.0128542\pi\) | ||||
−0.999185 | + | 0.0403718i | \(0.987146\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −507.598 | − | 111.315i | −0.924587 | − | 0.202759i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 169.696i | − | 0.307978i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 308.978i | 0.558730i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −753.685 | −1.35312 | −0.676558 | − | 0.736390i | \(-0.736529\pi\) | ||||
−0.676558 | + | 0.736390i | \(0.736529\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −60.2195 | −0.107727 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 380.613 | + | 41.2435i | 0.678454 | + | 0.0735179i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −609.590 | −1.08275 | −0.541376 | − | 0.840780i | \(-0.682097\pi\) | ||||
−0.541376 | + | 0.840780i | \(0.682097\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 160.206 | − | 347.706i | 0.282550 | − | 0.613238i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 528.082i | − | 0.928088i | −0.885812 | − | 0.464044i | \(-0.846398\pi\) | ||
0.885812 | − | 0.464044i | \(-0.153602\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −708.097 | −1.24010 | −0.620050 | − | 0.784562i | \(-0.712888\pi\) | ||||
−0.620050 | + | 0.784562i | \(0.712888\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 501.246 | + | 54.3154i | 0.874774 | + | 0.0947913i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 55.0939i | 0.0954834i | 0.998860 | + | 0.0477417i | \(0.0152024\pi\) | ||||
−0.998860 | + | 0.0477417i | \(0.984798\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −933.313 | − | 101.135i | −1.61194 | − | 0.174671i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 557.184i | − | 0.959009i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 443.748i | − | 0.761145i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 596.377 | 1.01598 | 0.507988 | − | 0.861364i | \(-0.330390\pi\) | ||||
0.507988 | + | 0.861364i | \(0.330390\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −274.660 | −0.466315 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 53.6981 | − | 495.549i | 0.0908597 | − | 0.838492i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −269.915 | −0.455169 | −0.227584 | − | 0.973758i | \(-0.573083\pi\) | ||||
−0.227584 | + | 0.973758i | \(0.573083\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −34.1079 | + | 314.762i | −0.0571322 | + | 0.527240i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 622.634i | 1.03946i | 0.854332 | + | 0.519728i | \(0.173967\pi\) | ||||
−0.854332 | + | 0.519728i | \(0.826033\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 865.760 | 1.44053 | 0.720266 | − | 0.693698i | \(-0.244020\pi\) | ||||
0.720266 | + | 0.693698i | \(0.244020\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −195.738 | + | 892.570i | −0.324606 | + | 1.48022i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 390.780i | − | 0.643790i | −0.946775 | − | 0.321895i | \(-0.895680\pi\) | ||
0.946775 | − | 0.321895i | \(-0.104320\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 31.8863 | − | 294.260i | 0.0523584 | − | 0.483185i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.3378i | 0.0169195i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 398.441i | − | 0.649985i | −0.945717 | − | 0.324993i | \(-0.894638\pi\) | ||
0.945717 | − | 0.324993i | \(-0.105362\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 178.765 | 0.289732 | 0.144866 | − | 0.989451i | \(-0.453725\pi\) | ||||
0.144866 | + | 0.989451i | \(0.453725\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 224.867 | 0.363274 | 0.181637 | − | 0.983366i | \(-0.441860\pi\) | ||||
0.181637 | + | 0.983366i | \(0.441860\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 344.047 | − | 1025.07i | 0.554021 | − | 1.65067i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −565.653 | −0.907950 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 115.519 | + | 12.5178i | 0.184241 | + | 0.0199645i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1618.74i | 2.57351i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.36019 | −0.0148339 | −0.00741695 | − | 0.999972i | \(-0.502361\pi\) | ||||
−0.00741695 | + | 0.999972i | \(0.502361\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −91.5836 | + | 845.172i | −0.144682 | + | 1.33518i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 28.4453i | − | 0.0446550i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 173.844 | − | 792.733i | 0.272056 | − | 1.24058i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 785.281i | − | 1.22509i | −0.790437 | − | 0.612543i | \(-0.790146\pi\) | ||
0.790437 | − | 0.612543i | \(-0.209854\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 131.320i | 0.204230i | 0.994773 | + | 0.102115i | \(0.0325610\pi\) | ||||
−0.994773 | + | 0.102115i | \(0.967439\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 155.225 | 0.239915 | 0.119958 | − | 0.992779i | \(-0.461724\pi\) | ||||
0.119958 | + | 0.992779i | \(0.461724\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −83.3333 | −0.128403 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −476.271 | − | 51.6092i | −0.731599 | − | 0.0792768i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −668.464 | −1.02368 | −0.511841 | − | 0.859080i | \(-0.671036\pi\) | ||||
−0.511841 | + | 0.859080i | \(0.671036\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 77.2493 | − | 352.259i | 0.117579 | − | 0.536163i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 579.510i | − | 0.879377i | −0.898150 | − | 0.439689i | \(-0.855089\pi\) | ||
0.898150 | − | 0.439689i | \(-0.144911\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −307.070 | −0.464553 | −0.232277 | − | 0.972650i | \(-0.574617\pi\) | ||||
−0.232277 | + | 0.972650i | \(0.574617\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 85.2324 | + | 9.23586i | 0.128556 | + | 0.0139304i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 835.953i | − | 1.25330i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 298.576 | + | 32.3540i | 0.446302 | + | 0.0483617i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 275.098i | − | 0.409982i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.02018i | 0.0104312i | 0.999986 | + | 0.00521559i | \(0.00166018\pi\) | ||||
−0.999986 | + | 0.00521559i | \(0.998340\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.21742 | −0.00179825 | −0.000899127 | − | 1.00000i | \(-0.500286\pi\) | ||||
−0.000899127 | 1.00000i | \(0.500286\pi\) | ||||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 72.0881 | 0.106168 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 77.4993 | − | 715.196i | 0.113802 | − | 1.05021i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1261.23 | −1.84661 | −0.923305 | − | 0.384067i | \(-0.874523\pi\) | ||||
−0.923305 | + | 0.384067i | \(0.874523\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 127.026 | − | 1172.25i | 0.184899 | − | 1.70633i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 99.3706i | − | 0.144224i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −158.177 | −0.228910 | −0.114455 | − | 0.993428i | \(-0.536512\pi\) | ||||
−0.114455 | + | 0.993428i | \(0.536512\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 197.963 | + | 43.4126i | 0.285661 | + | 0.0626445i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1587.29i | 2.27732i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −90.0705 | + | 831.208i | −0.128856 | + | 1.18914i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 331.746i | − | 0.473247i | −0.971601 | − | 0.236623i | \(-0.923959\pi\) | ||
0.971601 | − | 0.236623i | \(-0.0760408\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 491.300i | 0.698863i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −340.323 | −0.481363 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −854.366 | −1.20503 | −0.602515 | − | 0.798108i | \(-0.705835\pi\) | ||||
−0.602515 | + | 0.798108i | \(0.705835\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 574.697 | + | 126.029i | 0.808295 | + | 0.177256i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1353.02 | −1.89765 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 586.350 | + | 63.5374i | 0.817782 | + | 0.0886156i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 218.882i | − | 0.304426i | −0.988348 | − | 0.152213i | \(-0.951360\pi\) | ||
0.988348 | − | 0.152213i | \(-0.0486400\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 524.394 | 0.727314 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 74.7064 | − | 689.422i | 0.103328 | − | 0.953557i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 12.2420i | − | 0.0168391i | −0.999965 | − | 0.00841954i | \(-0.997320\pi\) | ||
0.999965 | − | 0.00841954i | \(-0.00268006\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −581.385 | − | 439.809i | −0.797511 | − | 0.603305i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 1511.79i | − | 2.06812i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 86.8331i | 0.118463i | 0.998244 | + | 0.0592313i | \(0.0188650\pi\) | ||||
−0.998244 | + | 0.0592313i | \(0.981135\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −483.737 | −0.656360 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 187.725 | 0.254026 | 0.127013 | − | 0.991901i | \(-0.459461\pi\) | ||||
0.127013 | + | 0.991901i | \(0.459461\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 25.8688 | + | 2.80316i | 0.0349106 | + | 0.00378294i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 178.264 | 0.239925 | 0.119963 | − | 0.992778i | \(-0.461723\pi\) | ||||
0.119963 | + | 0.992778i | \(0.461723\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1036.36 | − | 227.271i | −1.38736 | − | 0.304244i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 144.637i | 0.193107i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1328.32 | −1.76874 | −0.884370 | − | 0.466786i | \(-0.845412\pi\) | ||||
−0.884370 | + | 0.466786i | \(0.845412\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −726.075 | − | 78.6781i | −0.964243 | − | 0.104486i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 545.957i | 0.721211i | 0.932718 | + | 0.360606i | \(0.117430\pi\) | ||||
−0.932718 | + | 0.360606i | \(0.882570\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 569.068 | + | 61.6648i | 0.749761 | + | 0.0812448i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 828.655i | 1.08890i | 0.838793 | + | 0.544451i | \(0.183262\pi\) | ||||
−0.838793 | + | 0.544451i | \(0.816738\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 82.0950i | − | 0.107595i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −18.6612 | −0.0243301 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 303.757 | 0.395002 | 0.197501 | − | 0.980303i | \(-0.436717\pi\) | ||||
0.197501 | + | 0.980303i | \(0.436717\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 115.858 | − | 1069.19i | 0.150270 | − | 1.38676i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −59.2137 | −0.0766025 | −0.0383013 | − | 0.999266i | \(-0.512195\pi\) | ||||
−0.0383013 | + | 0.999266i | \(0.512195\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −92.3165 | + | 851.936i | −0.118811 | + | 1.09644i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 481.756i | 0.618429i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 429.629 | 0.550102 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −534.316 | − | 179.334i | −0.682396 | − | 0.229035i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 214.281i | − | 0.272276i | −0.990690 | − | 0.136138i | \(-0.956531\pi\) | ||
0.990690 | − | 0.136138i | \(-0.0434691\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 106.948 | − | 986.963i | 0.135549 | − | 1.25090i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 22.2862i | 0.0281748i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 61.6040i | − | 0.0776847i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 124.487 | 0.156195 | 0.0780974 | − | 0.996946i | \(-0.475115\pi\) | ||||
0.0780974 | + | 0.996946i | \(0.475115\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −259.528 | −0.324816 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −230.725 | + | 1052.11i | −0.288046 | + | 1.31350i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 190.910 | 0.237746 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −289.412 | − | 31.3610i | −0.358627 | − | 0.0388612i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 44.3423i | − | 0.0548113i | −0.999624 | − | 0.0274056i | \(-0.991275\pi\) | ||
0.999624 | − | 0.0274056i | \(-0.00872458\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −686.962 | −0.847056 | −0.423528 | − | 0.905883i | \(-0.639208\pi\) | ||||
−0.423528 | + | 0.905883i | \(0.639208\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −21.7136 | + | 200.382i | −0.0267080 | + | 0.246473i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 458.842i | − | 0.561618i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 44.3308 | + | 9.72160i | 0.0541280 | + | 0.0118701i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 865.772i | − | 1.05453i | −0.849700 | − | 0.527267i | \(-0.823217\pi\) | ||
0.849700 | − | 0.527267i | \(-0.176783\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 240.142i | − | 0.291789i | −0.989300 | − | 0.145895i | \(-0.953394\pi\) | ||
0.989300 | − | 0.145895i | \(-0.0466060\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −311.704 | −0.376910 | −0.188455 | − | 0.982082i | \(-0.560348\pi\) | ||||
−0.188455 | + | 0.982082i | \(0.560348\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1125.26 | 1.35737 | 0.678684 | − | 0.734430i | \(-0.262551\pi\) | ||||
0.678684 | + | 0.734430i | \(0.262551\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1079.08 | − | 116.931i | −1.29854 | − | 0.140711i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 714.110 | 0.857274 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −290.260 | + | 864.812i | −0.346786 | + | 1.03323i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 40.3794i | 0.0481280i | 0.999710 | + | 0.0240640i | \(0.00766055\pi\) | ||||
−0.999710 | + | 0.0240640i | \(0.992339\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 405.259 | 0.481878 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 859.546 | + | 93.1412i | 1.01963 | + | 0.110488i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 464.607i | − | 0.548532i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 812.664 | + | 88.0610i | 0.957201 | + | 0.103723i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2420.24i | 2.84399i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 290.487i | − | 0.340547i | −0.985397 | − | 0.170274i | \(-0.945535\pi\) | ||
0.985397 | − | 0.170274i | \(-0.0544652\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1111.79 | 1.29731 | 0.648655 | − | 0.761083i | \(-0.275332\pi\) | ||||
0.648655 | + | 0.761083i | \(0.275332\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 159.069 | 0.185179 | 0.0925894 | − | 0.995704i | \(-0.470486\pi\) | ||||
0.0925894 | + | 0.995704i | \(0.470486\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −90.5231 | + | 835.385i | −0.105137 | + | 0.970250i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −75.4630 | −0.0874426 | −0.0437213 | − | 0.999044i | \(-0.513921\pi\) | ||||
−0.0437213 | + | 0.999044i | \(0.513921\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −138.461 | + | 1277.78i | −0.159702 | + | 1.47379i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 311.463i | 0.358415i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −108.326 | −0.124369 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 29.4041 | − | 134.084i | 0.0336817 | − | 0.153589i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 511.799i | 0.583579i | 0.956483 | + | 0.291790i | \(0.0942507\pi\) | ||||
−0.956483 | + | 0.291790i | \(0.905749\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −22.8067 | + | 210.470i | −0.0259462 | + | 0.239443i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 855.549i | − | 0.971111i | −0.874206 | − | 0.485556i | \(-0.838617\pi\) | ||
0.874206 | − | 0.485556i | \(-0.161383\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.2299i | 0.0127179i | 0.999980 | + | 0.00635894i | \(0.00202413\pi\) | ||||
−0.999980 | + | 0.00635894i | \(0.997976\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −733.251 | −0.826664 | −0.413332 | − | 0.910580i | \(-0.635635\pi\) | ||||
−0.413332 | + | 0.910580i | \(0.635635\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.59468 | 0.00741808 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 161.495 | − | 350.503i | 0.181251 | − | 0.393381i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −78.7690 | −0.0882072 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 127.434 | + | 13.8089i | 0.142067 | + | 0.0153945i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 705.263i | 0.784497i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2494.67 | 2.76878 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 86.2175 | − | 795.652i | 0.0954790 | − | 0.881120i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 1141.39i | − | 1.25843i | −0.777232 | − | 0.629214i | \(-0.783377\pi\) | ||
0.777232 | − | 0.629214i | \(-0.216623\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −138.815 | + | 633.000i | −0.152712 | + | 0.696370i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 157.145i | 0.172497i | 0.996274 | + | 0.0862487i | \(0.0274880\pi\) | ||||
−0.996274 | + | 0.0862487i | \(0.972512\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 561.666i | − | 0.615187i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1069.21 | −1.16598 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1542.94 | −1.67893 | −0.839466 | − | 0.543412i | \(-0.817132\pi\) | ||||
−0.839466 | + | 0.543412i | \(0.817132\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −370.652 | − | 40.1642i | −0.402446 | − | 0.0436094i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 96.2090 | 0.104235 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 213.896 | − | 975.371i | 0.230740 | − | 1.05218i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 165.617i | 0.178274i | 0.996019 | + | 0.0891372i | \(0.0284110\pi\) | ||||
−0.996019 | + | 0.0891372i | \(0.971589\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 216.738 | 0.232802 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −683.019 | − | 74.0125i | −0.732067 | − | 0.0793275i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1418.05i | − | 1.51339i | −0.653768 | − | 0.756695i | \(-0.726813\pi\) | ||
0.653768 | − | 0.756695i | \(-0.273187\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1388.34 | − | 150.442i | −1.47853 | − | 0.160215i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1274.33i | 1.35423i | 0.735878 | + | 0.677114i | \(0.236769\pi\) | ||||
−0.735878 | + | 0.677114i | \(0.763231\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2373.22i | 2.51667i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1406.16 | 1.48486 | 0.742428 | − | 0.669926i | \(-0.233674\pi\) | ||||
0.742428 | + | 0.669926i | \(0.233674\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 42.7515 | 0.0450490 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −131.040 | + | 1209.30i | −0.137792 | + | 1.27160i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1415.36 | 1.48516 | 0.742579 | − | 0.669759i | \(-0.233602\pi\) | ||||
0.742579 | + | 0.669759i | \(0.233602\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 32.1427 | − | 296.627i | 0.0335870 | − | 0.309955i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 360.430i | − | 0.375840i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 180.496 | 0.187821 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 269.025 | + | 58.9963i | 0.279361 | + | 0.0612630i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1662.07i | 1.71879i | 0.511315 | + | 0.859394i | \(0.329159\pi\) | ||||
−0.511315 | + | 0.859394i | \(0.670841\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −70.3725 | + | 649.427i | −0.0726239 | + | 0.670204i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 868.901i | 0.894852i | 0.894321 | + | 0.447426i | \(0.147659\pi\) | ||||
−0.894321 | + | 0.447426i | \(0.852341\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 603.373i | 0.620116i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1336.81 | −1.36828 | −0.684140 | − | 0.729350i | \(-0.739822\pi\) | ||||
−0.684140 | + | 0.729350i | \(0.739822\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −570.203 | −0.582434 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −152.696 | − | 33.4858i | −0.155654 | − | 0.0341344i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1193.86 | 1.21451 | 0.607254 | − | 0.794508i | \(-0.292271\pi\) | ||||
0.607254 | + | 0.794508i | \(0.292271\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −136.589 | − | 14.8009i | −0.138388 | − | 0.0149958i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 2260.34i | − | 2.28548i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −460.690 | −0.464874 | −0.232437 | − | 0.972611i | \(-0.574670\pi\) | ||||
−0.232437 | + | 0.972611i | \(0.574670\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −14.8432 | + | 136.980i | −0.0149479 | + | 0.137945i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 673.924i | − | 0.675952i | −0.941155 | − | 0.337976i | \(-0.890258\pi\) | ||
0.941155 | − | 0.337976i | \(-0.109742\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1546.94 | + | 519.205i | 1.54849 | + | 0.519725i |
(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 | 600.3.c.d.449.8 | 16 | ||
3.2 | odd | 2 | inner | 600.3.c.d.449.10 | 16 | ||
4.3 | odd | 2 | 1200.3.c.m.449.9 | 16 | |||
5.2 | odd | 4 | 120.3.l.a.41.8 | yes | 8 | ||
5.3 | odd | 4 | 600.3.l.f.401.1 | 8 | |||
5.4 | even | 2 | inner | 600.3.c.d.449.9 | 16 | ||
12.11 | even | 2 | 1200.3.c.m.449.7 | 16 | |||
15.2 | even | 4 | 120.3.l.a.41.7 | ✓ | 8 | ||
15.8 | even | 4 | 600.3.l.f.401.2 | 8 | |||
15.14 | odd | 2 | inner | 600.3.c.d.449.7 | 16 | ||
20.3 | even | 4 | 1200.3.l.x.401.8 | 8 | |||
20.7 | even | 4 | 240.3.l.d.161.1 | 8 | |||
20.19 | odd | 2 | 1200.3.c.m.449.8 | 16 | |||
40.27 | even | 4 | 960.3.l.g.641.8 | 8 | |||
40.37 | odd | 4 | 960.3.l.h.641.1 | 8 | |||
60.23 | odd | 4 | 1200.3.l.x.401.7 | 8 | |||
60.47 | odd | 4 | 240.3.l.d.161.2 | 8 | |||
60.59 | even | 2 | 1200.3.c.m.449.10 | 16 | |||
120.77 | even | 4 | 960.3.l.h.641.2 | 8 | |||
120.107 | odd | 4 | 960.3.l.g.641.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
120.3.l.a.41.7 | ✓ | 8 | 15.2 | even | 4 | ||
120.3.l.a.41.8 | yes | 8 | 5.2 | odd | 4 | ||
240.3.l.d.161.1 | 8 | 20.7 | even | 4 | |||
240.3.l.d.161.2 | 8 | 60.47 | odd | 4 | |||
600.3.c.d.449.7 | 16 | 15.14 | odd | 2 | inner | ||
600.3.c.d.449.8 | 16 | 1.1 | even | 1 | trivial | ||
600.3.c.d.449.9 | 16 | 5.4 | even | 2 | inner | ||
600.3.c.d.449.10 | 16 | 3.2 | odd | 2 | inner | ||
600.3.l.f.401.1 | 8 | 5.3 | odd | 4 | |||
600.3.l.f.401.2 | 8 | 15.8 | even | 4 | |||
960.3.l.g.641.7 | 8 | 120.107 | odd | 4 | |||
960.3.l.g.641.8 | 8 | 40.27 | even | 4 | |||
960.3.l.h.641.1 | 8 | 40.37 | odd | 4 | |||
960.3.l.h.641.2 | 8 | 120.77 | even | 4 | |||
1200.3.c.m.449.7 | 16 | 12.11 | even | 2 | |||
1200.3.c.m.449.8 | 16 | 20.19 | odd | 2 | |||
1200.3.c.m.449.9 | 16 | 4.3 | odd | 2 | |||
1200.3.c.m.449.10 | 16 | 60.59 | even | 2 | |||
1200.3.l.x.401.7 | 8 | 60.23 | odd | 4 | |||
1200.3.l.x.401.8 | 8 | 20.3 | even | 4 |