Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2288,2,Mod(2287,2288)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2288, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2288.2287");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2288 = 2^{4} \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2288.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(18.2697719825\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2287.9 | ||
Character | \(\chi\) | \(=\) | 2288.2287 |
Dual form | 2288.2.b.c.2287.48 |
$q$-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 \(\left(\mathbb{Z}/2288\mathbb{Z}\right)^\times\).
\(n\) | \(287\) | \(353\) | \(1717\) | \(2081\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − | 2.08094i | − | 1.20143i | −0.799463 | − | 0.600715i | \(-0.794882\pi\) | ||
0.799463 | − | 0.600715i | \(-0.205118\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 4.28515i | − | 1.91638i | −0.286136 | − | 0.958189i | \(-0.592371\pi\) | ||
0.286136 | − | 0.958189i | \(-0.407629\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 3.10047i | − | 1.17187i | −0.810358 | − | 0.585935i | \(-0.800728\pi\) | ||
0.810358 | − | 0.585935i | \(-0.199272\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.33031 | −0.443436 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.55800 | − | 2.92791i | 0.469754 | − | 0.882797i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.54217 | + | 0.673063i | −0.982422 | + | 0.186674i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −8.91714 | −2.30240 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.56760i | 0.865269i | 0.901569 | + | 0.432634i | \(0.142416\pi\) | ||||
−0.901569 | + | 0.432634i | \(0.857584\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.02006i | 1.15168i | 0.817562 | + | 0.575840i | \(0.195325\pi\) | ||||
−0.817562 | + | 0.575840i | \(0.804675\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.45190 | −1.40792 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 0.541694i | − | 0.112951i | −0.998404 | − | 0.0564755i | \(-0.982014\pi\) | ||
0.998404 | − | 0.0564755i | \(-0.0179863\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −13.3625 | −2.67250 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 3.47453i | − | 0.668673i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 1.94427i | − | 0.361041i | −0.983571 | − | 0.180521i | \(-0.942222\pi\) | ||
0.983571 | − | 0.180521i | \(-0.0577782\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.14410 | −0.385091 | −0.192546 | − | 0.981288i | \(-0.561674\pi\) | ||||
−0.192546 | + | 0.981288i | \(0.561674\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.09280 | − | 3.24210i | −1.06062 | − | 0.564377i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −13.2860 | −2.24574 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 8.93120i | − | 1.46828i | −0.678998 | − | 0.734140i | \(-0.737585\pi\) | ||
0.678998 | − | 0.734140i | \(-0.262415\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.40060 | + | 7.37105i | 0.224276 | + | 1.18031i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.19930 | 1.43669 | 0.718345 | − | 0.695687i | \(-0.244900\pi\) | ||||
0.718345 | + | 0.695687i | \(0.244900\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.7202 | 1.63481 | 0.817407 | − | 0.576061i | \(-0.195411\pi\) | ||||
0.817407 | + | 0.576061i | \(0.195411\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.70058i | 0.849792i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.98486 | −0.289522 | −0.144761 | − | 0.989467i | \(-0.546241\pi\) | ||||
−0.144761 | + | 0.989467i | \(0.546241\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.61294 | −0.373277 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.42395 | 1.03956 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.94221 | −0.816226 | −0.408113 | − | 0.912932i | \(-0.633813\pi\) | ||||
−0.408113 | + | 0.912932i | \(0.633813\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −12.5465 | − | 6.67625i | −1.69177 | − | 0.900226i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 10.4464 | 1.38366 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.4260 | 1.48754 | 0.743770 | − | 0.668436i | \(-0.233036\pi\) | ||||
0.743770 | + | 0.668436i | \(0.233036\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.0928i | 1.54832i | 0.632987 | + | 0.774162i | \(0.281829\pi\) | ||||
−0.632987 | + | 0.774162i | \(0.718171\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.12459i | 0.519649i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.88418 | + | 15.1787i | 0.357738 | + | 1.88269i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.01909 | 1.10186 | 0.550929 | − | 0.834552i | \(-0.314274\pi\) | ||||
0.550929 | + | 0.834552i | \(0.314274\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.12723 | −0.135703 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.50892 | 1.12850 | 0.564250 | − | 0.825604i | \(-0.309165\pi\) | ||||
0.564250 | + | 0.825604i | \(0.309165\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.8221 | −1.38367 | −0.691835 | − | 0.722056i | \(-0.743197\pi\) | ||||
−0.691835 | + | 0.722056i | \(0.743197\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 27.8066i | 3.21083i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −9.07790 | − | 4.83053i | −1.03452 | − | 0.550490i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.82604 | 0.542972 | 0.271486 | − | 0.962442i | \(-0.412485\pi\) | ||||
0.271486 | + | 0.962442i | \(0.412485\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.2212 | −1.24680 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 10.4470i | − | 1.14671i | −0.819308 | − | 0.573354i | \(-0.805642\pi\) | ||
0.819308 | − | 0.573354i | \(-0.194358\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 15.2877 | 1.65818 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.04590 | −0.433766 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.71165i | 0.287434i | 0.989619 | + | 0.143717i | \(0.0459055\pi\) | ||||
−0.989619 | + | 0.143717i | \(0.954094\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.08681 | + | 10.9824i | 0.218758 | + | 1.15127i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.46174i | 0.462661i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 21.5117 | 2.20705 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 2.77051i | − | 0.281303i | −0.990059 | − | 0.140651i | \(-0.955080\pi\) | ||
0.990059 | − | 0.140651i | \(-0.0449197\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.07262 | + | 3.89502i | −0.208306 | + | 0.391464i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 10.9014i | − | 1.08473i | −0.840144 | − | 0.542363i | \(-0.817530\pi\) | ||
0.840144 | − | 0.542363i | \(-0.182470\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 6.40451i | − | 0.631055i | −0.948916 | − | 0.315527i | \(-0.897819\pi\) | ||
0.948916 | − | 0.315527i | \(-0.102181\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 27.6474i | 2.69811i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.0734 | 1.16718 | 0.583590 | − | 0.812049i | \(-0.301648\pi\) | ||||
0.583590 | + | 0.812049i | \(0.301648\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.75577 | −0.647085 | −0.323542 | − | 0.946214i | \(-0.604874\pi\) | ||||
−0.323542 | + | 0.946214i | \(0.604874\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −18.5853 | −1.76404 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.1594 | −1.23794 | −0.618968 | − | 0.785416i | \(-0.712449\pi\) | ||||
−0.618968 | + | 0.785416i | \(0.712449\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.32124 | −0.216457 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.71218 | − | 0.895382i | 0.435642 | − | 0.0827781i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 11.0612 | 1.01398 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.14529 | − | 9.12335i | −0.558663 | − | 0.829395i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 19.1432i | − | 1.72608i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 35.8347i | 3.20515i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.4658 | −1.54984 | −0.774920 | − | 0.632060i | \(-0.782210\pi\) | ||||
−0.774920 | + | 0.632060i | \(0.782210\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 22.3081i | − | 1.96412i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.81169 | 0.245658 | 0.122829 | − | 0.992428i | \(-0.460803\pi\) | ||||
0.122829 | + | 0.992428i | \(0.460803\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 15.5646 | 1.34962 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −14.8889 | −1.28143 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.85331i | 0.414646i | 0.978273 | + | 0.207323i | \(0.0664751\pi\) | ||||
−0.978273 | + | 0.207323i | \(0.933525\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.883564 | 0.0749429 | 0.0374715 | − | 0.999298i | \(-0.488070\pi\) | ||||
0.0374715 | + | 0.999298i | \(0.488070\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.13038i | 0.347841i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.54803 | + | 11.4198i | −0.296701 | + | 0.954970i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.33148 | −0.691891 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.43737i | 0.448467i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.3264 | 1.00982 | 0.504909 | − | 0.863173i | \(-0.331526\pi\) | ||||
0.504909 | + | 0.863173i | \(0.331526\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 8.86095i | − | 0.721094i | −0.932741 | − | 0.360547i | \(-0.882590\pi\) | ||
0.932741 | − | 0.360547i | \(-0.117410\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 4.74600i | − | 0.383692i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.18778i | 0.737980i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 19.2494 | 1.53627 | 0.768137 | − | 0.640286i | \(-0.221184\pi\) | ||||
0.768137 | + | 0.640286i | \(0.221184\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 12.3654i | 0.980639i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.67951 | −0.132364 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −20.5129 | −1.60669 | −0.803346 | − | 0.595513i | \(-0.796949\pi\) | ||||
−0.803346 | + | 0.595513i | \(0.796949\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −13.8929 | + | 26.1086i | −1.08156 | + | 2.03255i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.2930i | 0.796499i | 0.917277 | + | 0.398249i | \(0.130382\pi\) | ||||
−0.917277 | + | 0.398249i | \(0.869618\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.0940 | − | 4.76821i | 0.930306 | − | 0.366785i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 6.67823i | − | 0.510697i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.50733i | 0.646801i | 0.946262 | + | 0.323400i | \(0.104826\pi\) | ||||
−0.946262 | + | 0.323400i | \(0.895174\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 41.4302i | 3.13183i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 23.7768i | − | 1.78718i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.5310i | 0.936614i | 0.883566 | + | 0.468307i | \(0.155136\pi\) | ||||
−0.883566 | + | 0.468307i | \(0.844864\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.05683 | 0.152883 | 0.0764413 | − | 0.997074i | \(-0.475644\pi\) | ||||
0.0764413 | + | 0.997074i | \(0.475644\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 25.1644 | 1.86020 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −38.2716 | −2.81378 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.4456 | + | 5.55830i | 0.763857 | + | 0.406463i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −10.7727 | −0.783597 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 5.57546i | − | 0.403426i | −0.979445 | − | 0.201713i | \(-0.935349\pi\) | ||
0.979445 | − | 0.201713i | \(-0.0646508\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.46449 | −0.393343 | −0.196671 | − | 0.980469i | \(-0.563013\pi\) | ||||
−0.196671 | + | 0.980469i | \(0.563013\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 31.5861 | − | 6.00180i | 2.26192 | − | 0.429798i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −18.7783 | −1.33790 | −0.668949 | − | 0.743308i | \(-0.733255\pi\) | ||||
−0.668949 | + | 0.743308i | \(0.733255\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 1.41073i | − | 0.100004i | −0.998749 | − | 0.0500020i | \(-0.984077\pi\) | ||
0.998749 | − | 0.0500020i | \(-0.0159228\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 18.7682i | − | 1.32381i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.02815 | −0.423093 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 39.4204i | − | 2.75324i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.720621i | 0.0500866i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 14.6983 | + | 7.82124i | 1.01670 | + | 0.541006i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.09239 | −0.350575 | −0.175287 | − | 0.984517i | \(-0.556085\pi\) | ||||
−0.175287 | + | 0.984517i | \(0.556085\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 19.7875i | − | 1.35582i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 45.9376i | − | 3.13292i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.64772i | 0.451277i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 24.6010i | 1.66238i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.40122 | − | 12.6370i | −0.161523 | − | 0.850059i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.6850 | 0.983378 | 0.491689 | − | 0.870771i | \(-0.336380\pi\) | ||||
0.491689 | + | 0.870771i | \(0.336380\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 17.7763 | 1.18509 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.68412i | 0.244524i | 0.992498 | + | 0.122262i | \(0.0390147\pi\) | ||||
−0.992498 | + | 0.122262i | \(0.960985\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 23.9534i | − | 1.58289i | −0.611243 | − | 0.791443i | \(-0.709330\pi\) | ||
0.611243 | − | 0.791443i | \(-0.290670\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −10.0520 | + | 18.8906i | −0.661376 | + | 1.24291i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 19.7216i | 1.29201i | 0.763334 | + | 0.646004i | \(0.223561\pi\) | ||||
−0.763334 | + | 0.646004i | \(0.776439\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.50544i | 0.554834i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 10.0427i | − | 0.652344i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 6.00099i | − | 0.388172i | −0.980985 | − | 0.194086i | \(-0.937826\pi\) | ||
0.980985 | − | 0.194086i | \(-0.0621740\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.6409 | 1.00752 | 0.503759 | − | 0.863844i | \(-0.331950\pi\) | ||||
0.503759 | + | 0.863844i | \(0.331950\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 12.9271i | 0.829272i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 11.1969i | 0.715341i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.37882 | − | 17.7819i | −0.214989 | − | 1.13144i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −21.7396 | −1.37769 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 8.05122i | − | 0.508189i | −0.967179 | − | 0.254094i | \(-0.918223\pi\) | ||
0.967179 | − | 0.254094i | \(-0.0817774\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.58603 | − | 0.843958i | −0.0997129 | − | 0.0530592i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 31.8127i | − | 1.99219i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −18.2403 | −1.13780 | −0.568899 | − | 0.822407i | \(-0.692631\pi\) | ||||
−0.568899 | + | 0.822407i | \(0.692631\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −27.6910 | −1.72063 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.58648i | 0.160099i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −21.2305 | −1.30913 | −0.654563 | − | 0.756007i | \(-0.727147\pi\) | ||||
−0.654563 | + | 0.756007i | \(0.727147\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 25.4633i | 1.56420i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.64277 | 0.345332 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 22.4461 | 1.36856 | 0.684280 | − | 0.729219i | \(-0.260117\pi\) | ||||
0.684280 | + | 0.729219i | \(0.260117\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.0466i | 1.15700i | 0.815684 | + | 0.578498i | \(0.196361\pi\) | ||||
−0.815684 | + | 0.578498i | \(0.803639\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 22.8537 | − | 4.34254i | 1.38317 | − | 0.262822i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −20.8188 | + | 39.1242i | −1.25542 | + | 2.35928i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 29.1220i | 1.74977i | 0.484328 | + | 0.874887i | \(0.339064\pi\) | ||||
−0.484328 | + | 0.874887i | \(0.660936\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.85231 | 0.170763 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.7005 | −0.936616 | −0.468308 | − | 0.883565i | \(-0.655136\pi\) | ||||
−0.468308 | + | 0.883565i | \(0.655136\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21.1796 | 1.25900 | 0.629498 | − | 0.777002i | \(-0.283260\pi\) | ||||
0.629498 | + | 0.777002i | \(0.283260\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − | 44.7646i | − | 2.65162i | ||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 28.5222i | − | 1.68361i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.27226 | 0.251310 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.76527 | −0.337966 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −15.1673 | −0.886082 | −0.443041 | − | 0.896501i | \(-0.646100\pi\) | ||||
−0.443041 | + | 0.896501i | \(0.646100\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 48.9622i | − | 2.85069i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −10.1731 | − | 5.41330i | −0.590303 | − | 0.314112i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.364594 | + | 1.91877i | 0.0210850 | + | 0.110966i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 33.2377i | − | 1.91579i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −22.6851 | −1.30322 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 51.8195 | 2.96717 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 2.22871i | − | 0.127199i | −0.997975 | − | 0.0635997i | \(-0.979742\pi\) | ||
0.997975 | − | 0.0635997i | \(-0.0202581\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −13.3274 | −0.758169 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 24.4208i | 1.38478i | 0.721525 | + | 0.692388i | \(0.243441\pi\) | ||||
−0.721525 | + | 0.692388i | \(0.756559\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.34489 | −0.245588 | −0.122794 | − | 0.992432i | \(-0.539185\pi\) | ||||
−0.122794 | + | 0.992432i | \(0.539185\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 17.6745 | 0.995845 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.56482i | 0.537214i | 0.963250 | + | 0.268607i | \(0.0865633\pi\) | ||||
−0.963250 | + | 0.268607i | \(0.913437\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.69263 | − | 3.02916i | −0.318726 | − | 0.169601i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 25.1240i | − | 1.40229i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −17.9095 | −0.996513 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 47.3324 | − | 8.99382i | 2.62553 | − | 0.498887i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 14.0583i | 0.777428i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.15402i | 0.339282i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.6897 | −1.08224 | −0.541121 | − | 0.840945i | \(-0.682000\pi\) | ||||
−0.541121 | + | 0.840945i | \(0.682000\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 11.8813i | 0.651089i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 38.6482i | − | 2.11158i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 7.60479i | − | 0.414259i | −0.978313 | − | 0.207130i | \(-0.933588\pi\) | ||
0.978313 | − | 0.207130i | \(-0.0664122\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 27.3840i | 1.48730i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.34050 | + | 6.27772i | −0.180898 | + | 0.339958i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 13.6020i | − | 0.734437i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.83036i | 0.260058i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.69917 | −0.252265 | −0.126132 | − | 0.992013i | \(-0.540256\pi\) | ||||
−0.126132 | + | 0.992013i | \(0.540256\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.7299 | 0.895528 | 0.447764 | − | 0.894152i | \(-0.352220\pi\) | ||||
0.447764 | + | 0.894152i | \(0.352220\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.33858 | + | 12.3074i | 0.124824 | + | 0.656919i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 33.6048i | 1.78861i | 0.447463 | + | 0.894303i | \(0.352328\pi\) | ||||
−0.447463 | + | 0.894303i | \(0.647672\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 40.7471i | − | 2.16263i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 23.0178i | − | 1.21823i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 13.9272i | − | 0.735051i | −0.930013 | − | 0.367526i | \(-0.880205\pi\) | ||
0.930013 | − | 0.367526i | \(-0.119795\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.20098 | −0.326367 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −18.9851 | + | 12.7880i | −0.996461 | + | 0.671194i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 50.6594i | 2.65163i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.49880i | 0.130437i | 0.997871 | + | 0.0652183i | \(0.0207744\pi\) | ||||
−0.997871 | + | 0.0652183i | \(0.979226\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −12.2379 | −0.637081 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 18.4237i | 0.956510i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 9.67276i | − | 0.500836i | −0.968138 | − | 0.250418i | \(-0.919432\pi\) | ||
0.968138 | − | 0.250418i | \(-0.0805681\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 74.5698 | 3.85077 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.30861 | + | 6.88693i | 0.0673970 | + | 0.354695i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.728681 | −0.0374298 | −0.0187149 | − | 0.999825i | \(-0.505957\pi\) | ||||
−0.0187149 | + | 0.999825i | \(0.505957\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 36.3453i | 1.86203i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 14.3889 | 0.735238 | 0.367619 | − | 0.929977i | \(-0.380173\pi\) | ||||
0.367619 | + | 0.929977i | \(0.380173\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −20.6996 | + | 38.9002i | −1.05495 | + | 1.98254i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −14.2612 | −0.724936 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.5337 | 0.686187 | 0.343093 | − | 0.939301i | \(-0.388525\pi\) | ||||
0.343093 | + | 0.939301i | \(0.388525\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.93255 | 0.0977330 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 5.85095i | − | 0.295142i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 20.6803i | − | 1.04054i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 12.8184i | − | 0.643337i | −0.946852 | − | 0.321669i | \(-0.895756\pi\) | ||
0.946852 | − | 0.321669i | \(-0.104244\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 32.3889i | − | 1.62147i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 21.5061i | 1.07396i | 0.843594 | + | 0.536981i | \(0.180435\pi\) | ||||
−0.843594 | + | 0.536981i | \(0.819565\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.59476 | − | 1.44311i | 0.378322 | − | 0.0718866i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 48.0846i | 2.38934i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −26.1497 | − | 13.9148i | −1.29619 | − | 0.689730i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14.9792 | −0.740674 | −0.370337 | − | 0.928897i | \(-0.620758\pi\) | ||||
−0.370337 | + | 0.928897i | \(0.620758\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 10.0994 | 0.498169 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 35.4261i | − | 1.74320i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −44.7670 | −2.19753 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 1.83864i | − | 0.0900387i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.9824i | 0.536526i | 0.963346 | + | 0.268263i | \(0.0864496\pi\) | ||||
−0.963346 | + | 0.268263i | \(0.913550\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.77502i | 0.281457i | 0.990048 | + | 0.140729i | \(0.0449445\pi\) | ||||
−0.990048 | + | 0.140729i | \(0.955056\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.64048 | 0.128385 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 47.6721i | − | 2.31244i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 37.4934 | 1.81443 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 23.7639 | + | 7.38323i | 1.14733 | + | 0.356466i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.836564i | 0.0402959i | 0.999797 | + | 0.0201479i | \(0.00641372\pi\) | ||||
−0.999797 | + | 0.0201479i | \(0.993586\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.6220 | 0.654631 | 0.327316 | − | 0.944915i | \(-0.393856\pi\) | ||||
0.327316 | + | 0.944915i | \(0.393856\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 17.3373i | 0.831260i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.71934 | 0.130083 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.41288 | 0.258343 | 0.129171 | − | 0.991622i | \(-0.458768\pi\) | ||||
0.129171 | + | 0.991622i | \(0.458768\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.47602 | 0.165525 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.992538i | 0.0471569i | 0.999722 | + | 0.0235785i | \(0.00750595\pi\) | ||||
−0.999722 | + | 0.0235785i | \(0.992494\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11.6198 | 0.550832 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 25.6505i | − | 1.21323i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 10.2799i | − | 0.485139i | −0.970134 | − | 0.242570i | \(-0.922010\pi\) | ||
0.970134 | − | 0.242570i | \(-0.0779903\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14.3325 | − | 26.9347i | 0.674891 | − | 1.26831i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −18.4391 | −0.866345 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 47.0613 | − | 8.94232i | 2.20627 | − | 0.419222i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 32.0244 | 1.49804 | 0.749019 | − | 0.662548i | \(-0.230525\pi\) | ||||
0.749019 | + | 0.662548i | \(0.230525\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 12.3957 | 0.578582 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −28.2365 | −1.31510 | −0.657552 | − | 0.753409i | \(-0.728408\pi\) | ||||
−0.657552 | + | 0.753409i | \(0.728408\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −23.2418 | −1.08014 | −0.540068 | − | 0.841621i | \(-0.681602\pi\) | ||||
−0.540068 | + | 0.841621i | \(0.681602\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 19.1192 | 0.886632 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 23.1424i | − | 1.07090i | −0.844566 | − | 0.535452i | \(-0.820141\pi\) | ||
0.844566 | − | 0.535452i | \(-0.179859\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 27.9635i | − | 1.29123i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 40.0569i | − | 1.84573i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 16.7020 | − | 31.3877i | 0.767960 | − | 1.44321i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 67.0806i | − | 3.07787i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.90498 | 0.361944 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 22.0062i | − | 1.00549i | −0.864435 | − | 0.502745i | \(-0.832324\pi\) | ||
0.864435 | − | 0.502745i | \(-0.167676\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.01126 | + | 31.6359i | 0.274090 | + | 1.44247i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.49496i | 0.159026i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −11.8721 | −0.539083 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 32.1947 | 1.45888 | 0.729441 | − | 0.684044i | \(-0.239780\pi\) | ||||
0.729441 | + | 0.684044i | \(0.239780\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 42.6860i | 1.93033i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −20.4908 | −0.924736 | −0.462368 | − | 0.886688i | \(-0.653000\pi\) | ||||
−0.462368 | + | 0.886688i | \(0.653000\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.93636 | 0.312398 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 16.6908 | + | 8.88148i | 0.750194 | + | 0.399193i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 29.4821i | − | 1.32246i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.2514 | −0.727511 | −0.363756 | − | 0.931494i | \(-0.618506\pi\) | ||||
−0.363756 | + | 0.931494i | \(0.618506\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 21.4192 | 0.956938 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 33.8633 | 1.50989 | 0.754945 | − | 0.655788i | \(-0.227664\pi\) | ||||
0.754945 | + | 0.655788i | \(0.227664\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −46.7140 | −2.07874 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.92236 | − | 25.1668i | −0.440667 | − | 1.11770i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 17.1485i | − | 0.760092i | −0.924968 | − | 0.380046i | \(-0.875908\pi\) | ||
0.924968 | − | 0.380046i | \(-0.124092\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 36.6541i | 1.62148i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 17.4423 | 0.770097 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −27.4443 | −1.20934 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.09241 | + | 5.81150i | −0.136004 | + | 0.255589i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 17.7032 | 0.777086 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.02281 | 0.395297 | 0.197648 | − | 0.980273i | \(-0.436670\pi\) | ||||
0.197648 | + | 0.980273i | \(0.436670\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −29.1135 | −1.27304 | −0.636522 | − | 0.771259i | \(-0.719628\pi\) | ||||
−0.636522 | + | 0.771259i | \(0.719628\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 86.2137 | 3.76267 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 7.64927i | − | 0.333207i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.7066 | 0.987242 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −15.2001 | −0.659629 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −32.5855 | + | 6.19171i | −1.41144 | + | 0.268193i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 51.7363i | − | 2.23676i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 26.0763 | 1.12528 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.07096 | + | 7.65045i | −0.175349 | + | 0.329528i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −28.4104 | −1.22146 | −0.610730 | − | 0.791839i | \(-0.709124\pi\) | ||||
−0.610730 | + | 0.791839i | \(0.709124\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 4.28013i | − | 0.183678i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 28.9495i | 1.24006i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −37.2991 | −1.59480 | −0.797398 | − | 0.603454i | \(-0.793791\pi\) | ||||
−0.797398 | + | 0.603454i | \(0.793791\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 16.0872i | − | 0.686583i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.76033 | 0.415804 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 14.9630i | − | 0.636293i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 79.6408i | 3.38056i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.61902 | 0.153343 | 0.0766714 | − | 0.997056i | \(-0.475571\pi\) | ||||
0.0766714 | + | 0.997056i | \(0.475571\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −37.9728 | + | 7.21536i | −1.60608 | + | 0.305177i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 11.5665 | − | 21.7366i | 0.488338 | − | 0.917722i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 18.2342 | 0.768481 | 0.384241 | − | 0.923233i | \(-0.374463\pi\) | ||||
0.384241 | + | 0.923233i | \(0.374463\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 56.3902i | 2.37235i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 34.7911i | 1.46109i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 3.94924i | − | 0.165561i | −0.996568 | − | 0.0827803i | \(-0.973620\pi\) | ||
0.996568 | − | 0.0827803i | \(-0.0263800\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.105264 | −0.00440515 | −0.00220258 | − | 0.999998i | \(-0.500701\pi\) | ||||
−0.00220258 | + | 0.999998i | \(0.500701\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −11.6022 | −0.484689 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.23840i | 0.301862i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 21.7958i | − | 0.907372i | −0.891162 | − | 0.453686i | \(-0.850109\pi\) | ||
0.891162 | − | 0.453686i | \(-0.149891\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 11.3713i | 0.472574i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −32.3907 | −1.34379 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.25795 | + | 17.3982i | −0.383425 | + | 0.720562i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.83685 | − | 20.1924i | −0.158634 | − | 0.834854i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −21.9528 | −0.906087 | −0.453044 | − | 0.891488i | \(-0.649662\pi\) | ||||
−0.453044 | + | 0.891488i | \(0.649662\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 10.7635i | − | 0.443502i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 39.0765i | 1.60739i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −15.7973 | −0.648719 | −0.324360 | − | 0.945934i | \(-0.605149\pi\) | ||||
−0.324360 | + | 0.945934i | \(0.605149\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 47.3991i | − | 1.94317i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.93564 | −0.120148 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 19.7920i | − | 0.808679i | −0.914609 | − | 0.404339i | \(-0.867501\pi\) | ||
0.914609 | − | 0.404339i | \(-0.132499\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.8510i | 0.850529i | 0.905069 | + | 0.425265i | \(0.139819\pi\) | ||||
−0.905069 | + | 0.425265i | \(0.860181\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −11.9982 | −0.488604 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −39.0949 | + | 26.3335i | −1.58943 | + | 1.07061i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17.3977 | 0.706149 | 0.353075 | − | 0.935595i | \(-0.385136\pi\) | ||||
0.353075 | + | 0.935595i | \(0.385136\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 12.5442i | 0.508317i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.03073 | − | 1.33594i | 0.284433 | − | 0.0540463i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.35288 | −0.135422 | −0.0677109 | − | 0.997705i | \(-0.521570\pi\) | ||||
−0.0677109 | + | 0.997705i | \(0.521570\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −82.0315 | −3.30783 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 33.8911i | − | 1.36440i | −0.731164 | − | 0.682201i | \(-0.761023\pi\) | ||
0.731164 | − | 0.682201i | \(-0.238977\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.8464 | −0.476148 | −0.238074 | − | 0.971247i | \(-0.576516\pi\) | ||||
−0.238074 | + | 0.971247i | \(0.576516\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.88213 | −0.0755273 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.40739 | 0.336835 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 86.7444 | 3.46978 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 16.2755 | − | 30.5862i | 0.649982 | − | 1.22150i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 31.8629 | 1.27046 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −34.4272 | −1.37053 | −0.685263 | − | 0.728296i | \(-0.740313\pi\) | ||||
−0.685263 | + | 0.728296i | \(0.740313\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 10.5970i | 0.421191i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 74.8436i | 2.97008i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.25549 | − | 1.75867i | 0.366716 | − | 0.0696812i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −12.6498 | −0.500418 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.98522 | 0.354895 | 0.177447 | − | 0.984130i | \(-0.443216\pi\) | ||||
0.177447 | + | 0.984130i | \(0.443216\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 44.5317 | 1.75616 | 0.878080 | − | 0.478514i | \(-0.158824\pi\) | ||||
0.878080 | + | 0.478514i | \(0.158824\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −95.5934 | −3.76399 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 19.3528i | 0.760837i | 0.924814 | + | 0.380419i | \(0.124220\pi\) | ||||
−0.924814 | + | 0.380419i | \(0.875780\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 17.8017 | − | 33.4543i | 0.698778 | − | 1.31320i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 13.8335 | 0.542178 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 48.6327 | 1.90314 | 0.951572 | − | 0.307425i | \(-0.0994672\pi\) | ||||
0.951572 | + | 0.307425i | \(0.0994672\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 12.0485i | − | 0.470774i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 15.7270 | 0.613569 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.3530 | 0.714932 | 0.357466 | − | 0.933926i | \(-0.383641\pi\) | ||||
0.357466 | + | 0.933926i | \(0.383641\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.88425i | 0.151080i | 0.997143 | + | 0.0755399i | \(0.0240680\pi\) | ||||
−0.997143 | + | 0.0755399i | \(0.975932\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −26.2969 | + | 4.99679i | −1.02129 | + | 0.194059i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 66.6965i | − | 2.58638i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.05320 | −0.0407800 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 30.5585i | − | 1.18146i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 35.4066 | + | 18.8406i | 1.36686 | + | 0.727331i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 42.2955i | − | 1.63037i | −0.579201 | − | 0.815185i | \(-0.696635\pi\) | ||
0.579201 | − | 0.815185i | \(-0.303365\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 46.4284i | 1.78703i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 16.1036i | − | 0.618913i | −0.950914 | − | 0.309457i | \(-0.899853\pi\) | ||
0.950914 | − | 0.309457i | \(-0.100147\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.58990 | −0.329650 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.66643 | 0.293778 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −14.9120 | −0.570591 | −0.285295 | − | 0.958440i | \(-0.592092\pi\) | ||||
−0.285295 | + | 0.958440i | \(0.592092\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 20.7972 | 0.794619 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −49.8456 | −1.90173 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 21.0483 | − | 3.99948i | 0.801878 | − | 0.152368i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 39.5014 | 1.50270 | 0.751352 | − | 0.659902i | \(-0.229402\pi\) | ||||
0.751352 | + | 0.659902i | \(0.229402\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 12.0764 | + | 6.42610i | 0.458745 | + | 0.244107i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 3.78621i | − | 0.143619i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 32.8194i | 1.24312i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 41.0395 | 1.55226 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.87079i | 0.146198i | 0.997325 | + | 0.0730989i | \(0.0232889\pi\) | ||||
−0.997325 | + | 0.0730989i | \(0.976711\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 44.8351 | 1.69099 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 17.6993 | 0.666594 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −33.7994 | −1.27116 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.99859i | 0.112614i | 0.998413 | + | 0.0563072i | \(0.0179326\pi\) | ||||
−0.998413 | + | 0.0563072i | \(0.982067\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.42013 | −0.240774 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.16145i | 0.0434965i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 48.9355 | + | 15.2038i | 1.83008 | + | 0.568591i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −12.4877 | −0.466362 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 12.8814i | − | 0.480397i | −0.970724 | − | 0.240198i | \(-0.922787\pi\) | ||
0.970724 | − | 0.240198i | \(-0.0772125\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −19.8570 | −0.739514 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 32.5477i | − | 1.21046i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 25.9803i | 0.964884i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 51.4961i | − | 1.90989i | −0.296790 | − | 0.954943i | \(-0.595916\pi\) | ||
0.296790 | − | 0.954943i | \(-0.404084\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −6.76316 | −0.250488 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 38.2453i | 1.41455i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −25.9838 | −0.959734 | −0.479867 | − | 0.877341i | \(-0.659315\pi\) | ||||
−0.479867 | + | 0.877341i | \(0.659315\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 23.3000 | 0.859432 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 14.0517 | − | 26.4071i | 0.517602 | − | 0.972717i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 20.9635i | − | 0.771155i | −0.922675 | − | 0.385578i | \(-0.874002\pi\) | ||
0.922675 | − | 0.385578i | \(-0.125998\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −37.0031 | + | 7.03111i | −1.35934 | + | 0.258294i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 3.51692i | − | 0.129023i | −0.997917 | − | 0.0645116i | \(-0.979451\pi\) | ||
0.997917 | − | 0.0645116i | \(-0.0205490\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 52.8204i | − | 1.93519i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 13.8977i | 0.508492i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 37.4333i | − | 1.36778i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.03675i | 0.183794i | 0.995769 | + | 0.0918968i | \(0.0292930\pi\) | ||||
−0.995769 | + | 0.0918968i | \(0.970707\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −16.7541 | −0.610554 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −37.9705 | −1.38189 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29.1106 | 1.05804 | 0.529022 | − | 0.848608i | \(-0.322559\pi\) | ||||
0.529022 | + | 0.848608i | \(0.322559\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.75623 | + | 3.30043i | −0.0637470 | + | 0.119798i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15.6962 | −0.568988 | −0.284494 | − | 0.958678i | \(-0.591826\pi\) | ||||
−0.284494 | + | 0.958678i | \(0.591826\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 20.9461i | 0.758299i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −20.3373 | −0.735298 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −40.4729 | + | 7.69043i | −1.46139 | + | 0.277685i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27.0006 | 0.973665 | 0.486833 | − | 0.873495i | \(-0.338152\pi\) | ||||
0.486833 | + | 0.873495i | \(0.338152\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 37.9570i | 1.36699i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 10.1763i | − | 0.366016i | −0.983111 | − | 0.183008i | \(-0.941417\pi\) | ||
0.983111 | − | 0.183008i | \(-0.0585835\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 28.6505 | 1.02916 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 57.6232i | 2.06722i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 46.1810i | 1.65461i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.8149 | − | 27.8412i | 0.530118 | − | 0.996237i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.75540 | −0.241418 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 82.4868i | − | 2.94408i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 15.9052i | − | 0.566960i | −0.958978 | − | 0.283480i | \(-0.908511\pi\) | ||
0.958978 | − | 0.283480i | \(-0.0914890\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 44.1793i | 1.57282i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 40.8005i | 1.45070i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.13922 | − | 42.8348i | −0.289032 | − | 1.52111i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 52.9875 | 1.87927 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −10.8184 | −0.383207 | −0.191603 | − | 0.981472i | \(-0.561369\pi\) | ||||
−0.191603 | + | 0.981472i | \(0.561369\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 7.08119i | − | 0.250514i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 3.60733i | − | 0.127459i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −18.4188 | + | 34.6140i | −0.649984 | + | 1.22150i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.19695i | 0.253659i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 46.7089i | − | 1.64423i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 17.8199i | 0.626515i | 0.949668 | + | 0.313258i | \(0.101420\pi\) | ||||
−0.949668 | + | 0.313258i | \(0.898580\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 21.4177i | − | 0.752078i | −0.926604 | − | 0.376039i | \(-0.877286\pi\) | ||
0.926604 | − | 0.376039i | \(-0.122714\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 39.6347 | 1.39005 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 87.9008i | 3.07903i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 53.8160i | 1.88278i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.77611 | − | 14.6100i | −0.0970051 | − | 0.510515i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −23.3726 | −0.815710 | −0.407855 | − | 0.913047i | \(-0.633723\pi\) | ||||
−0.407855 | + | 0.913047i | \(0.633723\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.90745i | 0.205921i | 0.994685 | + | 0.102960i | \(0.0328315\pi\) | ||||
−0.994685 | + | 0.102960i | \(0.967169\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 81.4152 | + | 43.3226i | 2.83451 | + | 1.50830i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 51.0312i | − | 1.77453i | −0.461260 | − | 0.887265i | \(-0.652603\pi\) | ||
0.461260 | − | 0.887265i | \(-0.347397\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25.6839 | 0.892039 | 0.446020 | − | 0.895023i | \(-0.352841\pi\) | ||||
0.446020 | + | 0.895023i | \(0.352841\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 60.6012 | 2.10223 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 9.32192i | − | 0.322985i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 44.1072 | 1.52639 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.44972i | 0.257500i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8.40722 | −0.290249 | −0.145125 | − | 0.989413i | \(-0.546358\pi\) | ||||
−0.145125 | + | 0.989413i | \(0.546358\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.2198 | 0.869649 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 32.6719i | 1.12528i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −20.4325 | − | 51.8245i | −0.702900 | − | 1.78282i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −28.2867 | + | 19.0533i | −0.971943 | + | 0.654679i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 44.0735i | − | 1.51260i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.83798 | −0.165844 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.47719 | 0.119057 | 0.0595284 | − | 0.998227i | \(-0.481040\pi\) | ||||
0.0595284 | + | 0.998227i | \(0.481040\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −28.6172 | −0.978688 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 56.3032i | 1.92328i | 0.274311 | + | 0.961641i | \(0.411550\pi\) | ||||
−0.274311 | + | 0.961641i | \(0.588450\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 36.1680i | 1.23404i | 0.786949 | + | 0.617019i | \(0.211660\pi\) | ||||
−0.786949 | + | 0.617019i | \(0.788340\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −59.3530 | −2.02274 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −26.9972 | −0.918995 | −0.459498 | − | 0.888179i | \(-0.651971\pi\) | ||||
−0.459498 | + | 0.888179i | \(0.651971\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 36.4552 | 1.23951 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 8.89032i | − | 0.301931i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.51896 | − | 14.1302i | 0.255063 | − | 0.479335i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −31.9472 | + | 6.07042i | −1.08249 | + | 0.205688i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.68564i | 0.124740i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 111.105 | 3.75602 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −25.3482 | −0.855949 | −0.427974 | − | 0.903791i | \(-0.640773\pi\) | ||||
−0.427974 | + | 0.903791i | \(0.640773\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 31.5622i | 1.06457i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −14.2695 | −0.480752 | −0.240376 | − | 0.970680i | \(-0.577271\pi\) | ||||
−0.240376 | + | 0.970680i | \(0.577271\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 55.3201i | − | 1.86167i | −0.365442 | − | 0.930834i | \(-0.619082\pi\) | ||
0.365442 | − | 0.930834i | \(-0.380918\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −101.887 | −3.42491 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −54.8398 | −1.84134 | −0.920670 | − | 0.390341i | \(-0.872357\pi\) | ||||
−0.920670 | + | 0.390341i | \(0.872357\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 54.1523i | 1.81621i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −17.4826 | + | 32.8547i | −0.585689 | + | 1.10067i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 9.96413i | − | 0.333437i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 53.6974 | 1.79491 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.99285 | − | 0.758699i | 0.133317 | − | 0.0253322i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.16870i | 0.139034i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 21.1994i | − | 0.706255i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −69.1656 | −2.30169 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 8.81381i | − | 0.292981i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 37.6971i | − | 1.25171i | −0.779939 | − | 0.625855i | \(-0.784750\pi\) | ||
0.779939 | − | 0.625855i | \(-0.215250\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 14.5022i | 0.481007i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 36.3316i | − | 1.20372i | −0.798602 | − | 0.601859i | \(-0.794427\pi\) | ||
0.798602 | − | 0.601859i | \(-0.205573\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −30.5879 | − | 16.2764i | −1.01231 | − | 0.538670i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 107.833i | − | 3.56486i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 8.71757i | − | 0.287879i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.5756 | 0.414830 | 0.207415 | − | 0.978253i | \(-0.433495\pi\) | ||||
0.207415 | + | 0.978253i | \(0.433495\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.63782 | −0.152821 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −33.6822 | + | 6.40010i | −1.10866 | + | 0.210662i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 119.343i | 3.92399i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8.51997i | 0.279833i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 23.2242i | 0.761962i | 0.924583 | + | 0.380981i | \(0.124414\pi\) | ||||
−0.924583 | + | 0.380981i | \(0.875586\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 13.1171i | − | 0.429896i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 50.8182 | 1.66371 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 23.8182 | − | 44.7609i | 0.778938 | − | 1.46384i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 51.5572i | − | 1.68430i | −0.539242 | − | 0.842151i | \(-0.681289\pi\) | ||
0.539242 | − | 0.842151i | \(-0.318711\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.04146i | 0.295057i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 11.7867 | 0.384236 | 0.192118 | − | 0.981372i | \(-0.438464\pi\) | ||||
0.192118 | + | 0.981372i | \(0.438464\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 4.98321i | − | 0.162276i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 46.1626i | 1.50167i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 35.4878 | 1.15320 | 0.576599 | − | 0.817027i | \(-0.304379\pi\) | ||||
0.576599 | + | 0.817027i | \(0.304379\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 41.8758 | − | 7.95701i | 1.35935 | − | 0.258295i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 19.9038 | 0.645425 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 27.8984i | 0.903718i | 0.892089 | + | 0.451859i | \(0.149239\pi\) | ||||
−0.892089 | + | 0.451859i | \(0.850761\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −23.8917 | −0.773117 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −6.30350 | + | 11.8460i | −0.203763 | + | 0.382928i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 15.0476 | 0.485911 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.4028 | −0.851705 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −16.0614 | −0.517570 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 23.4162i | 0.753793i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 58.2565i | 1.87340i | 0.350130 | + | 0.936701i | \(0.386137\pi\) | ||||
−0.350130 | + | 0.936701i | \(0.613863\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 37.2687i | 1.19724i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 25.5721i | 0.820648i | 0.911940 | + | 0.410324i | \(0.134584\pi\) | ||||
−0.911940 | + | 0.410324i | \(0.865416\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 2.73947i | − | 0.0878233i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −18.7156 | − | 98.4958i | −0.599379 | − | 3.15439i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 19.5165i | 0.624387i | 0.950019 | + | 0.312193i | \(0.101064\pi\) | ||||
−0.950019 | + | 0.312193i | \(0.898936\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.93945 | + | 4.22474i | 0.253746 | + | 0.135023i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.98726 | 0.286941 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.72839 | 0.0870220 | 0.0435110 | − | 0.999053i | \(-0.486146\pi\) | ||||
0.0435110 | + | 0.999053i | \(0.486146\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 80.4678i | 2.56392i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 12.8061 | 0.407624 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 5.80706i | − | 0.184654i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 46.4565i | 1.47574i | 0.674943 | + | 0.737870i | \(0.264168\pi\) | ||||
−0.674943 | + | 0.737870i | \(0.735832\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 40.9730i | 1.30024i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.04519 | −0.191646 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 23.9559i | 0.758692i | 0.925255 | + | 0.379346i | \(0.123851\pi\) | ||||
−0.925255 | + | 0.379346i | \(0.876149\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −31.0317 | −0.981799 |
(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 | 2288.2.b.c.2287.9 | ✓ | 56 | |
4.3 | odd | 2 | inner | 2288.2.b.c.2287.46 | yes | 56 | |
11.10 | odd | 2 | inner | 2288.2.b.c.2287.10 | yes | 56 | |
13.12 | even | 2 | inner | 2288.2.b.c.2287.12 | yes | 56 | |
44.43 | even | 2 | inner | 2288.2.b.c.2287.45 | yes | 56 | |
52.51 | odd | 2 | inner | 2288.2.b.c.2287.47 | yes | 56 | |
143.142 | odd | 2 | inner | 2288.2.b.c.2287.11 | yes | 56 | |
572.571 | even | 2 | inner | 2288.2.b.c.2287.48 | yes | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2288.2.b.c.2287.9 | ✓ | 56 | 1.1 | even | 1 | trivial | |
2288.2.b.c.2287.10 | yes | 56 | 11.10 | odd | 2 | inner | |
2288.2.b.c.2287.11 | yes | 56 | 143.142 | odd | 2 | inner | |
2288.2.b.c.2287.12 | yes | 56 | 13.12 | even | 2 | inner | |
2288.2.b.c.2287.45 | yes | 56 | 44.43 | even | 2 | inner | |
2288.2.b.c.2287.46 | yes | 56 | 4.3 | odd | 2 | inner | |
2288.2.b.c.2287.47 | yes | 56 | 52.51 | odd | 2 | inner | |
2288.2.b.c.2287.48 | yes | 56 | 572.571 | even | 2 | inner |