Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [552,2,Mod(137,552)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(552, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("552.137");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 552 = 2^{3} \cdot 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 552.m (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.40774219157\) |
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: | \( x^{16} - 2x^{14} - 2x^{12} + 8x^{10} - 8x^{8} + 32x^{6} - 32x^{4} - 128x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{18} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 137.14 | ||
Root | \(1.39495 - 0.232632i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 552.137 |
Dual form | 552.2.m.b.137.16 |
$q$-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 \(\left(\mathbb{Z}/552\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(185\) | \(277\) | \(415\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 1.72779 | − | 0.121372i | 0.997542 | − | 0.0700743i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.32463 | 1.03961 | 0.519804 | − | 0.854286i | \(-0.326005\pi\) | ||||
0.519804 | + | 0.854286i | \(0.326005\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 3.25516i | − | 1.23034i | −0.788396 | − | 0.615168i | \(-0.789088\pi\) | ||
0.788396 | − | 0.615168i | \(-0.210912\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.97054 | − | 0.419412i | 0.990179 | − | 0.139804i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.65123 | −0.799376 | −0.399688 | − | 0.916651i | \(-0.630882\pi\) | ||||
−0.399688 | + | 0.916651i | \(0.630882\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.62598 | 0.450967 | 0.225483 | − | 0.974247i | \(-0.427604\pi\) | ||||
0.225483 | + | 0.974247i | \(0.427604\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.01649 | − | 0.282146i | 1.03705 | − | 0.0728498i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.32463 | −0.563806 | −0.281903 | − | 0.959443i | \(-0.590966\pi\) | ||||
−0.281903 | + | 0.959443i | \(0.590966\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 2.69087i | − | 0.617328i | −0.951171 | − | 0.308664i | \(-0.900118\pi\) | ||
0.951171 | − | 0.308664i | \(-0.0998819\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.395086 | − | 5.62425i | −0.0862149 | − | 1.22731i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.65123 | + | 3.99637i | −0.552820 | + | 0.833301i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.403920 | 0.0807840 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.08157 | − | 1.08520i | 0.977948 | − | 0.208847i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.83882i | 0.898547i | 0.893394 | + | 0.449274i | \(0.148317\pi\) | ||||
−0.893394 | + | 0.449274i | \(0.851683\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.544414 | 0.0977796 | 0.0488898 | − | 0.998804i | \(-0.484432\pi\) | ||||
0.0488898 | + | 0.998804i | \(0.484432\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.58078 | + | 0.321786i | −0.797411 | + | 0.0560157i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 7.56706i | − | 1.27907i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.29677i | 0.213187i | 0.994303 | + | 0.106593i | \(0.0339943\pi\) | ||||
−0.994303 | + | 0.106593i | \(0.966006\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.80936 | − | 0.197349i | 0.449858 | − | 0.0316012i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.32431i | 0.831518i | 0.909475 | + | 0.415759i | \(0.136484\pi\) | ||||
−0.909475 | + | 0.415759i | \(0.863516\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12.6426i | 1.92798i | 0.265942 | + | 0.963989i | \(0.414317\pi\) | ||||
−0.265942 | + | 0.963989i | \(0.585683\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.90541 | − | 0.974980i | 1.02940 | − | 0.145341i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 3.32431i | − | 0.484901i | −0.970164 | − | 0.242450i | \(-0.922049\pi\) | ||
0.970164 | − | 0.242450i | \(-0.0779512\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.59608 | −0.513726 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.01649 | + | 0.282146i | −0.562420 | + | 0.0395083i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.2187 | 1.67836 | 0.839181 | − | 0.543852i | \(-0.183035\pi\) | ||||
0.839181 | + | 0.543852i | \(0.183035\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.16314 | −0.831037 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.326597 | − | 4.64927i | −0.0432588 | − | 0.615810i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 13.3967i | − | 1.74410i | −0.489420 | − | 0.872048i | \(-0.662791\pi\) | ||
0.489420 | − | 0.872048i | \(-0.337209\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.82314i | 1.12969i | 0.825198 | + | 0.564844i | \(0.191064\pi\) | ||||
−0.825198 | + | 0.564844i | \(0.808936\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.36525 | − | 9.66958i | −0.172006 | − | 1.21825i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.77981 | 0.468828 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 8.63690i | − | 1.05517i | −0.849504 | − | 0.527583i | \(-0.823098\pi\) | ||
0.849504 | − | 0.527583i | \(-0.176902\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.09573 | + | 7.22669i | −0.493068 | + | 0.869991i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 1.43490i | − | 0.170292i | −0.996368 | − | 0.0851459i | \(-0.972864\pi\) | ||
0.996368 | − | 0.0851459i | \(-0.0271356\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.85225 | −1.03608 | −0.518039 | − | 0.855357i | \(-0.673338\pi\) | ||||
−0.518039 | + | 0.855357i | \(0.673338\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.697890 | − | 0.0490247i | 0.0805854 | − | 0.00566088i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.63018i | 0.983501i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.85439i | 1.10871i | 0.832282 | + | 0.554353i | \(0.187034\pi\) | ||||
−0.832282 | + | 0.554353i | \(0.812966\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.64819 | − | 2.49176i | 0.960910 | − | 0.276862i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −15.6719 | −1.72021 | −0.860106 | − | 0.510115i | \(-0.829603\pi\) | ||||
−0.860106 | + | 0.510115i | \(0.829603\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.40392 | −0.586137 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.587299 | + | 8.36049i | 0.0629651 | + | 0.896338i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.14974 | 0.969871 | 0.484935 | − | 0.874550i | \(-0.338843\pi\) | ||||
0.484935 | + | 0.874550i | \(0.338843\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 5.29284i | − | 0.554840i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.940635 | − | 0.0660767i | 0.0975393 | − | 0.00685184i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 6.25529i | − | 0.641779i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 10.1199i | − | 1.02752i | −0.857934 | − | 0.513761i | \(-0.828252\pi\) | ||
0.857934 | − | 0.513761i | \(-0.171748\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −7.87558 | + | 1.11196i | −0.791525 | + | 0.111756i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.1631i | 1.01127i | 0.862747 | + | 0.505635i | \(0.168742\pi\) | ||||
−0.862747 | + | 0.505635i | \(0.831258\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.60197i | 0.256380i | 0.991750 | + | 0.128190i | \(0.0409167\pi\) | ||||
−0.991750 | + | 0.128190i | \(0.959083\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.918431 | − | 13.0743i | −0.0896297 | − | 1.27592i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.6842 | 1.03288 | 0.516440 | − | 0.856323i | \(-0.327257\pi\) | ||||
0.516440 | + | 0.856323i | \(0.327257\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.0803i | 1.06130i | 0.847591 | + | 0.530651i | \(0.178052\pi\) | ||||
−0.847591 | + | 0.530651i | \(0.821948\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.157391 | + | 2.24054i | 0.0149389 | + | 0.212663i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.05711 | −0.287588 | −0.143794 | − | 0.989608i | \(-0.545930\pi\) | ||||
−0.143794 | + | 0.989608i | \(0.545930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.16314 | + | 9.29010i | −0.574716 | + | 0.866306i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.83004 | − | 0.681957i | 0.446538 | − | 0.0630470i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.56706i | 0.693671i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.97098 | −0.360998 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.646224 | + | 9.19931i | 0.0582681 | + | 0.829474i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.6842 | −0.955624 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.17460 | −0.814114 | −0.407057 | − | 0.913403i | \(-0.633445\pi\) | ||||
−0.407057 | + | 0.913403i | \(0.633445\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.53446 | + | 21.8438i | 0.135102 | + | 1.92324i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 15.0361i | − | 1.31371i | −0.754018 | − | 0.656854i | \(-0.771887\pi\) | ||
0.754018 | − | 0.656854i | \(-0.228113\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.75922 | −0.759521 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 11.8128 | − | 2.52269i | 1.01668 | − | 0.217118i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.18373 | −0.528311 | −0.264156 | − | 0.964480i | \(-0.585093\pi\) | ||||
−0.264156 | + | 0.964480i | \(0.585093\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.23440 | −0.613614 | −0.306807 | − | 0.951772i | \(-0.599261\pi\) | ||||
−0.306807 | + | 0.951772i | \(0.599261\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.403479 | − | 5.74373i | −0.0339791 | − | 0.483709i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.31086 | −0.360492 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.2485i | 0.934136i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.21328 | + | 0.436464i | −0.512463 | + | 0.0359990i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −11.5655 | −0.947480 | −0.473740 | − | 0.880665i | \(-0.657096\pi\) | ||||
−0.473740 | + | 0.880665i | \(0.657096\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.426564 | 0.0347133 | 0.0173566 | − | 0.999849i | \(-0.494475\pi\) | ||||
0.0173566 | + | 0.999849i | \(0.494475\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.90541 | + | 0.974980i | −0.558269 | + | 0.0788224i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.26556 | 0.101652 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 9.95173i | − | 0.794234i | −0.917768 | − | 0.397117i | \(-0.870011\pi\) | ||
0.917768 | − | 0.397117i | \(-0.129989\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 21.1113 | − | 1.48301i | 1.67424 | − | 0.117610i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 13.0088 | + | 8.63018i | 1.02524 | + | 0.680154i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −15.5589 | −1.21867 | −0.609334 | − | 0.792913i | \(-0.708563\pi\) | ||||
−0.609334 | + | 0.792913i | \(0.708563\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −10.6486 | + | 0.748034i | −0.828995 | + | 0.0582344i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 15.9927i | 1.23756i | 0.785566 | + | 0.618778i | \(0.212372\pi\) | ||||
−0.785566 | + | 0.618778i | \(0.787628\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.3562 | −0.796629 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.12858 | − | 7.99333i | −0.0863050 | − | 0.611265i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 12.9710i | − | 0.986165i | −0.869982 | − | 0.493083i | \(-0.835870\pi\) | ||
0.869982 | − | 0.493083i | \(-0.164130\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 1.31482i | − | 0.0993914i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.62598 | − | 23.1467i | −0.122216 | − | 1.73981i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 6.35334i | − | 0.474871i | −0.971403 | − | 0.237435i | \(-0.923693\pi\) | ||
0.971403 | − | 0.237435i | \(-0.0763068\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 2.42535i | − | 0.180275i | −0.995929 | − | 0.0901374i | \(-0.971269\pi\) | ||
0.995929 | − | 0.0901374i | \(-0.0287306\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.07088 | + | 15.2446i | 0.0791621 | + | 1.12691i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.01450i | 0.221631i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.16314 | 0.450693 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.53250 | − | 16.5413i | −0.256951 | − | 1.20320i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.26556 | 0.0915729 | 0.0457865 | − | 0.998951i | \(-0.485421\pi\) | ||||
0.0457865 | + | 0.998951i | \(0.485421\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.7601 | 0.918492 | 0.459246 | − | 0.888309i | \(-0.348120\pi\) | ||||
0.459246 | + | 0.888309i | \(0.348120\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.53074 | − | 0.458765i | 0.467676 | − | 0.0328528i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 19.2914i | − | 1.37445i | −0.726444 | − | 0.687226i | \(-0.758828\pi\) | ||
0.726444 | − | 0.687226i | \(-0.241172\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.0640i | 1.35141i | 0.737171 | + | 0.675706i | \(0.236161\pi\) | ||||
−0.737171 | + | 0.675706i | \(0.763839\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.04828 | − | 14.9228i | −0.0739400 | − | 1.05257i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 15.7512 | 1.10551 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12.3771i | 0.864453i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.19945 | + | 12.9833i | −0.430892 | + | 0.902404i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7.13412i | 0.493477i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 26.4525 | 1.82107 | 0.910534 | − | 0.413435i | \(-0.135671\pi\) | ||||
0.910534 | + | 0.413435i | \(0.135671\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.174158 | − | 2.47922i | −0.0119331 | − | 0.169873i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 29.3894i | 2.00434i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 1.77216i | − | 0.120302i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −15.2949 | + | 1.07442i | −1.03353 | + | 0.0726024i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.77981 | −0.254258 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.1051 | 1.07848 | 0.539238 | − | 0.842153i | \(-0.318712\pi\) | ||||
0.539238 | + | 0.842153i | \(0.318712\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.19986 | − | 0.169409i | 0.0799906 | − | 0.0112939i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −22.5547 | −1.49701 | −0.748503 | − | 0.663131i | \(-0.769227\pi\) | ||||
−0.748503 | + | 0.663131i | \(0.769227\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 19.2503i | − | 1.27209i | −0.771651 | − | 0.636047i | \(-0.780569\pi\) | ||
0.771651 | − | 0.636047i | \(-0.219431\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.04746 | + | 14.9112i | 0.0689181 | + | 0.981083i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 20.2768i | − | 1.32838i | −0.747564 | − | 0.664190i | \(-0.768776\pi\) | ||
0.747564 | − | 0.664190i | \(-0.231224\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 7.72781i | − | 0.504107i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.19605 | + | 17.0263i | 0.0776918 | + | 1.10598i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.53607i | 0.487468i | 0.969842 | + | 0.243734i | \(0.0783724\pi\) | ||||
−0.969842 | + | 0.243734i | \(0.921628\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 1.94996i | − | 0.125608i | −0.998026 | − | 0.0628040i | \(-0.979996\pi\) | ||
0.998026 | − | 0.0628040i | \(-0.0200043\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.6398 | − | 5.35490i | 0.939147 | − | 0.343517i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −8.35957 | −0.534073 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 4.37531i | − | 0.278394i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −27.0778 | + | 1.90213i | −1.71598 | + | 0.120543i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −24.9704 | −1.57612 | −0.788059 | − | 0.615599i | \(-0.788914\pi\) | ||||
−0.788059 | + | 0.615599i | \(0.788914\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.02902 | − | 10.5953i | 0.441911 | − | 0.666121i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −9.33686 | + | 0.655886i | −0.584697 | + | 0.0410732i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 16.4980i | 1.02912i | 0.857455 | + | 0.514559i | \(0.172045\pi\) | ||||
−0.857455 | + | 0.514559i | \(0.827955\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.22118 | 0.262291 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.02946 | + | 14.3739i | 0.125621 | + | 0.889723i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 29.0866 | 1.79356 | 0.896778 | − | 0.442481i | \(-0.145902\pi\) | ||||
0.896778 | + | 0.442481i | \(0.145902\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 28.4039 | 1.74484 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 15.8089 | − | 1.11052i | 0.967486 | − | 0.0679630i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 27.4729i | − | 1.67505i | −0.546396 | − | 0.837527i | \(-0.684001\pi\) | ||
0.546396 | − | 0.837527i | \(-0.315999\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.9420 | 1.08990 | 0.544948 | − | 0.838470i | \(-0.316549\pi\) | ||||
0.544948 | + | 0.838470i | \(0.316549\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.642404 | − | 9.14493i | −0.0388800 | − | 0.553476i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.07088 | −0.0645768 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 21.2964 | 1.27958 | 0.639788 | − | 0.768552i | \(-0.279022\pi\) | ||||
0.639788 | + | 0.768552i | \(0.279022\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.61720 | − | 0.228334i | 0.0968194 | − | 0.0136700i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 23.0398 | 1.37444 | 0.687221 | − | 0.726449i | \(-0.258830\pi\) | ||||
0.687221 | + | 0.726449i | \(0.258830\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 16.6483i | − | 0.989638i | −0.868996 | − | 0.494819i | \(-0.835234\pi\) | ||
0.868996 | − | 0.494819i | \(-0.164766\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.759218 | − | 10.8078i | −0.0449722 | − | 0.640201i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 17.3315 | 1.02305 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.5961 | −0.682122 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.22828 | − | 17.4851i | −0.0720028 | − | 1.02500i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.9511 | 0.756613 | 0.378307 | − | 0.925680i | \(-0.376506\pi\) | ||||
0.378307 | + | 0.925680i | \(0.376506\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 31.1423i | − | 1.81318i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −13.4724 | + | 2.87711i | −0.781749 | + | 0.166947i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.31086 | + | 6.49803i | −0.249303 | + | 0.375791i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 41.1537 | 2.37206 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.23352 | + | 17.5598i | 0.0708640 | + | 1.00878i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 20.5106i | 1.17443i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.00000 | 0.228292 | 0.114146 | − | 0.993464i | \(-0.463587\pi\) | ||||
0.114146 | + | 0.993464i | \(0.463587\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.315807 | + | 4.49566i | 0.0179656 | + | 0.255749i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 4.29529i | − | 0.243564i | −0.992557 | − | 0.121782i | \(-0.961139\pi\) | ||
0.992557 | − | 0.121782i | \(-0.0388608\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 24.9127i | − | 1.40815i | −0.710126 | − | 0.704075i | \(-0.751362\pi\) | ||
0.710126 | − | 0.704075i | \(-0.248638\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.17372 | − | 22.4782i | −0.178819 | − | 1.26650i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 23.3553i | − | 1.31176i | −0.754863 | − | 0.655882i | \(-0.772297\pi\) | ||
0.754863 | − | 0.655882i | \(-0.227703\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 12.8288i | − | 0.718277i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 18.4601 | − | 1.29677i | 1.03034 | − | 0.0723784i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.25529i | 0.348053i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.656767 | 0.0364309 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.34484 | + | 19.1445i | 0.0743700 | + | 1.05869i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −10.8212 | −0.596591 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.48461 | 0.136566 | 0.0682832 | − | 0.997666i | \(-0.478248\pi\) | ||||
0.0682832 | + | 0.997666i | \(0.478248\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.543879 | + | 3.85209i | 0.0298044 | + | 0.211093i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 20.0776i | − | 1.09696i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 10.6049i | − | 0.577687i | −0.957376 | − | 0.288843i | \(-0.906729\pi\) | ||
0.957376 | − | 0.288843i | \(-0.0932707\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.28205 | + | 0.371048i | −0.286881 | + | 0.0201526i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.44337 | −0.0781627 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 11.0803i | − | 0.598281i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −9.52107 | + | 16.7994i | −0.512597 | + | 0.904449i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 11.2190i | − | 0.602268i | −0.953582 | − | 0.301134i | \(-0.902635\pi\) | ||
0.953582 | − | 0.301134i | \(-0.0973651\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −30.1383 | −1.61327 | −0.806634 | − | 0.591052i | \(-0.798713\pi\) | ||||
−0.806634 | + | 0.591052i | \(0.798713\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.26254 | − | 1.76451i | 0.441022 | − | 0.0941828i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 34.9874i | 1.86219i | 0.364772 | + | 0.931097i | \(0.381147\pi\) | ||||
−0.364772 | + | 0.931097i | \(0.618853\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 3.33563i | − | 0.177037i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.918431 | + | 13.0743i | 0.0486085 | + | 0.691966i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 23.6256 | 1.24691 | 0.623455 | − | 0.781859i | \(-0.285728\pi\) | ||||
0.623455 | + | 0.781859i | \(0.285728\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.7592 | 0.618906 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6.86103 | + | 0.481967i | −0.360111 | + | 0.0252967i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −20.5782 | −1.07711 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.19550i | 0.271203i | 0.990763 | + | 0.135601i | \(0.0432967\pi\) | ||||
−0.990763 | + | 0.135601i | \(0.956703\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.23308 | + | 15.8161i | 0.116250 | + | 0.823352i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 39.7737i | − | 2.06495i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 31.7859i | 1.64581i | 0.568178 | + | 0.822906i | \(0.307648\pi\) | ||||
−0.568178 | + | 0.822906i | \(0.692352\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −18.4601 | + | 1.29677i | −0.953275 | + | 0.0669647i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.86785i | 0.405215i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.2475i | 1.19414i | 0.802187 | + | 0.597072i | \(0.203670\pi\) | ||||
−0.802187 | + | 0.597072i | \(0.796330\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −15.8518 | + | 1.11354i | −0.812113 | + | 0.0570485i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −14.6010 | −0.746076 | −0.373038 | − | 0.927816i | \(-0.621684\pi\) | ||||
−0.373038 | + | 0.927816i | \(0.621684\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 20.0620i | 1.02245i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.30246 | + | 37.5553i | 0.269539 | + | 1.90904i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 23.8300 | 1.20823 | 0.604115 | − | 0.796897i | \(-0.293527\pi\) | ||||
0.604115 | + | 0.796897i | \(0.293527\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.16314 | − | 9.29010i | 0.311683 | − | 0.469820i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.82496 | − | 25.9792i | −0.0920571 | − | 1.31048i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 22.9078i | 1.15262i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.82323 | −0.292259 | −0.146130 | − | 0.989265i | \(-0.546682\pi\) | ||||
−0.146130 | + | 0.989265i | \(0.546682\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −15.1341 | + | 1.06313i | −0.757653 | + | 0.0532229i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.9985 | 0.798926 | 0.399463 | − | 0.916749i | \(-0.369197\pi\) | ||||
0.399463 | + | 0.916749i | \(0.369197\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.885208 | 0.0440953 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 20.1039 | − | 5.79243i | 0.998969 | − | 0.287828i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 3.43802i | − | 0.170417i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.21088 | −0.208215 | −0.104107 | − | 0.994566i | \(-0.533199\pi\) | ||||
−0.104107 | + | 0.994566i | \(0.533199\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.6842 | + | 0.750533i | −0.527013 | + | 0.0370211i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −43.6083 | −2.14582 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −36.4314 | −1.78835 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −12.4996 | + | 0.878056i | −0.612106 | + | 0.0429986i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.80139 | −0.185710 | −0.0928551 | − | 0.995680i | \(-0.529599\pi\) | ||||
−0.0928551 | + | 0.995680i | \(0.529599\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 29.3702i | − | 1.43141i | −0.698400 | − | 0.715707i | \(-0.746105\pi\) | ||
0.698400 | − | 0.715707i | \(-0.253895\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.39426 | − | 9.87500i | −0.0677911 | − | 0.480139i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.938966 | −0.0455465 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 28.7208 | 1.38990 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7.44827 | + | 0.523218i | −0.359606 | + | 0.0252612i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −22.3192 | −1.07508 | −0.537539 | − | 0.843239i | \(-0.680646\pi\) | ||||
−0.537539 | + | 0.843239i | \(0.680646\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.8420i | 0.665205i | 0.943067 | + | 0.332603i | \(0.107927\pi\) | ||||
−0.943067 | + | 0.332603i | \(0.892073\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.36525 | + | 19.4351i | 0.0654590 | + | 0.931840i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 10.7537 | + | 7.13412i | 0.514420 | + | 0.341271i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −35.4411 | −1.69151 | −0.845755 | − | 0.533572i | \(-0.820850\pi\) | ||||
−0.845755 | + | 0.533572i | \(0.820850\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −10.6823 | + | 1.50824i | −0.508681 | + | 0.0718210i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 25.0176i | 1.18862i | 0.804235 | + | 0.594312i | \(0.202575\pi\) | ||||
−0.804235 | + | 0.594312i | \(0.797425\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 21.2698 | 1.00828 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −19.9827 | + | 1.40373i | −0.945151 | + | 0.0663940i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 17.0761i | 0.805870i | 0.915229 | + | 0.402935i | \(0.132010\pi\) | ||||
−0.915229 | + | 0.402935i | \(0.867990\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 14.1160i | − | 0.664696i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.737015 | − | 0.0517731i | 0.0346280 | − | 0.00243251i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 12.3039i | − | 0.576816i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.90074i | 0.135691i | 0.997696 | + | 0.0678454i | \(0.0216125\pi\) | ||||
−0.997696 | + | 0.0678454i | \(0.978388\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −11.8128 | + | 2.52269i | −0.551374 | + | 0.117749i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.1757i | 0.660227i | 0.943941 | + | 0.330114i | \(0.107087\pi\) | ||||
−0.943941 | + | 0.330114i | \(0.892913\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.6157 | 0.958091 | 0.479046 | − | 0.877790i | \(-0.340983\pi\) | ||||
0.479046 | + | 0.877790i | \(0.340983\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.18663 | − | 0.153604i | 0.101403 | − | 0.00712322i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.63891 | 0.353487 | 0.176743 | − | 0.984257i | \(-0.443444\pi\) | ||||
0.176743 | + | 0.984257i | \(0.443444\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −28.1145 | −1.29821 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.20786 | − | 17.1945i | −0.0556554 | − | 0.792282i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 33.5184i | − | 1.54118i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 1.08690i | − | 0.0498702i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 36.2960 | − | 5.12466i | 1.66188 | − | 0.234642i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.98768 | −0.227893 | −0.113946 | − | 0.993487i | \(-0.536349\pi\) | ||||
−0.113946 | + | 0.993487i | \(0.536349\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.10852i | 0.0961402i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 23.5240 | + | 13.3323i | 1.07038 | + | 0.606639i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 23.5251i | − | 1.06822i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.5879 | 0.842300 | 0.421150 | − | 0.906991i | \(-0.361627\pi\) | ||||
0.421150 | + | 0.906991i | \(0.361627\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −26.8826 | + | 1.88842i | −1.21567 | + | 0.0853974i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.3494i | 0.512191i | 0.966651 | + | 0.256096i | \(0.0824362\pi\) | ||||
−0.966651 | + | 0.256096i | \(0.917564\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 11.2485i | − | 0.506607i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −18.3078 | + | 2.58490i | −0.822876 | + | 0.116182i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.67085 | −0.209516 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −25.6187 | −1.14685 | −0.573426 | − | 0.819257i | \(-0.694386\pi\) | ||||
−0.573426 | + | 0.819257i | \(0.694386\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.94108 | + | 27.6321i | 0.0867208 | + | 1.23451i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0.115398 | 0.00514536 | 0.00257268 | − | 0.999997i | \(-0.499181\pi\) | ||||
0.00257268 | + | 0.999997i | \(0.499181\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 23.6256i | 1.05132i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −17.8933 | + | 1.25695i | −0.794671 | + | 0.0558232i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 33.4545i | − | 1.48284i | −0.671039 | − | 0.741422i | \(-0.734152\pi\) | ||
0.671039 | − | 0.741422i | \(-0.265848\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 28.8155i | 1.27472i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.92013 | − | 13.6738i | −0.128927 | − | 0.603715i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.04862i | 0.266534i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.81352i | 0.387618i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.57432 | − | 22.4112i | −0.0691048 | − | 0.983741i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.79806 | 0.210207 | 0.105103 | − | 0.994461i | \(-0.466483\pi\) | ||||
0.105103 | + | 0.994461i | \(0.466483\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.7315i | 0.556710i | 0.960478 | + | 0.278355i | \(0.0897891\pi\) | ||||
−0.960478 | + | 0.278355i | \(0.910211\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.159583 | − | 2.27175i | −0.00696478 | − | 0.0991471i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.26556 | −0.0551288 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.94196 | − | 21.1906i | −0.388781 | − | 0.921330i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.61872 | − | 39.7953i | −0.243832 | − | 1.72697i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.65724i | 0.374987i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 24.8368 | 1.07379 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.771119 | − | 10.9772i | −0.0332762 | − | 0.473703i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 9.53404 | 0.410660 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −25.2042 | −1.08361 | −0.541807 | − | 0.840503i | \(-0.682260\pi\) | ||||
−0.541807 | + | 0.840503i | \(0.682260\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.294370 | − | 4.19050i | −0.0126326 | − | 0.179832i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 25.7577i | 1.10334i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.51539 | −0.235821 | −0.117911 | − | 0.993024i | \(-0.537620\pi\) | ||||
−0.117911 | + | 0.993024i | \(0.537620\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.70053 | + | 26.2095i | 0.157935 | + | 1.11859i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 13.0206 | 0.554698 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 32.0776 | 1.36408 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.365877 | + | 5.20844i | 0.0155306 | + | 0.221086i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −20.4871 | −0.868068 | −0.434034 | − | 0.900897i | \(-0.642910\pi\) | ||||
−0.434034 | + | 0.900897i | \(0.642910\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 20.5566i | 0.869454i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10.6486 | − | 0.748034i | 0.449585 | − | 0.0315820i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.37781 | 0.395228 | 0.197614 | − | 0.980280i | \(-0.436681\pi\) | ||||
0.197614 | + | 0.980280i | \(0.436681\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.10665 | −0.298979 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −8.11108 | − | 28.1512i | −0.340633 | − | 1.18224i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.21567 | −0.134808 | −0.0674039 | − | 0.997726i | \(-0.521472\pi\) | ||||
−0.0674039 | + | 0.997726i | \(0.521472\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.0536i | 0.839216i | 0.907705 | + | 0.419608i | \(0.137832\pi\) | ||||
−0.907705 | + | 0.419608i | \(0.862168\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.18663 | − | 0.153604i | 0.0913478 | − | 0.00641691i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.07088 | + | 1.61421i | −0.0446590 | + | 0.0673174i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16.1981 | 0.674337 | 0.337168 | − | 0.941444i | \(-0.390531\pi\) | ||||
0.337168 | + | 0.941444i | \(0.390531\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 22.0468 | − | 1.54872i | 0.916234 | − | 0.0643627i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 51.0145i | 2.11644i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −32.3945 | −1.34164 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 11.2281 | − | 1.58530i | 0.464224 | − | 0.0655441i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.11255i | 0.128469i | 0.997935 | + | 0.0642344i | \(0.0204605\pi\) | ||||
−0.997935 | + | 0.0642344i | \(0.979539\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 1.46495i | − | 0.0603621i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.34144 | − | 33.3315i | −0.0963138 | − | 1.37107i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 28.9565i | − | 1.18910i | −0.804059 | − | 0.594550i | \(-0.797330\pi\) | ||
0.804059 | − | 0.594550i | \(-0.202670\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 17.5906i | 0.721146i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.31384 | + | 32.9387i | 0.0946993 | + | 1.34809i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 17.2531i | 0.704943i | 0.935823 | + | 0.352471i | \(0.114659\pi\) | ||||
−0.935823 | + | 0.352471i | \(0.885341\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.4175 | −0.506522 | −0.253261 | − | 0.967398i | \(-0.581503\pi\) | ||||
−0.253261 | + | 0.967398i | \(0.581503\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.62242 | − | 25.6562i | −0.147516 | − | 1.04480i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.23107 | −0.375296 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 32.8368 | 1.33281 | 0.666403 | − | 0.745591i | \(-0.267833\pi\) | ||||
0.666403 | + | 0.745591i | \(0.267833\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 27.2147 | − | 1.91175i | 1.10280 | − | 0.0774682i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 5.40528i | − | 0.218674i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 26.3873i | − | 1.06577i | −0.846187 | − | 0.532886i | \(-0.821107\pi\) | ||
0.846187 | − | 0.532886i | \(-0.178893\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.50223 | + | 21.3850i | 0.0605759 | + | 0.862328i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.43155 | 0.0576321 | 0.0288161 | − | 0.999585i | \(-0.490826\pi\) | ||||
0.0288161 | + | 0.999585i | \(0.490826\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.9904i | 0.843673i | 0.906672 | + | 0.421837i | \(0.138614\pi\) | ||||
−0.906672 | + | 0.421837i | \(0.861386\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −9.13555 | + | 23.1849i | −0.366597 | + | 0.930380i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 29.7839i | − | 1.19327i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −26.8564 | −1.07426 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.865884 | + | 12.3263i | 0.0345801 | + | 0.492264i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 3.01450i | − | 0.120196i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.12584i | 0.204057i | 0.994781 | + | 0.102028i | \(0.0325332\pi\) | ||||
−0.994781 | + | 0.102028i | \(0.967467\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 45.7045 | − | 3.21060i | 1.81659 | − | 0.127610i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −21.3276 | −0.846359 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.84717 | −0.231673 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.601817 | − | 4.26244i | −0.0238075 | − | 0.168619i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 37.2299 | 1.47049 | 0.735246 | − | 0.677800i | \(-0.237066\pi\) | ||||
0.735246 | + | 0.677800i | \(0.237066\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 46.1310i | − | 1.81923i | −0.415454 | − | 0.909614i | \(-0.636377\pi\) | ||
0.415454 | − | 0.909614i | \(-0.363623\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.56706 | + | 50.7788i | 0.140453 | + | 1.99941i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 20.5310i | − | 0.807157i | −0.914945 | − | 0.403578i | \(-0.867766\pi\) | ||
0.914945 | − | 0.403578i | \(-0.132234\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 35.5176i | 1.39419i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.215091 | − | 3.06192i | −0.00843006 | − | 0.120006i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 19.2663i | − | 0.753947i | −0.926224 | − | 0.376974i | \(-0.876965\pi\) | ||
0.926224 | − | 0.376974i | \(-0.123035\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 34.9533i | − | 1.36574i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −26.2959 | + | 3.71274i | −1.02590 | + | 0.144848i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −17.4108 | −0.678228 | −0.339114 | − | 0.940745i | \(-0.610127\pi\) | ||||
−0.339114 | + | 0.940745i | \(0.610127\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.89112i | 0.112451i | 0.998418 | + | 0.0562257i | \(0.0179066\pi\) | ||||
−0.998418 | + | 0.0562257i | \(0.982093\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6.53074 | + | 0.458765i | −0.253633 | + | 0.0178169i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −20.3620 | −0.789603 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −19.3377 | − | 12.8288i | −0.748760 | − | 0.496735i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 27.8263 | − | 1.95471i | 1.07583 | − | 0.0755735i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 23.3922i | − | 0.903045i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18.6858 | −0.720284 | −0.360142 | − | 0.932898i | \(-0.617272\pi\) | ||||
−0.360142 | + | 0.932898i | \(0.617272\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.05255 | − | 0.438333i | 0.0790026 | − | 0.0168715i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −12.9873 | −0.499141 | −0.249570 | − | 0.968357i | \(-0.580289\pi\) | ||||
−0.249570 | + | 0.968357i | \(0.580289\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −32.9419 | −1.26420 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −38.9698 | + | 2.73751i | −1.49333 | + | 0.104902i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 47.5216i | 1.81836i | 0.416401 | + | 0.909181i | \(0.363291\pi\) | ||||
−0.416401 | + | 0.909181i | \(0.636709\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14.3749 | −0.549237 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.33645 | − | 33.2605i | −0.0891410 | − | 1.26897i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 19.8673 | 0.756885 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.45253 | −0.0932986 | −0.0466493 | − | 0.998911i | \(-0.514854\pi\) | ||||
−0.0466493 | + | 0.998911i | \(0.514854\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.61961 | + | 25.6363i | 0.137497 | + | 0.973842i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −16.8173 | −0.637918 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 12.3771i | − | 0.468815i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.46105 | − | 35.0342i | −0.0930853 | − | 1.32512i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.46640 | 0.168694 | 0.0843469 | − | 0.996436i | \(-0.473120\pi\) | ||||
0.0843469 | + | 0.996436i | \(0.473120\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.48943 | 0.131606 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.937942 | − | 13.3521i | −0.0353249 | − | 0.502868i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 33.0827 | 1.24420 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 34.3987i | 1.29187i | 0.763393 | + | 0.645935i | \(0.223532\pi\) | ||||
−0.763393 | + | 0.645935i | \(0.776468\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.13305 | + | 29.2728i | 0.155002 | + | 1.09782i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.44337 | + | 2.17568i | −0.0540545 | + | 0.0814798i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10.0212 | −0.374770 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.914670 | + | 13.0208i | 0.0341590 | + | 0.486270i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 53.3676i | 1.99028i | 0.0984873 | + | 0.995138i | \(0.468600\pi\) | ||||
−0.0984873 | + | 0.995138i | \(0.531400\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.46983 | 0.315433 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.236671 | − | 3.36913i | −0.00880189 | − | 0.125299i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.95450i | 0.0725882i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 37.9610i | 1.40790i | 0.710251 | + | 0.703949i | \(0.248581\pi\) | ||||
−0.710251 | + | 0.703949i | \(0.751419\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 24.6447 | − | 11.0290i | 0.912766 | − | 0.408482i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 29.3894i | − | 1.08701i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 45.9351i | − | 1.69665i | −0.529474 | − | 0.848326i | \(-0.677611\pi\) | ||
0.529474 | − | 0.848326i | \(-0.322389\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −14.4436 | + | 1.01462i | −0.532760 | + | 0.0374248i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 22.8984i | 0.843474i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.3438 | −0.748360 | −0.374180 | − | 0.927356i | \(-0.622076\pi\) | ||||
−0.374180 | + | 0.927356i | \(0.622076\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.531041 | − | 7.55963i | −0.0195083 | − | 0.277710i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12.0290 | 0.441303 | 0.220651 | − | 0.975353i | \(-0.429182\pi\) | ||||
0.220651 | + | 0.975353i | \(0.429182\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −26.8855 | −0.985007 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −46.5539 | + | 6.57298i | −1.70332 | + | 0.240493i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 34.7788i | − | 1.27079i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.99726i | 0.145862i | 0.997337 | + | 0.0729310i | \(0.0232353\pi\) | ||||
−0.997337 | + | 0.0729310i | \(0.976765\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −43.1437 | + | 3.03072i | −1.57224 | + | 0.110445i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.991605 | 0.0360882 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 10.7731i | − | 0.391555i | −0.980648 | − | 0.195778i | \(-0.937277\pi\) | ||
0.980648 | − | 0.195778i | \(-0.0627230\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 10.8587 | − | 19.1596i | 0.394147 | − | 0.695450i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 28.7478i | − | 1.04211i | −0.853524 | − | 0.521054i | \(-0.825539\pi\) | ||
0.853524 | − | 0.521054i | \(-0.174461\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 36.0682 | 1.30576 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −16.0525 | + | 2.26647i | −0.580381 | + | 0.0819444i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 21.7827i | − | 0.786529i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 0.662816i | − | 0.0239018i | −0.999929 | − | 0.0119509i | \(-0.996196\pi\) | ||
0.999929 | − | 0.0119509i | \(-0.00380417\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.00240 | + | 28.5052i | 0.0721148 | + | 1.02659i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 27.9290 | 1.00454 | 0.502268 | − | 0.864712i | \(-0.332499\pi\) | ||||
0.502268 | + | 0.864712i | \(0.332499\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.219900 | 0.00789903 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.29333 | − | 0.512334i | 0.261647 | − | 0.0183799i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 14.3270 | 0.513319 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.80426i | 0.136127i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.25108 | + | 24.5888i | 0.187658 | + | 0.878733i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 23.1341i | − | 0.825692i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 41.6499i | − | 1.48466i | −0.670035 | − | 0.742329i | \(-0.733721\pi\) | ||
0.670035 | − | 0.742329i | \(-0.266279\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 50.2556 | − | 3.53030i | 1.78915 | − | 0.125682i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.95138i | 0.353830i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14.3463i | 0.509451i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 49.0761 | − | 3.44745i | 1.74055 | − | 0.122268i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 52.1841 | 1.84846 | 0.924228 | − | 0.381840i | \(-0.124710\pi\) | ||||
0.924228 | + | 0.381840i | \(0.124710\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.72781i | 0.273390i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 27.1796 | − | 3.83751i | 0.960346 | − | 0.135592i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 23.4693 | 0.828215 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 30.2408 | + | 20.0620i | 1.06585 | + | 0.707093i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.33445 | − | 47.4675i | −0.117378 | − | 1.67094i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 25.7063i | − | 0.903784i | −0.892073 | − | 0.451892i | \(-0.850749\pi\) | ||
0.892073 | − | 0.451892i | \(-0.149251\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19.9015 | −0.698835 | −0.349418 | − | 0.936967i | \(-0.613621\pi\) | ||||
−0.349418 | + | 0.936967i | \(0.613621\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 31.0000 | − | 2.17766i | 1.08722 | − | 0.0763737i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −36.1688 | −1.26694 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 34.0196 | 1.19019 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.21988 | − | 15.7226i | −0.0775689 | − | 0.549391i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 31.7788i | 1.10909i | 0.832154 | + | 0.554544i | \(0.187107\pi\) | ||||
−0.832154 | + | 0.554544i | \(0.812893\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 47.1020 | 1.64187 | 0.820937 | − | 0.571019i | \(-0.193452\pi\) | ||||
0.820937 | + | 0.571019i | \(0.193452\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.85027 | + | 0.129976i | −0.0644180 | + | 0.00452517i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 32.1680 | 1.11859 | 0.559295 | − | 0.828968i | \(-0.311072\pi\) | ||||
0.559295 | + | 0.828968i | \(0.311072\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19.3749 | −0.672918 | −0.336459 | − | 0.941698i | \(-0.609229\pi\) | ||||
−0.336459 | + | 0.941698i | \(0.609229\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 36.7957 | − | 2.58479i | 1.27643 | − | 0.0896653i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.35957 | 0.289642 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 37.1773i | 1.28657i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.76648 | − | 0.590797i | 0.0956234 | − | 0.0204209i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −35.5392 | −1.22695 | −0.613475 | − | 0.789714i | \(-0.710229\pi\) | ||||
−0.613475 | + | 0.789714i | \(0.710229\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.58578 | 0.192613 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 39.8081 | − | 2.79640i | 1.37106 | − | 0.0963130i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −24.0743 | −0.828182 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 12.9262i | 0.444149i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.02064 | − | 28.7648i | −0.0693482 | − | 0.987205i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.18236 | − | 3.43802i | −0.177649 | − | 0.117854i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 45.0000 | 1.54077 | 0.770385 | − | 0.637579i | \(-0.220064\pi\) | ||||
0.770385 | + | 0.637579i | \(0.220064\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.62354 | − | 18.5816i | −0.0897233 | − | 0.635476i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 29.9796i | 1.02408i | 0.858961 | + | 0.512041i | \(0.171111\pi\) | ||||
−0.858961 | + | 0.512041i | \(0.828889\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.4556 | 0.390860 | 0.195430 | − | 0.980718i | \(-0.437390\pi\) | ||||
0.195430 | + | 0.980718i | \(0.437390\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 29.9453 | − | 2.10356i | 1.02053 | − | 0.0716893i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 19.4690i | 0.662733i | 0.943502 | + | 0.331366i | \(0.107510\pi\) | ||||
−0.943502 | + | 0.331366i | \(0.892490\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 30.1528i | − | 1.02522i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −20.0356 | + | 1.40744i | −0.680446 | + | 0.0477993i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 26.1263i | − | 0.886272i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 14.0435i | − | 0.475844i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.24441 | − | 30.0616i | −0.143652 | − | 1.01743i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 34.7788i | 1.17574i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −18.2894 | −0.617589 | −0.308794 | − | 0.951129i | \(-0.599926\pi\) | ||||
−0.308794 | + | 0.951129i | \(0.599926\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 22.3769 | − | 1.57191i | 0.754753 | − | 0.0530192i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −38.1786 | −1.28627 | −0.643135 | − | 0.765753i | \(-0.722367\pi\) | ||||
−0.643135 | + | 0.765753i | \(0.722367\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22.2000 | 0.747090 | 0.373545 | − | 0.927612i | \(-0.378142\pi\) | ||||
0.373545 | + | 0.927612i | \(0.378142\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.77981 | − | 53.8075i | −0.127057 | − | 1.80872i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 20.2126i | − | 0.678672i | −0.940665 | − | 0.339336i | \(-0.889798\pi\) | ||
0.940665 | − | 0.339336i | \(-0.110202\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 29.8648i | 1.00163i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −22.9283 | + | 6.60623i | −0.768128 | + | 0.221317i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8.94530 | −0.299343 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 14.7692i | − | 0.493679i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.65959 | + | 11.7505i | −0.222357 | + | 0.392337i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.63432i | 0.0878596i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −28.4039 | −0.946271 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 71.1051 | − | 4.99492i | 2.36623 | − | 0.166220i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 5.63805i | − | 0.187415i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 39.9042i | − | 1.32500i | −0.749062 | − | 0.662499i | \(-0.769496\pi\) | ||
0.749062 | − | 0.662499i | \(-0.230504\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.26254 | + | 30.1900i | 0.141380 | + | 1.00134i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −17.2138 | −0.570318 | −0.285159 | − | 0.958480i | \(-0.592046\pi\) | ||||
−0.285159 | + | 0.958480i | \(0.592046\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 41.5498 | 1.37510 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.48941 | + | 35.4380i | 0.0822975 | + | 1.17154i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −48.9448 | −1.61630 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26.1246i | 0.861772i | 0.902406 | + | 0.430886i | \(0.141799\pi\) | ||||
−0.902406 | + | 0.430886i | \(0.858201\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.91117 | − | 0.485489i | 0.227731 | − | 0.0159974i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 2.33313i | − | 0.0767959i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.523789i | 0.0172221i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.09130 | + | 7.72924i | 0.0358429 | + | 0.253862i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 27.3824i | 0.898386i | 0.893435 | + | 0.449193i | \(0.148288\pi\) | ||||
−0.893435 | + | 0.449193i | \(0.851712\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.67658i | 0.317137i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −0.521329 | − | 7.42137i | −0.0170676 | − | 0.242965i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 14.3270 | 0.468544 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 35.8248i | − | 1.17035i | −0.810908 | − | 0.585173i | \(-0.801026\pi\) | ||
0.810908 | − | 0.585173i | \(-0.198974\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.02371 | − | 43.0440i | −0.0986751 | − | 1.40469i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 11.3492 | 0.369974 | 0.184987 | − | 0.982741i | \(-0.440776\pi\) | ||||
0.184987 | + | 0.982741i | \(0.440776\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −21.2779 | − | 14.1160i | −0.692905 | − | 0.459680i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −8.21176 | − | 38.4525i | −0.267129 | − | 1.25086i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 30.9439i | 1.00554i | 0.864420 | + | 0.502771i | \(0.167686\pi\) | ||||
−0.864420 | + | 0.502771i | \(0.832314\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14.3936 | −0.467236 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.83469 | − | 40.3531i | −0.0919210 | − | 1.30854i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −53.8117 | −1.74313 | −0.871566 | − | 0.490277i | \(-0.836895\pi\) | ||||
−0.871566 | + | 0.490277i | \(0.836895\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.94197 | 0.0951999 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.55707 | − | 22.1656i | −0.0503328 | − | 0.716511i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 20.1290i | 0.650000i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.7036 | −0.990439 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 31.7378 | − | 4.48108i | 1.02274 | − | 0.144401i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 29.6626 | 0.954871 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.54441 | −0.274770 | −0.137385 | − | 0.990518i | \(-0.543870\pi\) | ||||
−0.137385 | + | 0.990518i | \(0.543870\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.759218 | + | 10.8078i | 0.0243896 | + | 0.347198i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 59.9482 | 1.92383 | 0.961915 | − | 0.273350i | \(-0.0881317\pi\) | ||||
0.961915 | + | 0.273350i | \(0.0881317\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 23.5492i | 0.754951i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.13476 | − | 0.0797133i | 0.0363413 | − | 0.00255287i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −15.9192 | −0.509300 | −0.254650 | − | 0.967033i | \(-0.581960\pi\) | ||||
−0.254650 | + | 0.967033i | \(0.581960\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −24.2581 | −0.775291 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.64722 | + | 32.9145i | 0.148374 | + | 1.05088i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 16.7428 | 0.534011 | 0.267006 | − | 0.963695i | \(-0.413966\pi\) | ||||
0.267006 | + | 0.963695i | \(0.413966\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 44.8453i | − | 1.42889i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −18.6968 | + | 1.31339i | −0.595124 | + | 0.0418057i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −50.5245 | − | 33.5184i | −1.60659 | − | 1.06582i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −38.4525 | −1.22148 | −0.610742 | − | 0.791829i | \(-0.709129\pi\) | ||||
−0.610742 | + | 0.791829i | \(0.709129\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.29289 | − | 0.301562i | 0.136231 | − | 0.00956980i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 44.3169i | 1.40494i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.2408 | 0.767713 | 0.383856 | − | 0.923393i | \(-0.374596\pi\) | ||||
0.383856 | + | 0.923393i | \(0.374596\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.40725 | + | 6.58960i | 0.0445234 | + | 0.208486i |
(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 | 552.2.m.b.137.14 | yes | 16 | |
3.2 | odd | 2 | inner | 552.2.m.b.137.15 | yes | 16 | |
4.3 | odd | 2 | 1104.2.m.e.689.4 | 16 | |||
12.11 | even | 2 | 1104.2.m.e.689.1 | 16 | |||
23.22 | odd | 2 | inner | 552.2.m.b.137.13 | ✓ | 16 | |
69.68 | even | 2 | inner | 552.2.m.b.137.16 | yes | 16 | |
92.91 | even | 2 | 1104.2.m.e.689.3 | 16 | |||
276.275 | odd | 2 | 1104.2.m.e.689.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
552.2.m.b.137.13 | ✓ | 16 | 23.22 | odd | 2 | inner | |
552.2.m.b.137.14 | yes | 16 | 1.1 | even | 1 | trivial | |
552.2.m.b.137.15 | yes | 16 | 3.2 | odd | 2 | inner | |
552.2.m.b.137.16 | yes | 16 | 69.68 | even | 2 | inner | |
1104.2.m.e.689.1 | 16 | 12.11 | even | 2 | |||
1104.2.m.e.689.2 | 16 | 276.275 | odd | 2 | |||
1104.2.m.e.689.3 | 16 | 92.91 | even | 2 | |||
1104.2.m.e.689.4 | 16 | 4.3 | odd | 2 |