Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [288,4,Mod(287,288)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(288, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("288.287");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 288 = 2^{5} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 288.c (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: | \(16.9925500817\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.77720518656.8 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 161x^{4} + 4096 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{20} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 287.1 | ||
Root | \(-1.67746 + 1.67746i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 288.287 |
Dual form | 288.4.c.b.287.8 |
$q$-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 \(\left(\mathbb{Z}/288\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(65\) | \(127\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 17.6623i | − 1.57976i | −0.613259 | − | 0.789882i | \(-0.710142\pi\) | ||||
0.613259 | − | 0.789882i | \(-0.289858\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 14.9783i | − 0.808750i | −0.914593 | − | 0.404375i | \(-0.867489\pi\) | ||||
0.914593 | − | 0.404375i | \(-0.132511\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −55.1236 | −1.51094 | −0.755472 | − | 0.655181i | \(-0.772592\pi\) | ||||
−0.755472 | + | 0.655181i | \(0.772592\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −9.02175 | −0.192476 | −0.0962378 | − | 0.995358i | \(-0.530681\pi\) | ||||
−0.0962378 | + | 0.995358i | \(0.530681\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 14.1729i | − 0.202202i | −0.994876 | − | 0.101101i | \(-0.967763\pi\) | ||||
0.994876 | − | 0.101101i | \(-0.0322365\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 139.913i | 1.68938i | 0.535255 | + | 0.844691i | \(0.320216\pi\) | ||||
−0.535255 | + | 0.844691i | \(0.679784\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 86.1748 | 0.781247 | 0.390623 | − | 0.920551i | \(-0.372259\pi\) | ||||
0.390623 | + | 0.920551i | \(0.372259\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −186.957 | −1.49565 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 3.64319i | − 0.0233284i | −0.999932 | − | 0.0116642i | \(-0.996287\pi\) | ||||
0.999932 | − | 0.0116642i | \(-0.00371291\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 273.022i | 1.58181i | 0.611938 | + | 0.790906i | \(0.290390\pi\) | ||||
−0.611938 | + | 0.790906i | \(0.709610\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −264.550 | −1.27763 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −405.826 | −1.80317 | −0.901586 | − | 0.432599i | \(-0.857596\pi\) | ||||
−0.901586 | + | 0.432599i | \(0.857596\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 344.853i | − 1.31358i | −0.754072 | − | 0.656792i | \(-0.771913\pi\) | ||||
0.754072 | − | 0.656792i | \(-0.228087\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 241.696i | − 0.857168i | −0.903502 | − | 0.428584i | \(-0.859013\pi\) | ||||
0.903502 | − | 0.428584i | \(-0.140987\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −297.999 | −0.924844 | −0.462422 | − | 0.886660i | \(-0.653019\pi\) | ||||
−0.462422 | + | 0.886660i | \(0.653019\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 118.652 | 0.345924 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 602.901i | − 1.56254i | −0.624191 | − | 0.781271i | \(-0.714571\pi\) | ||||
0.624191 | − | 0.781271i | \(-0.285429\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 973.609i | 2.38693i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −630.678 | −1.39165 | −0.695824 | − | 0.718212i | \(-0.744961\pi\) | ||||
−0.695824 | + | 0.718212i | \(0.744961\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 237.478 | 0.498458 | 0.249229 | − | 0.968445i | \(-0.419823\pi\) | ||||
0.249229 | + | 0.968445i | \(0.419823\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 159.345i | 0.304066i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 397.957i | − 0.725644i | −0.931859 | − | 0.362822i | \(-0.881813\pi\) | ||||
0.931859 | − | 0.362822i | \(-0.118187\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 778.955 | 1.30204 | 0.651021 | − | 0.759060i | \(-0.274341\pi\) | ||||
0.651021 | + | 0.759060i | \(0.274341\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1155.04 | −1.85188 | −0.925942 | − | 0.377665i | \(-0.876727\pi\) | ||||
−0.925942 | + | 0.377665i | \(0.876727\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 825.655i | 1.22198i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 127.326i | 0.181333i | 0.995881 | + | 0.0906666i | \(0.0288998\pi\) | ||||
−0.995881 | + | 0.0906666i | \(0.971100\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −301.627 | −0.398890 | −0.199445 | − | 0.979909i | \(-0.563914\pi\) | ||||
−0.199445 | + | 0.979909i | \(0.563914\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −250.326 | −0.319431 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 338.059i | 0.402631i | 0.979526 | + | 0.201315i | \(0.0645216\pi\) | ||||
−0.979526 | + | 0.201315i | \(0.935478\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 135.130i | 0.155665i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2471.18 | 2.66882 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1617.35 | 1.69296 | 0.846478 | − | 0.532423i | \(-0.178719\pi\) | ||||
0.846478 | + | 0.532423i | \(0.178719\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 451.672i | − 0.444981i | −0.974935 | − | 0.222490i | \(-0.928581\pi\) | ||||
0.974935 | − | 0.222490i | \(-0.0714186\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 1000.15i | − 0.956776i | −0.878149 | − | 0.478388i | \(-0.841221\pi\) | ||||
0.878149 | − | 0.478388i | \(-0.158779\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1582.93 | −1.43017 | −0.715085 | − | 0.699038i | \(-0.753612\pi\) | ||||
−0.715085 | + | 0.699038i | \(0.753612\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 636.761 | 0.559547 | 0.279773 | − | 0.960066i | \(-0.409741\pi\) | ||||
0.279773 | + | 0.960066i | \(0.409741\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 83.9922i | 0.0699232i | 0.999389 | + | 0.0349616i | \(0.0111309\pi\) | ||||
−0.999389 | + | 0.0349616i | \(0.988869\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 1522.04i | − 1.23419i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −212.285 | −0.163531 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1707.61 | 1.28295 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1094.29i | 0.783013i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 923.239i | − 0.645073i | −0.946557 | − | 0.322536i | \(-0.895465\pi\) | ||||
0.946557 | − | 0.322536i | \(-0.104535\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −363.452 | −0.242404 | −0.121202 | − | 0.992628i | \(-0.538675\pi\) | ||||
−0.121202 | + | 0.992628i | \(0.538675\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2095.65 | 1.36629 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 704.986i | 0.439642i | 0.975540 | + | 0.219821i | \(0.0705474\pi\) | ||||
−0.975540 | + | 0.219821i | \(0.929453\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 2065.35i | − 1.26029i | −0.776477 | − | 0.630146i | \(-0.782995\pi\) | ||||
0.776477 | − | 0.630146i | \(-0.217005\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 497.311 | 0.290820 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −64.3470 | −0.0368533 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1123.27i | 0.617596i | 0.951128 | + | 0.308798i | \(0.0999267\pi\) | ||||
−0.951128 | + | 0.308798i | \(0.900073\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 748.239i | 0.403250i | 0.979463 | + | 0.201625i | \(0.0646223\pi\) | ||||
−0.979463 | + | 0.201625i | \(0.935378\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4822.19 | 2.49889 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1164.78 | −0.592100 | −0.296050 | − | 0.955172i | \(-0.595670\pi\) | ||||
−0.296050 | + | 0.955172i | \(0.595670\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 1290.75i | − 0.631833i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 976.304i | − 0.469141i | −0.972099 | − | 0.234571i | \(-0.924632\pi\) | ||||
0.972099 | − | 0.234571i | \(-0.0753684\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1603.66 | 0.743082 | 0.371541 | − | 0.928417i | \(-0.378830\pi\) | ||||
0.371541 | + | 0.928417i | \(0.378830\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2115.61 | −0.962953 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 266.534i | 0.117134i | 0.998283 | + | 0.0585670i | \(0.0186531\pi\) | ||||
−0.998283 | + | 0.0585670i | \(0.981347\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2800.28i | 1.20961i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −197.867 | −0.0826216 | −0.0413108 | − | 0.999146i | \(-0.513153\pi\) | ||||
−0.0413108 | + | 0.999146i | \(0.513153\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2834.50 | 1.16401 | 0.582007 | − | 0.813184i | \(-0.302268\pi\) | ||||
0.582007 | + | 0.813184i | \(0.302268\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7167.82i | 2.84859i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 781.261i | 0.305516i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5188.38 | −1.96554 | −0.982770 | − | 0.184835i | \(-0.940825\pi\) | ||||
−0.982770 | + | 0.184835i | \(0.940825\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 206.348 | 0.0769599 | 0.0384799 | − | 0.999259i | \(-0.487748\pi\) | ||||
0.0384799 | + | 0.999259i | \(0.487748\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 3306.60i | − 1.19587i | −0.801546 | − | 0.597933i | \(-0.795989\pi\) | ||||
0.801546 | − | 0.597933i | \(-0.204011\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 3491.37i | − 1.24370i | −0.783136 | − | 0.621851i | \(-0.786381\pi\) | ||||
0.783136 | − | 0.621851i | \(-0.213619\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −54.5686 | −0.0188668 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6090.89 | −2.07515 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 7712.50i | − 2.55256i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4808.48i | 1.56886i | 0.620218 | + | 0.784429i | \(0.287044\pi\) | ||||
−0.620218 | + | 0.784429i | \(0.712956\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4268.90 | −1.35412 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4089.39 | 1.27929 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 127.864i | 0.0389189i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 1620.37i | − 0.486582i | −0.969953 | − | 0.243291i | \(-0.921773\pi\) | ||||
0.969953 | − | 0.243291i | \(-0.0782271\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −761.369 | −0.222616 | −0.111308 | − | 0.993786i | \(-0.535504\pi\) | ||||
−0.111308 | + | 0.993786i | \(0.535504\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2397.76 | 0.691915 | 0.345957 | − | 0.938250i | \(-0.387554\pi\) | ||||
0.345957 | + | 0.938250i | \(0.387554\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 4299.95i | − 1.20901i | −0.796602 | − | 0.604504i | \(-0.793371\pi\) | ||||
0.796602 | − | 0.604504i | \(-0.206629\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5263.35i | 1.46103i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1287.79 | 0.348538 | 0.174269 | − | 0.984698i | \(-0.444244\pi\) | ||||
0.174269 | + | 0.984698i | \(0.444244\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4906.82 | −1.31152 | −0.655760 | − | 0.754969i | \(-0.727652\pi\) | ||||
−0.655760 | + | 0.754969i | \(0.727652\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 2095.67i | − 0.546478i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 1262.26i | − 0.325165i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3501.68 | −0.880575 | −0.440288 | − | 0.897857i | \(-0.645124\pi\) | ||||
−0.440288 | + | 0.897857i | \(0.645124\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4750.26 | −1.18042 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 1295.48i | − 0.314435i | −0.987564 | − | 0.157218i | \(-0.949748\pi\) | ||||
0.987564 | − | 0.157218i | \(-0.0502524\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6078.56i | 1.45831i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4117.27 | −0.965329 | −0.482665 | − | 0.875805i | \(-0.660331\pi\) | ||||
−0.482665 | + | 0.875805i | \(0.660331\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10648.6 | −2.46845 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2974.78i | 0.674259i | 0.941458 | + | 0.337129i | \(0.109456\pi\) | ||||
−0.941458 | + | 0.337129i | \(0.890544\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 5000.11i | − 1.12079i | −0.828224 | − | 0.560396i | \(-0.810649\pi\) | ||||
0.828224 | − | 0.560396i | \(-0.189351\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 10305.7 | 2.25985 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −213.586 | −0.0463291 | −0.0231645 | − | 0.999732i | \(-0.507374\pi\) | ||||
−0.0231645 | + | 0.999732i | \(0.507374\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7291.74i | 1.54800i | 0.633184 | + | 0.774002i | \(0.281748\pi\) | ||||
−0.633184 | + | 0.774002i | \(0.718252\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4761.83i | 1.00022i | 0.865963 | + | 0.500108i | \(0.166706\pi\) | ||||
−0.865963 | + | 0.500108i | \(0.833294\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5165.29 | −1.06236 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4712.13 | 0.959114 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 1371.49i | − 0.273459i | −0.990608 | − | 0.136730i | \(-0.956341\pi\) | ||||
0.990608 | − | 0.136730i | \(-0.0436592\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11139.2i | 2.19847i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −777.447 | −0.150371 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3620.18 | −0.693234 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 4194.41i | − 0.787446i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 511.696i | 0.0951272i | 0.998868 | + | 0.0475636i | \(0.0151457\pi\) | ||||
−0.998868 | + | 0.0475636i | \(0.984854\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 518.033 | 0.0944532 | 0.0472266 | − | 0.998884i | \(-0.484962\pi\) | ||||
0.0472266 | + | 0.998884i | \(0.484962\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2726.17 | 0.492308 | 0.246154 | − | 0.969231i | \(-0.420833\pi\) | ||||
0.246154 | + | 0.969231i | \(0.420833\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 566.346i | − 0.100344i | −0.998741 | − | 0.0501722i | \(-0.984023\pi\) | ||||
0.998741 | − | 0.0501722i | \(-0.0159770\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 200.826i | 0.0352479i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1982.97 | 0.341596 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1686.67 | 0.287877 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4463.51i | 0.747967i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 7531.08i | − 1.25059i | −0.780388 | − | 0.625296i | \(-0.784978\pi\) | ||||
0.780388 | − | 0.625296i | \(-0.215022\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7028.82 | −1.14635 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7241.22 | 1.17049 | 0.585244 | − | 0.810857i | \(-0.300999\pi\) | ||||
0.585244 | + | 0.810857i | \(0.300999\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 15049.9i | − 2.39003i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 6914.74i | − 1.08852i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8937.55 | 1.38269 | 0.691344 | − | 0.722525i | \(-0.257019\pi\) | ||||
0.691344 | + | 0.722525i | \(0.257019\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7003.04 | 1.07411 | 0.537055 | − | 0.843547i | \(-0.319537\pi\) | ||||
0.537055 | + | 0.843547i | \(0.319537\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 3368.17i | − 0.507845i | −0.967225 | − | 0.253923i | \(-0.918279\pi\) | ||||
0.967225 | − | 0.253923i | \(-0.0817208\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 13758.1i | − 2.05692i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6019.78 | −0.884992 | −0.442496 | − | 0.896771i | \(-0.645907\pi\) | ||||
−0.442496 | + | 0.896771i | \(0.645907\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12716.6 | −1.85401 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 20400.7i | 2.92554i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 3759.59i | − 0.534738i | −0.963594 | − | 0.267369i | \(-0.913846\pi\) | ||||
0.963594 | − | 0.267369i | \(-0.0861542\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9030.40 | −1.26371 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5174.87 | 0.718350 | 0.359175 | − | 0.933270i | \(-0.383058\pi\) | ||||
0.359175 | + | 0.933270i | \(0.383058\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 32.8679i | 0.00449014i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3076.35i | 0.416943i | 0.978028 | + | 0.208471i | \(0.0668488\pi\) | ||||
−0.978028 | + | 0.208471i | \(0.933151\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10465.9 | 1.39630 | 0.698151 | − | 0.715951i | \(-0.254007\pi\) | ||||
0.698151 | + | 0.715951i | \(0.254007\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 14583.0 | 1.93043 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 2556.64i | − 0.333231i | −0.986022 | − | 0.166615i | \(-0.946716\pi\) | ||||
0.986022 | − | 0.166615i | \(-0.0532838\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 1221.35i | − 0.157970i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2248.87 | 0.286464 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1232.61 | 0.155826 | 0.0779130 | − | 0.996960i | \(-0.475174\pi\) | ||||
0.0779130 | + | 0.996960i | \(0.475174\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2278.88i | 0.283795i | 0.989881 | + | 0.141898i | \(0.0453204\pi\) | ||||
−0.989881 | + | 0.141898i | \(0.954680\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 2463.13i | − 0.304460i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 22370.6 | 2.72449 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 950.130 | 0.114868 | 0.0574339 | − | 0.998349i | \(-0.481708\pi\) | ||||
0.0574339 | + | 0.998349i | \(0.481708\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9446.45i | 1.12549i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5327.43i | 0.630152i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6974.81 | 0.813226 | 0.406613 | − | 0.913600i | \(-0.366710\pi\) | ||||
0.406613 | + | 0.913600i | \(0.366710\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1713.41 | −0.198353 | −0.0991764 | − | 0.995070i | \(-0.531621\pi\) | ||||
−0.0991764 | + | 0.995070i | \(0.531621\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2649.71i | 0.302424i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 3557.01i | − 0.403128i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7234.34 | 0.808506 | 0.404253 | − | 0.914647i | \(-0.367532\pi\) | ||||
0.404253 | + | 0.914647i | \(0.367532\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8283.91 | 0.919398 | 0.459699 | − | 0.888075i | \(-0.347957\pi\) | ||||
0.459699 | + | 0.888075i | \(0.347957\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 12057.0i | 1.31982i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 11500.7i | − 1.25034i | −0.780489 | − | 0.625170i | \(-0.785030\pi\) | ||||
0.780489 | − | 0.625170i | \(-0.214970\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12976.7 | −1.39174 | −0.695869 | − | 0.718169i | \(-0.744981\pi\) | ||||
−0.695869 | + | 0.718169i | \(0.744981\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5970.89 | 0.636061 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8302.07i | 0.872604i | 0.899800 | + | 0.436302i | \(0.143712\pi\) | ||||
−0.899800 | + | 0.436302i | \(0.856288\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19009.5i | 1.98475i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2386.71 | 0.245913 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1977.43 | −0.202408 | −0.101204 | − | 0.994866i | \(-0.532269\pi\) | ||||
−0.101204 | + | 0.994866i | \(0.532269\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 1616.73i | − 0.163338i | −0.996660 | − | 0.0816690i | \(-0.973975\pi\) | ||||
0.996660 | − | 0.0816690i | \(-0.0260250\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1476.11i | 0.148165i | 0.997252 | + | 0.0740827i | \(0.0236029\pi\) | ||||
−0.997252 | + | 0.0740827i | \(0.976397\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −15942.8 | −1.57975 | −0.789875 | − | 0.613268i | \(-0.789855\pi\) | ||||
−0.789875 | + | 0.613268i | \(0.789855\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5960.69 | −0.586864 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 13323.1i | 1.29513i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 26157.6i | − 2.52673i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14684.4 | 1.40073 | 0.700363 | − | 0.713786i | \(-0.253021\pi\) | ||||
0.700363 | + | 0.713786i | \(0.253021\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3661.26 | 0.347067 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 28566.1i | − 2.67447i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 9871.54i | − 0.918526i | −0.888300 | − | 0.459263i | \(-0.848114\pi\) | ||||
0.888300 | − | 0.459263i | \(-0.151886\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4356.26 | 0.400398 | 0.200199 | − | 0.979755i | \(-0.435841\pi\) | ||||
0.200199 | + | 0.979755i | \(0.435841\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −51.6345 | −0.00471704 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 11667.4i | − 1.05303i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 15900.3i | − 1.42645i | −0.700937 | − | 0.713224i | \(-0.747234\pi\) | ||||
0.700937 | − | 0.713224i | \(-0.252766\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9083.46 | −0.805192 | −0.402596 | − | 0.915378i | \(-0.631892\pi\) | ||||
−0.402596 | + | 0.915378i | \(0.631892\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7977.56 | −0.702964 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 4733.57i | − 0.412204i | −0.978531 | − | 0.206102i | \(-0.933922\pi\) | ||||
0.978531 | − | 0.206102i | \(-0.0660778\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 17300.5i | 1.49771i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −17665.0 | −1.51148 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 16426.8 | 1.39739 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 14468.8i | − 1.21668i | −0.793675 | − | 0.608341i | \(-0.791835\pi\) | ||||
0.793675 | − | 0.608341i | \(-0.208165\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12945.2i | 1.08232i | 0.840919 | + | 0.541161i | \(0.182015\pi\) | ||||
−0.840919 | + | 0.541161i | \(0.817985\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3869.51 | 0.319845 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4740.91 | −0.389653 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3111.18i | 0.252833i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 27958.3i | 2.25933i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6540.52 | −0.522672 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7859.59 | −0.624603 | −0.312301 | − | 0.949983i | \(-0.601100\pi\) | ||||
−0.312301 | + | 0.949983i | \(0.601100\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 11246.7i | − 0.883952i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 20633.2i | − 1.61282i | −0.591359 | − | 0.806408i | \(-0.701408\pi\) | ||||
0.591359 | − | 0.806408i | \(-0.298592\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 509.729 | 0.0394105 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1907.12 | 0.146653 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 22253.3i | 1.69282i | 0.532531 | + | 0.846411i | \(0.321241\pi\) | ||||
−0.532531 | + | 0.846411i | \(0.678759\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2180.52i | 0.164984i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7722.80 | 0.578112 | 0.289056 | − | 0.957312i | \(-0.406659\pi\) | ||||
0.289056 | + | 0.957312i | \(0.406659\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1483.50 | 0.110462 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5085.66i | 0.374696i | 0.982294 | + | 0.187348i | \(0.0599892\pi\) | ||||
−0.982294 | + | 0.187348i | \(0.940011\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11021.0i | 0.807728i | 0.914819 | + | 0.403864i | \(0.132333\pi\) | ||||
−0.914819 | + | 0.403864i | \(0.867667\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −16110.9 | −1.16847 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16881.8 | −1.21802 | −0.609012 | − | 0.793161i | \(-0.708434\pi\) | ||||
−0.609012 | + | 0.793161i | \(0.708434\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4517.85i | 0.322602i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 33234.0i | 2.36091i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3641.73 | −0.256065 | −0.128032 | − | 0.991770i | \(-0.540866\pi\) | ||||
−0.128032 | + | 0.991770i | \(0.540866\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −38199.3 | −2.67228 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2475.73i | 0.171444i | 0.996319 | + | 0.0857219i | \(0.0273197\pi\) | ||||
−0.996319 | + | 0.0857219i | \(0.972680\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3749.44i | 0.258340i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 306.543 | 0.0209099 | 0.0104549 | − | 0.999945i | \(-0.496672\pi\) | ||||
0.0104549 | + | 0.999945i | \(0.496672\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12411.0 | −0.842358 | −0.421179 | − | 0.906978i | \(-0.638384\pi\) | ||||
−0.421179 | + | 0.906978i | \(0.638384\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 30160.3i | − 2.02676i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 1572.02i | − 0.105118i | −0.998618 | − | 0.0525588i | \(-0.983262\pi\) | ||||
0.998618 | − | 0.0525588i | \(-0.0167377\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2688.47 | 0.178010 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3597.65 | −0.237044 | −0.118522 | − | 0.992951i | \(-0.537816\pi\) | ||||
−0.118522 | + | 0.992951i | \(0.537816\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 26075.4i | 1.70139i | 0.525659 | + | 0.850695i | \(0.323819\pi\) | ||||
−0.525659 | + | 0.850695i | \(0.676181\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13844.9i | 0.898986i | 0.893284 | + | 0.449493i | \(0.148395\pi\) | ||||
−0.893284 | + | 0.449493i | \(0.851605\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5063.53 | 0.325627 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4041.83 | −0.258677 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5751.73i | 0.364605i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 906.847i | − 0.0572124i | −0.999591 | − | 0.0286062i | \(-0.990893\pi\) | ||||
0.999591 | − | 0.0286062i | \(-0.00910687\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −16306.5 | −1.01906 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1070.45 | −0.0665820 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 28362.9i | − 1.74769i | −0.486209 | − | 0.873843i | \(-0.661621\pi\) | ||||
0.486209 | − | 0.873843i | \(-0.338379\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6606.82i | 0.405206i | 0.979261 | + | 0.202603i | \(0.0649401\pi\) | ||||
−0.979261 | + | 0.202603i | \(0.935060\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 18843.5 | 1.14500 | 0.572499 | − | 0.819905i | \(-0.305974\pi\) | ||||
0.572499 | + | 0.819905i | \(0.305974\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 34765.2 | 2.10270 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 15382.1i | − 0.921819i | −0.887447 | − | 0.460910i | \(-0.847523\pi\) | ||||
0.887447 | − | 0.460910i | \(-0.152477\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6419.40i | 0.382941i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6692.00 | 0.395574 | 0.197787 | − | 0.980245i | \(-0.436625\pi\) | ||||
0.197787 | + | 0.980245i | \(0.436625\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18708.8 | −1.10089 | −0.550444 | − | 0.834872i | \(-0.685542\pi\) | ||||
−0.550444 | + | 0.834872i | \(0.685542\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 37014.0i | − 2.15841i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 313.951i | − 0.0182252i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −13090.6 | −0.753142 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21815.7 | −1.24953 | −0.624766 | − | 0.780812i | \(-0.714805\pi\) | ||||
−0.624766 | + | 0.780812i | \(0.714805\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 14764.7i | 0.838191i | 0.907942 | + | 0.419095i | \(0.137653\pi\) | ||||
−0.907942 | + | 0.419095i | \(0.862347\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 24225.0i | − 1.36918i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −10522.2 | −0.589489 | −0.294744 | − | 0.955576i | \(-0.595235\pi\) | ||||
−0.294744 | + | 0.955576i | \(0.595235\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12451.7 | 0.694531 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5439.22i | 0.300751i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24495.2i | 1.34854i | 0.738486 | + | 0.674269i | \(0.235541\pi\) | ||||
−0.738486 | + | 0.674269i | \(0.764459\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −36478.8 | −1.99096 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4887.56 | −0.265609 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 22137.1i | − 1.19274i | −0.802711 | − | 0.596368i | \(-0.796610\pi\) | ||||
0.802711 | − | 0.596368i | \(-0.203390\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 56780.3i | − 3.04625i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6765.26 | −0.359878 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 23366.2 | 1.23771 | 0.618854 | − | 0.785506i | \(-0.287597\pi\) | ||||
0.618854 | + | 0.785506i | \(0.287597\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 23527.6i | 1.23579i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 8783.65i | − 0.459427i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3714.68 | −0.192676 | −0.0963380 | − | 0.995349i | \(-0.530713\pi\) | ||||
−0.0963380 | + | 0.995349i | \(0.530713\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14980.5 | −0.773792 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 681.118i | 0.0348911i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6646.80i | 0.339087i | 0.985523 | + | 0.169543i | \(0.0542293\pi\) | ||||
−0.985523 | + | 0.169543i | \(0.945771\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3425.52 | −0.173321 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22683.9 | 1.14304 | 0.571519 | − | 0.820589i | \(-0.306354\pi\) | ||||
0.571519 | + | 0.820589i | \(0.306354\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 21936.8i | 1.09641i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 30377.3i | 1.51211i | 0.654510 | + | 0.756053i | \(0.272875\pi\) | ||||
−0.654510 | + | 0.756053i | \(0.727125\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 17871.8 | 0.882439 | 0.441219 | − | 0.897399i | \(-0.354546\pi\) | ||||
0.441219 | + | 0.897399i | \(0.354546\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 19839.5 | 0.975656 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 23709.6i | 1.15665i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 33183.5i | 1.61236i | 0.591669 | + | 0.806181i | \(0.298469\pi\) | ||||
−0.591669 | + | 0.806181i | \(0.701531\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 13215.6 | 0.637040 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 30541.7 | 1.46639 | 0.733194 | − | 0.680020i | \(-0.238029\pi\) | ||||
0.733194 | + | 0.680020i | \(0.238029\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 14713.4i | − 0.700870i | −0.936587 | − | 0.350435i | \(-0.886034\pi\) | ||||
0.936587 | − | 0.350435i | \(-0.113966\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 9537.56i | − 0.452533i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5689.82 | 0.267858 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1182.88 | 0.0554689 | 0.0277345 | − | 0.999615i | \(-0.491171\pi\) | ||||
0.0277345 | + | 0.999615i | \(0.491171\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8341.02i | 0.388106i | 0.980991 | + | 0.194053i | \(0.0621633\pi\) | ||||
−0.980991 | + | 0.194053i | \(0.937837\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 51043.2i | − 2.36584i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 48249.4 | 2.21914 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −42938.8 | −1.96731 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20572.7i | 0.935378i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 9835.39i | − 0.445482i | −0.974878 | − | 0.222741i | \(-0.928500\pi\) | ||||
0.974878 | − | 0.222741i | \(-0.0715003\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1258.06 | 0.0565504 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2142.47 | −0.0959410 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 20803.2i | − 0.924577i | −0.886730 | − | 0.462288i | \(-0.847028\pi\) | ||||
0.886730 | − | 0.462288i | \(-0.152972\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4223.51i | 0.187005i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 63670.1 | 2.79809 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −22797.5 | −0.998147 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 14439.4i | 0.627518i | 0.949503 | + | 0.313759i | \(0.101588\pi\) | ||||
−0.949503 | + | 0.313759i | \(0.898412\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6457.92i | 0.279616i | 0.990179 | + | 0.139808i | \(0.0446485\pi\) | ||||
−0.990179 | + | 0.139808i | \(0.955352\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −17243.8 | −0.741132 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 33816.3 | 1.44808 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 37203.3i | 1.58149i | 0.612144 | + | 0.790747i | \(0.290307\pi\) | ||||
−0.612144 | + | 0.790747i | \(0.709693\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 1916.63i | − 0.0811781i | −0.999176 | − | 0.0405890i | \(-0.987077\pi\) | ||||
0.999176 | − | 0.0405890i | \(-0.0129234\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 44003.2 | 1.85023 | 0.925117 | − | 0.379683i | \(-0.123967\pi\) | ||||
0.925117 | + | 0.379683i | \(0.123967\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 39853.8 | 1.66970 | 0.834849 | − | 0.550479i | \(-0.185555\pi\) | ||||
0.834849 | + | 0.550479i | \(0.185555\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 1681.64i | − 0.0699465i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 28324.2i | − 1.17389i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −30695.6 | −1.26309 | −0.631543 | − | 0.775341i | \(-0.717578\pi\) | ||||
−0.631543 | + | 0.775341i | \(0.717578\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24375.7 | 0.999456 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 37366.5i | 1.52124i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 25577.0i | − 1.03759i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −34972.0 | −1.40872 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −36152.2 | −1.45115 | −0.725574 | − | 0.688144i | \(-0.758426\pi\) | ||||
−0.725574 | + | 0.688144i | \(0.758426\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 13536.1i | − 0.539540i | −0.962925 | − | 0.269770i | \(-0.913052\pi\) | ||||
0.962925 | − | 0.269770i | \(-0.0869477\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 20932.8i | − 0.831454i | −0.909489 | − | 0.415727i | \(-0.863527\pi\) | ||||
0.909489 | − | 0.415727i | \(-0.136473\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −15068.3 | −0.594359 | −0.297179 | − | 0.954822i | \(-0.596046\pi\) | ||||
−0.297179 | + | 0.954822i | \(0.596046\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4707.60 | 0.185044 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 7018.68i | − 0.273984i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3590.26i | 0.139669i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 16390.6 | 0.633261 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 40198.2 | 1.54777 | 0.773886 | − | 0.633325i | \(-0.218311\pi\) | ||||
0.773886 | + | 0.633325i | \(0.218311\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 34387.5i | 1.31503i | 0.753441 | + | 0.657516i | \(0.228393\pi\) | ||||
−0.753441 | + | 0.657516i | \(0.771607\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 9041.95i | − 0.344604i | −0.985044 | − | 0.172302i | \(-0.944879\pi\) | ||||
0.985044 | − | 0.172302i | \(-0.0551206\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11974.5 | 0.453286 | 0.226643 | − | 0.973978i | \(-0.427225\pi\) | ||||
0.226643 | + | 0.973978i | \(0.427225\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −13828.5 | −0.521702 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 41694.0i | − 1.56241i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3494.78i | 0.130523i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 994.670 | 0.0369011 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8544.85 | −0.315949 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 50063.7i | − 1.83887i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 27657.0i | − 1.01250i | −0.862387 | − | 0.506249i | \(-0.831032\pi\) | ||||
0.862387 | − | 0.506249i | \(-0.168968\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −42952.4 | −1.56210 | −0.781052 | − | 0.624466i | \(-0.785317\pi\) | ||||
−0.781052 | + | 0.624466i | \(0.785317\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 16626.8 | 0.602701 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5443.88i | 0.196044i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 17076.0i | − 0.612934i | −0.951881 | − | 0.306467i | \(-0.900853\pi\) | ||||
0.951881 | − | 0.306467i | \(-0.0991469\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7027.54 | −0.250611 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 75871.8 | 2.69692 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 26818.3i | 0.947126i | 0.880760 | + | 0.473563i | \(0.157032\pi\) | ||||
−0.880760 | + | 0.473563i | \(0.842968\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 16601.0i | 0.584398i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 13798.9 | 0.482642 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 38163.9 | 1.33059 | 0.665294 | − | 0.746582i | \(-0.268306\pi\) | ||||
0.665294 | + | 0.746582i | \(0.268306\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10728.0i | 0.371650i | 0.982583 | + | 0.185825i | \(0.0594957\pi\) | ||||
−0.982583 | + | 0.185825i | \(0.940504\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 29717.6i | − 1.02623i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 28971.4 | 0.994133 | 0.497066 | − | 0.867713i | \(-0.334411\pi\) | ||||
0.497066 | + | 0.867713i | \(0.334411\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10420.5 | 0.356443 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 36897.2i | − 1.25416i | −0.778954 | − | 0.627081i | \(-0.784250\pi\) | ||||
0.778954 | − | 0.627081i | \(-0.215750\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 91638.7i | 3.10509i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 10559.5 | 0.355561 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −44749.9 | −1.50213 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 3644.58i | − 0.121578i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 2016.50i | − 0.0670591i | −0.999438 | − | 0.0335295i | \(-0.989325\pi\) | ||||
0.999438 | − | 0.0335295i | \(-0.0106748\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18482.0 | −0.610830 | −0.305415 | − | 0.952219i | \(-0.598795\pi\) | ||||
−0.305415 | + | 0.952219i | \(0.598795\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −30935.3 | −1.01926 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 22871.4i | 0.748945i | 0.927238 | + | 0.374473i | \(0.122176\pi\) | ||||
−0.927238 | + | 0.374473i | \(0.877824\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 18635.0i | − 0.608352i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −16630.8 | −0.539615 | −0.269808 | − | 0.962914i | \(-0.586960\pi\) | ||||
−0.269808 | + | 0.962914i | \(0.586960\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −58402.1 | −1.88918 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 20828.1i | − 0.669660i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21036.2i | 0.674307i | 0.941450 | + | 0.337153i | \(0.109464\pi\) | ||||
−0.941450 | + | 0.337153i | \(0.890536\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −61665.6 | −1.96475 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −31241.8 | −0.992416 | −0.496208 | − | 0.868204i | \(-0.665275\pi\) | ||||
−0.496208 | + | 0.868204i | \(0.665275\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 288.4.c.b.287.1 | ✓ | 8 | |
3.2 | odd | 2 | inner | 288.4.c.b.287.7 | yes | 8 | |
4.3 | odd | 2 | inner | 288.4.c.b.287.2 | yes | 8 | |
8.3 | odd | 2 | 576.4.c.f.575.8 | 8 | |||
8.5 | even | 2 | 576.4.c.f.575.7 | 8 | |||
12.11 | even | 2 | inner | 288.4.c.b.287.8 | yes | 8 | |
16.3 | odd | 4 | 2304.4.f.h.1151.1 | 8 | |||
16.5 | even | 4 | 2304.4.f.h.1151.8 | 8 | |||
16.11 | odd | 4 | 2304.4.f.e.1151.7 | 8 | |||
16.13 | even | 4 | 2304.4.f.e.1151.2 | 8 | |||
24.5 | odd | 2 | 576.4.c.f.575.1 | 8 | |||
24.11 | even | 2 | 576.4.c.f.575.2 | 8 | |||
48.5 | odd | 4 | 2304.4.f.h.1151.2 | 8 | |||
48.11 | even | 4 | 2304.4.f.e.1151.1 | 8 | |||
48.29 | odd | 4 | 2304.4.f.e.1151.8 | 8 | |||
48.35 | even | 4 | 2304.4.f.h.1151.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
288.4.c.b.287.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
288.4.c.b.287.2 | yes | 8 | 4.3 | odd | 2 | inner | |
288.4.c.b.287.7 | yes | 8 | 3.2 | odd | 2 | inner | |
288.4.c.b.287.8 | yes | 8 | 12.11 | even | 2 | inner | |
576.4.c.f.575.1 | 8 | 24.5 | odd | 2 | |||
576.4.c.f.575.2 | 8 | 24.11 | even | 2 | |||
576.4.c.f.575.7 | 8 | 8.5 | even | 2 | |||
576.4.c.f.575.8 | 8 | 8.3 | odd | 2 | |||
2304.4.f.e.1151.1 | 8 | 48.11 | even | 4 | |||
2304.4.f.e.1151.2 | 8 | 16.13 | even | 4 | |||
2304.4.f.e.1151.7 | 8 | 16.11 | odd | 4 | |||
2304.4.f.e.1151.8 | 8 | 48.29 | odd | 4 | |||
2304.4.f.h.1151.1 | 8 | 16.3 | odd | 4 | |||
2304.4.f.h.1151.2 | 8 | 48.5 | odd | 4 | |||
2304.4.f.h.1151.7 | 8 | 48.35 | even | 4 | |||
2304.4.f.h.1151.8 | 8 | 16.5 | even | 4 |