Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2304,4,Mod(1151,2304)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2304, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2304.1151");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2304 = 2^{8} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2304.f (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(135.940400653\) |
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: | \( 2^{16} \) |
Twist minimal: | no (minimal twist has level 288) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1151.8 | ||
Root | \(-1.67746 + 1.67746i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2304.1151 |
Dual form | 2304.4.f.e.1151.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2304\mathbb{Z}\right)^\times\).
\(n\) | \(1279\) | \(1793\) | \(2053\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(5\) | 17.6623 | 1.57976 | 0.789882 | − | 0.613259i | \(-0.210142\pi\) | ||||
0.789882 | + | 0.613259i | \(0.210142\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 14.9783i | 0.808750i | 0.914593 | + | 0.404375i | \(0.132511\pi\) | ||||
−0.914593 | + | 0.404375i | \(0.867489\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 55.1236i | − 1.51094i | −0.655181 | − | 0.755472i | \(-0.727408\pi\) | ||||
0.655181 | − | 0.755472i | \(-0.272592\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 9.02175i | − 0.192476i | −0.995358 | − | 0.0962378i | \(-0.969319\pi\) | ||||
0.995358 | − | 0.0962378i | \(-0.0306809\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 14.1729i | 0.202202i | 0.994876 | + | 0.101101i | \(0.0322365\pi\) | ||||
−0.994876 | + | 0.101101i | \(0.967763\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −139.913 | −1.68938 | −0.844691 | − | 0.535255i | \(-0.820216\pi\) | ||||
−0.844691 | + | 0.535255i | \(0.820216\pi\) | |||||||
\(20\) | 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 | ||||||||
\(29\) | −3.64319 | −0.0233284 | −0.0116642 | − | 0.999932i | \(-0.503713\pi\) | ||||
−0.0116642 | + | 0.999932i | \(0.503713\pi\) | |||||||
\(30\) | 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 | ||||||||
\(35\) | 264.550i | 1.27763i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 405.826i | 1.80317i | 0.432599 | + | 0.901586i | \(0.357596\pi\) | ||||
−0.432599 | + | 0.901586i | \(0.642404\pi\) | |||||||
\(38\) | 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 | ||||||||
\(43\) | −241.696 | −0.857168 | −0.428584 | − | 0.903502i | \(-0.640987\pi\) | ||||
−0.428584 | + | 0.903502i | \(0.640987\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 297.999 | 0.924844 | 0.462422 | − | 0.886660i | \(-0.346981\pi\) | ||||
0.462422 | + | 0.886660i | \(0.346981\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 118.652 | 0.345924 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 602.901 | 1.56254 | 0.781271 | − | 0.624191i | \(-0.214571\pi\) | ||||
0.781271 | + | 0.624191i | \(0.214571\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 973.609i | − 2.38693i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 630.678i | − 1.39165i | −0.718212 | − | 0.695824i | \(-0.755039\pi\) | ||||
0.718212 | − | 0.695824i | \(-0.244961\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 237.478i | 0.498458i | 0.968445 | + | 0.249229i | \(0.0801772\pi\) | ||||
−0.968445 | + | 0.249229i | \(0.919823\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 159.345i | − 0.304066i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 397.957 | 0.725644 | 0.362822 | − | 0.931859i | \(-0.381813\pi\) | ||||
0.362822 | + | 0.931859i | \(0.381813\pi\) | |||||||
\(68\) | 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 | \(-0.123273\pi\) | ||||
0.925942 | + | 0.377665i | \(0.123273\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 825.655 | 1.22198 | ||||||||
\(78\) | 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 | ||||||||
\(83\) | 301.627i | 0.398890i | 0.979909 | + | 0.199445i | \(0.0639140\pi\) | ||||
−0.979909 | + | 0.199445i | \(0.936086\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 250.326i | 0.319431i | ||||||||
\(86\) | 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 | ||||||||
\(91\) | 135.130 | 0.155665 | ||||||||
\(92\) | 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 | ||||||||
\(101\) | 451.672 | 0.444981 | 0.222490 | − | 0.974935i | \(-0.428581\pi\) | ||||
0.222490 | + | 0.974935i | \(0.428581\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1000.15i | 0.956776i | 0.878149 | + | 0.478388i | \(0.158779\pi\) | ||||
−0.878149 | + | 0.478388i | \(0.841221\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 1582.93i | − 1.43017i | −0.699038 | − | 0.715085i | \(-0.746388\pi\) | ||||
0.699038 | − | 0.715085i | \(-0.253612\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 636.761i | 0.559547i | 0.960066 | + | 0.279773i | \(0.0902594\pi\) | ||||
−0.960066 | + | 0.279773i | \(0.909741\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 83.9922i | − 0.0699232i | −0.999389 | − | 0.0349616i | \(-0.988869\pi\) | ||||
0.999389 | − | 0.0349616i | \(-0.0111309\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1522.04 | 1.23419 | ||||||||
\(116\) | 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 | ||||||||
\(125\) | 1094.29 | 0.783013 | ||||||||
\(126\) | 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 | ||||||||
\(131\) | 363.452i | 0.242404i | 0.992628 | + | 0.121202i | \(0.0386749\pi\) | ||||
−0.992628 | + | 0.121202i | \(0.961325\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 2095.65i | − 1.36629i | ||||||||
\(134\) | 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 | ||||||||
\(139\) | −2065.35 | −1.26029 | −0.630146 | − | 0.776477i | \(-0.717005\pi\) | ||||
−0.630146 | + | 0.776477i | \(0.717005\pi\) | |||||||
\(140\) | 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 | ||||||||
\(149\) | −1123.27 | −0.617596 | −0.308798 | − | 0.951128i | \(-0.599927\pi\) | ||||
−0.308798 | + | 0.951128i | \(0.599927\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 748.239i | − 0.403250i | −0.979463 | − | 0.201625i | \(-0.935378\pi\) | ||||
0.979463 | − | 0.201625i | \(-0.0646223\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4822.19i | 2.49889i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 1164.78i | − 0.592100i | −0.955172 | − | 0.296050i | \(-0.904330\pi\) | ||||
0.955172 | − | 0.296050i | \(-0.0956695\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1290.75i | 0.631833i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 976.304 | 0.469141 | 0.234571 | − | 0.972099i | \(-0.424632\pi\) | ||||
0.234571 | + | 0.972099i | \(0.424632\pi\) | |||||||
\(164\) | 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 | ||||||||
\(173\) | 266.534 | 0.117134 | 0.0585670 | − | 0.998283i | \(-0.481347\pi\) | ||||
0.0585670 | + | 0.998283i | \(0.481347\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2800.28i | 1.20961i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 197.867i | 0.0826216i | 0.999146 | + | 0.0413108i | \(0.0131534\pi\) | ||||
−0.999146 | + | 0.0413108i | \(0.986847\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 2834.50i | − 1.16401i | −0.813184 | − | 0.582007i | \(-0.802268\pi\) | ||||
0.813184 | − | 0.582007i | \(-0.197732\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7167.82i | 2.84859i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 781.261 | 0.305516 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5188.38 | 1.96554 | 0.982770 | − | 0.184835i | \(-0.0591750\pi\) | ||||
0.982770 | + | 0.184835i | \(0.0591750\pi\) | |||||||
\(192\) | 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 | ||||||||
\(197\) | 3306.60 | 1.19587 | 0.597933 | − | 0.801546i | \(-0.295989\pi\) | ||||
0.597933 | + | 0.801546i | \(0.295989\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3491.37i | 1.24370i | 0.783136 | + | 0.621851i | \(0.213619\pi\) | ||||
−0.783136 | + | 0.621851i | \(0.786381\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 54.5686i | − 0.0188668i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 6090.89i | − 2.07515i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7712.50i | 2.55256i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4808.48 | −1.56886 | −0.784429 | − | 0.620218i | \(-0.787044\pi\) | ||||
−0.784429 | + | 0.620218i | \(0.787044\pi\) | |||||||
\(212\) | 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 | ||||||||
\(221\) | 127.864 | 0.0389189 | ||||||||
\(222\) | 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 | ||||||||
\(227\) | 761.369i | 0.222616i | 0.993786 | + | 0.111308i | \(0.0355040\pi\) | ||||
−0.993786 | + | 0.111308i | \(0.964496\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 2397.76i | − 0.691915i | −0.938250 | − | 0.345957i | \(-0.887554\pi\) | ||||
0.938250 | − | 0.345957i | \(-0.112446\pi\) | |||||||
\(230\) | 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 | ||||||||
\(235\) | 5263.35 | 1.46103 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1287.79 | −0.348538 | −0.174269 | − | 0.984698i | \(-0.555756\pi\) | ||||
−0.174269 | + | 0.984698i | \(0.555756\pi\) | |||||||
\(240\) | 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 | ||||||||
\(245\) | 2095.67 | 0.546478 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1262.26i | 0.325165i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 3501.68i | − 0.880575i | −0.897857 | − | 0.440288i | \(-0.854876\pi\) | ||||
0.897857 | − | 0.440288i | \(-0.145124\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 4750.26i | − 1.18042i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1295.48i | 0.314435i | 0.987564 | + | 0.157218i | \(0.0502524\pi\) | ||||
−0.987564 | + | 0.157218i | \(0.949748\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6078.56 | −1.45831 | ||||||||
\(260\) | 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 | ||||||||
\(269\) | 2974.78 | 0.674259 | 0.337129 | − | 0.941458i | \(-0.390544\pi\) | ||||
0.337129 | + | 0.941458i | \(0.390544\pi\) | |||||||
\(270\) | 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 | ||||||||
\(275\) | − 10305.7i | − 2.25985i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 213.586i | 0.0463291i | 0.999732 | + | 0.0231645i | \(0.00737416\pi\) | ||||
−0.999732 | + | 0.0231645i | \(0.992626\pi\) | |||||||
\(278\) | 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 | ||||||||
\(283\) | 4761.83 | 1.00022 | 0.500108 | − | 0.865963i | \(-0.333294\pi\) | ||||
0.500108 | + | 0.865963i | \(0.333294\pi\) | |||||||
\(284\) | 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 | ||||||||
\(293\) | 1371.49 | 0.273459 | 0.136730 | − | 0.990608i | \(-0.456341\pi\) | ||||
0.136730 | + | 0.990608i | \(0.456341\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 11139.2i | − 2.19847i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 777.447i | − 0.150371i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 3620.18i | − 0.693234i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4194.41i | 0.787446i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −511.696 | −0.0951272 | −0.0475636 | − | 0.998868i | \(-0.515146\pi\) | ||||
−0.0475636 | + | 0.998868i | \(0.515146\pi\) | |||||||
\(308\) | 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 | \(-0.579167\pi\) | ||||
−0.246154 | + | 0.969231i | \(0.579167\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −566.346 | −0.100344 | −0.0501722 | − | 0.998741i | \(-0.515977\pi\) | ||||
−0.0501722 | + | 0.998741i | \(0.515977\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 200.826i | 0.0352479i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 1982.97i | − 0.341596i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 1686.67i | − 0.287877i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4463.51i | 0.747967i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7531.08 | −1.25059 | −0.625296 | − | 0.780388i | \(-0.715022\pi\) | ||||
−0.625296 | + | 0.780388i | \(0.715022\pi\) | |||||||
\(332\) | 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 | ||||||||
\(341\) | 15049.9 | 2.39003 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6914.74i | 1.08852i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8937.55i | 1.38269i | 0.722525 | + | 0.691344i | \(0.242981\pi\) | ||||
−0.722525 | + | 0.691344i | \(0.757019\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7003.04i | 1.07411i | 0.843547 | + | 0.537055i | \(0.180463\pi\) | ||||
−0.843547 | + | 0.537055i | \(0.819537\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3368.17i | 0.507845i | 0.967225 | + | 0.253923i | \(0.0817208\pi\) | ||||
−0.967225 | + | 0.253923i | \(0.918279\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 13758.1 | 2.05692 | ||||||||
\(356\) | 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 | ||||||||
\(365\) | 20400.7 | 2.92554 | ||||||||
\(366\) | 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 | ||||||||
\(371\) | 9030.40i | 1.26371i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 5174.87i | − 0.718350i | −0.933270 | − | 0.359175i | \(-0.883058\pi\) | ||||
0.933270 | − | 0.359175i | \(-0.116942\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 32.8679i | 0.00449014i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3076.35 | 0.416943 | 0.208471 | − | 0.978028i | \(-0.433151\pi\) | ||||
0.208471 | + | 0.978028i | \(0.433151\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10465.9 | −1.39630 | −0.698151 | − | 0.715951i | \(-0.745993\pi\) | ||||
−0.698151 | + | 0.715951i | \(0.745993\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 14583.0 | 1.93043 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2556.64 | 0.333231 | 0.166615 | − | 0.986022i | \(-0.446716\pi\) | ||||
0.166615 | + | 0.986022i | \(0.446716\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1221.35i | 0.157970i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2248.87i | 0.286464i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1232.61i | 0.155826i | 0.996960 | + | 0.0779130i | \(0.0248256\pi\) | ||||
−0.996960 | + | 0.0779130i | \(0.975174\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 2278.88i | − 0.283795i | −0.989881 | − | 0.141898i | \(-0.954680\pi\) | ||||
0.989881 | − | 0.141898i | \(-0.0453204\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2463.13 | 0.304460 | ||||||||
\(404\) | 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 | \(-0.518292\pi\) | ||||
−0.0574339 | + | 0.998349i | \(0.518292\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9446.45 | 1.12549 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5327.43i | 0.630152i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 6974.81i | − 0.813226i | −0.913600 | − | 0.406613i | \(-0.866710\pi\) | ||||
0.913600 | − | 0.406613i | \(-0.133290\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1713.41i | 0.198353i | 0.995070 | + | 0.0991764i | \(0.0316208\pi\) | ||||
−0.995070 | + | 0.0991764i | \(0.968379\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2649.71i | 0.302424i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3557.01 | −0.403128 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7234.34 | −0.808506 | −0.404253 | − | 0.914647i | \(-0.632468\pi\) | ||||
−0.404253 | + | 0.914647i | \(0.632468\pi\) | |||||||
\(432\) | 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 | ||||||||
\(437\) | −12057.0 | −1.31982 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11500.7i | 1.25034i | 0.780489 | + | 0.625170i | \(0.214970\pi\) | ||||
−0.780489 | + | 0.625170i | \(0.785030\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 12976.7i | − 1.39174i | −0.718169 | − | 0.695869i | \(-0.755019\pi\) | ||||
0.718169 | − | 0.695869i | \(-0.244981\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5970.89i | 0.636061i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 8302.07i | − 0.872604i | −0.899800 | − | 0.436302i | \(-0.856288\pi\) | ||||
0.899800 | − | 0.436302i | \(-0.143712\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −19009.5 | −1.98475 | ||||||||
\(452\) | 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 | \(-0.467731\pi\) | ||||
0.101204 | + | 0.994866i | \(0.467731\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1616.73 | −0.163338 | −0.0816690 | − | 0.996660i | \(-0.526025\pi\) | ||||
−0.0816690 | + | 0.996660i | \(0.526025\pi\) | |||||||
\(462\) | 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 | ||||||||
\(467\) | 15942.8i | 1.57975i | 0.613268 | + | 0.789875i | \(0.289855\pi\) | ||||
−0.613268 | + | 0.789875i | \(0.710145\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5960.69i | 0.586864i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 13323.1i | 1.29513i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −26157.6 | −2.52673 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14684.4 | −1.40073 | −0.700363 | − | 0.713786i | \(-0.746979\pi\) | ||||
−0.700363 | + | 0.713786i | \(0.746979\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3661.26 | 0.347067 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 28566.1 | 2.67447 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9871.54i | 0.918526i | 0.888300 | + | 0.459263i | \(0.151886\pi\) | ||||
−0.888300 | + | 0.459263i | \(0.848114\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4356.26i | 0.400398i | 0.979755 | + | 0.200199i | \(0.0641589\pi\) | ||||
−0.979755 | + | 0.200199i | \(0.935841\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 51.6345i | − 0.00471704i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 11667.4i | 1.05303i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15900.3 | 1.42645 | 0.713224 | − | 0.700937i | \(-0.247234\pi\) | ||||
0.713224 | + | 0.700937i | \(0.247234\pi\) | |||||||
\(500\) | 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 | ||||||||
\(509\) | −4733.57 | −0.412204 | −0.206102 | − | 0.978531i | \(-0.566078\pi\) | ||||
−0.206102 | + | 0.978531i | \(0.566078\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 17300.5i | 1.49771i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 17665.0i | 1.51148i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 16426.8i | − 1.39739i | ||||||||
\(518\) | 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 | ||||||||
\(523\) | 12945.2 | 1.08232 | 0.541161 | − | 0.840919i | \(-0.317985\pi\) | ||||
0.541161 | + | 0.840919i | \(0.317985\pi\) | |||||||
\(524\) | 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 | ||||||||
\(533\) | −3111.18 | −0.252833 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 27958.3i | − 2.25933i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 6540.52i | − 0.522672i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 7859.59i | − 0.624603i | −0.949983 | − | 0.312301i | \(-0.898900\pi\) | ||||
0.949983 | − | 0.312301i | \(-0.101100\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 11246.7i | 0.883952i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20633.2 | 1.61282 | 0.806408 | − | 0.591359i | \(-0.201408\pi\) | ||||
0.806408 | + | 0.591359i | \(0.201408\pi\) | |||||||
\(548\) | 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 | ||||||||
\(557\) | 22253.3 | 1.69282 | 0.846411 | − | 0.532531i | \(-0.178759\pi\) | ||||
0.846411 | + | 0.532531i | \(0.178759\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2180.52i | 0.164984i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 7722.80i | − 0.578112i | −0.957312 | − | 0.289056i | \(-0.906659\pi\) | ||||
0.957312 | − | 0.289056i | \(-0.0933415\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 1483.50i | − 0.110462i | ||||||||
\(566\) | 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 | ||||||||
\(571\) | 11021.0 | 0.807728 | 0.403864 | − | 0.914819i | \(-0.367667\pi\) | ||||
0.403864 | + | 0.914819i | \(0.367667\pi\) | |||||||
\(572\) | 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 | ||||||||
\(581\) | −4517.85 | −0.322602 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 33234.0i | − 2.36091i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 3641.73i | − 0.256065i | −0.991770 | − | 0.128032i | \(-0.959134\pi\) | ||||
0.991770 | − | 0.128032i | \(-0.0408662\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 38199.3i | − 2.67228i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 2475.73i | − 0.171444i | −0.996319 | − | 0.0857219i | \(-0.972680\pi\) | ||||
0.996319 | − | 0.0857219i | \(-0.0273197\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3749.44 | −0.258340 | ||||||||
\(596\) | 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 | \(-0.361616\pi\) | ||||
0.421179 | + | 0.906978i | \(0.361616\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −30160.3 | −2.02676 | ||||||||
\(606\) | 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 | ||||||||
\(611\) | − 2688.47i | − 0.178010i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3597.65i | 0.237044i | 0.992951 | + | 0.118522i | \(0.0378156\pi\) | ||||
−0.992951 | + | 0.118522i | \(0.962184\pi\) | |||||||
\(614\) | 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 | ||||||||
\(619\) | 13844.9 | 0.898986 | 0.449493 | − | 0.893284i | \(-0.351605\pi\) | ||||
0.449493 | + | 0.893284i | \(0.351605\pi\) | |||||||
\(620\) | 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 | ||||||||
\(629\) | −5751.73 | −0.364605 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 906.847i | 0.0572124i | 0.999591 | + | 0.0286062i | \(0.00910687\pi\) | ||||
−0.999591 | + | 0.0286062i | \(0.990893\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 16306.5i | − 1.01906i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 1070.45i | − 0.0665820i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 28362.9i | 1.74769i | 0.486209 | + | 0.873843i | \(0.338379\pi\) | ||||
−0.486209 | + | 0.873843i | \(0.661621\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6606.82 | −0.405206 | −0.202603 | − | 0.979261i | \(-0.564940\pi\) | ||||
−0.202603 | + | 0.979261i | \(0.564940\pi\) | |||||||
\(644\) | 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 | ||||||||
\(653\) | −15382.1 | −0.921819 | −0.460910 | − | 0.887447i | \(-0.652477\pi\) | ||||
−0.460910 | + | 0.887447i | \(0.652477\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6419.40i | 0.382941i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 6692.00i | − 0.395574i | −0.980245 | − | 0.197787i | \(-0.936625\pi\) | ||||
0.980245 | − | 0.197787i | \(-0.0633754\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18708.8i | 1.10089i | 0.834872 | + | 0.550444i | \(0.185542\pi\) | ||||
−0.834872 | + | 0.550444i | \(0.814458\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 37014.0i | − 2.15841i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −313.951 | −0.0182252 | ||||||||
\(668\) | 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 | ||||||||
\(677\) | −14764.7 | −0.838191 | −0.419095 | − | 0.907942i | \(-0.637653\pi\) | ||||
−0.419095 | + | 0.907942i | \(0.637653\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 24225.0i | 1.36918i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 10522.2i | − 0.589489i | −0.955576 | − | 0.294744i | \(-0.904765\pi\) | ||||
0.955576 | − | 0.294744i | \(-0.0952345\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12451.7i | 0.694531i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 5439.22i | − 0.300751i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −24495.2 | −1.34854 | −0.674269 | − | 0.738486i | \(-0.735541\pi\) | ||||
−0.674269 | + | 0.738486i | \(0.735541\pi\) | |||||||
\(692\) | 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 | ||||||||
\(701\) | −22137.1 | −1.19274 | −0.596368 | − | 0.802711i | \(-0.703390\pi\) | ||||
−0.596368 | + | 0.802711i | \(0.703390\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 56780.3i | − 3.04625i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6765.26i | 0.359878i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 23366.2i | − 1.23771i | −0.785506 | − | 0.618854i | \(-0.787597\pi\) | ||||
0.785506 | − | 0.618854i | \(-0.212403\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 23527.6i | 1.23579i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8783.65 | −0.459427 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3714.68 | 0.192676 | 0.0963380 | − | 0.995349i | \(-0.469287\pi\) | ||||
0.0963380 | + | 0.995349i | \(0.469287\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14980.5 | −0.773792 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −681.118 | −0.0348911 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 6646.80i | − 0.339087i | −0.985523 | − | 0.169543i | \(-0.945771\pi\) | ||||
0.985523 | − | 0.169543i | \(-0.0542293\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 3425.52i | − 0.173321i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22683.9i | 1.14304i | 0.820589 | + | 0.571519i | \(0.193646\pi\) | ||||
−0.820589 | + | 0.571519i | \(0.806354\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 21936.8i | − 1.09641i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −30377.3 | −1.51211 | −0.756053 | − | 0.654510i | \(-0.772875\pi\) | ||||
−0.756053 | + | 0.654510i | \(0.772875\pi\) | |||||||
\(740\) | 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 | ||||||||
\(749\) | 23709.6 | 1.15665 | ||||||||
\(750\) | 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 | ||||||||
\(755\) | − 13215.6i | − 0.637040i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 30541.7i | − 1.46639i | −0.680020 | − | 0.733194i | \(-0.738029\pi\) | ||||
0.680020 | − | 0.733194i | \(-0.261971\pi\) | |||||||
\(758\) | 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 | ||||||||
\(763\) | −9537.56 | −0.452533 | ||||||||
\(764\) | 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 | ||||||||
\(773\) | −8341.02 | −0.388106 | −0.194053 | − | 0.980991i | \(-0.562163\pi\) | ||||
−0.194053 | + | 0.980991i | \(0.562163\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 51043.2i | 2.36584i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 48249.4i | 2.21914i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 42938.8i | − 1.96731i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 20572.7i | − 0.935378i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9835.39 | 0.445482 | 0.222741 | − | 0.974878i | \(-0.428500\pi\) | ||||
0.222741 | + | 0.974878i | \(0.428500\pi\) | |||||||
\(788\) | 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 | ||||||||
\(797\) | −20803.2 | −0.924577 | −0.462288 | − | 0.886730i | \(-0.652972\pi\) | ||||
−0.462288 | + | 0.886730i | \(0.652972\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4223.51i | 0.187005i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 63670.1i | − 2.79809i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 22797.5i | 0.998147i | ||||||||
\(806\) | 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 | ||||||||
\(811\) | 6457.92 | 0.279616 | 0.139808 | − | 0.990179i | \(-0.455352\pi\) | ||||
0.139808 | + | 0.990179i | \(0.455352\pi\) | |||||||
\(812\) | 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 | ||||||||
\(821\) | −37203.3 | −1.58149 | −0.790747 | − | 0.612144i | \(-0.790307\pi\) | ||||
−0.790747 | + | 0.612144i | \(0.790307\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1916.63i | 0.0811781i | 0.999176 | + | 0.0405890i | \(0.0129234\pi\) | ||||
−0.999176 | + | 0.0405890i | \(0.987077\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 44003.2i | 1.85023i | 0.379683 | + | 0.925117i | \(0.376033\pi\) | ||||
−0.379683 | + | 0.925117i | \(0.623967\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 39853.8i | 1.66970i | 0.550479 | + | 0.834849i | \(0.314445\pi\) | ||||
−0.550479 | + | 0.834849i | \(0.685555\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1681.64i | 0.0699465i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 28324.2 | 1.17389 | ||||||||
\(836\) | 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 | ||||||||
\(845\) | 37366.5 | 1.52124 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 25577.0i | − 1.03759i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 34972.0i | 1.40872i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 36152.2i | 1.45115i | 0.688144 | + | 0.725574i | \(0.258426\pi\) | ||||
−0.688144 | + | 0.725574i | \(0.741574\pi\) | |||||||
\(854\) | 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 | ||||||||
\(859\) | −20932.8 | −0.831454 | −0.415727 | − | 0.909489i | \(-0.636473\pi\) | ||||
−0.415727 | + | 0.909489i | \(0.636473\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 15068.3 | 0.594359 | 0.297179 | − | 0.954822i | \(-0.403954\pi\) | ||||
0.297179 | + | 0.954822i | \(0.403954\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4707.60 | 0.185044 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7018.68 | 0.273984 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 3590.26i | − 0.139669i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 16390.6i | 0.633261i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 40198.2i | 1.54777i | 0.633325 | + | 0.773886i | \(0.281689\pi\) | ||||
−0.633325 | + | 0.773886i | \(0.718311\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 34387.5i | − 1.31503i | −0.753441 | − | 0.657516i | \(-0.771607\pi\) | ||||
0.753441 | − | 0.657516i | \(-0.228393\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9041.95 | 0.344604 | 0.172302 | − | 0.985044i | \(-0.444879\pi\) | ||||
0.172302 | + | 0.985044i | \(0.444879\pi\) | |||||||
\(884\) | 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 | ||||||||
\(893\) | −41694.0 | −1.56241 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3494.78i | 0.130523i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 994.670i | − 0.0369011i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8544.85i | 0.315949i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 50063.7i | − 1.83887i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −27657.0 | −1.01250 | −0.506249 | − | 0.862387i | \(-0.668968\pi\) | ||||
−0.506249 | + | 0.862387i | \(0.668968\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 42952.4 | 1.56210 | 0.781052 | − | 0.624466i | \(-0.214683\pi\) | ||||
0.781052 | + | 0.624466i | \(0.214683\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 16626.8 | 0.602701 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5443.88 | −0.196044 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17076.0i | 0.612934i | 0.951881 | + | 0.306467i | \(0.0991469\pi\) | ||||
−0.951881 | + | 0.306467i | \(0.900853\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 7027.54i | − 0.250611i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 75871.8i | 2.69692i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 26818.3i | − 0.947126i | −0.880760 | − | 0.473563i | \(-0.842968\pi\) | ||||
0.880760 | − | 0.473563i | \(-0.157032\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −16601.0 | −0.584398 | ||||||||
\(932\) | 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 | \(-0.731694\pi\) | ||||
−0.665294 | + | 0.746582i | \(0.731694\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10728.0 | 0.371650 | 0.185825 | − | 0.982583i | \(-0.440504\pi\) | ||||
0.185825 | + | 0.982583i | \(0.440504\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 29717.6i | − 1.02623i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 28971.4i | − 0.994133i | −0.867713 | − | 0.497066i | \(-0.834411\pi\) | ||||
0.867713 | − | 0.497066i | \(-0.165589\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 10420.5i | − 0.356443i | ||||||||
\(950\) | 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 | ||||||||
\(955\) | 91638.7 | 3.10509 | ||||||||
\(956\) | 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 | ||||||||
\(965\) | 3644.58 | 0.121578 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2016.50i | 0.0670591i | 0.999438 | + | 0.0335295i | \(0.0106748\pi\) | ||||
−0.999438 | + | 0.0335295i | \(0.989325\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 18482.0i | − 0.610830i | −0.952219 | − | 0.305415i | \(-0.901205\pi\) | ||||
0.952219 | − | 0.305415i | \(-0.0987952\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 30935.3i | − 1.01926i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 22871.4i | − 0.748945i | −0.927238 | − | 0.374473i | \(-0.877824\pi\) | ||||
0.927238 | − | 0.374473i | \(-0.122176\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18635.0 | 0.608352 | ||||||||
\(980\) | 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 | ||||||||
\(989\) | −20828.1 | −0.669660 | ||||||||
\(990\) | 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 | ||||||||
\(995\) | 61665.6i | 1.96475i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 31241.8i | 0.992416i | 0.868204 | + | 0.496208i | \(0.165275\pi\) | ||||
−0.868204 | + | 0.496208i | \(0.834725\pi\) | |||||||
\(998\) | 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 | 2304.4.f.e.1151.8 | 8 | ||
3.2 | odd | 2 | inner | 2304.4.f.e.1151.2 | 8 | ||
4.3 | odd | 2 | 2304.4.f.h.1151.7 | 8 | |||
8.3 | odd | 2 | inner | 2304.4.f.e.1151.1 | 8 | ||
8.5 | even | 2 | 2304.4.f.h.1151.2 | 8 | |||
12.11 | even | 2 | 2304.4.f.h.1151.1 | 8 | |||
16.3 | odd | 4 | 576.4.c.f.575.2 | 8 | |||
16.5 | even | 4 | 288.4.c.b.287.7 | yes | 8 | ||
16.11 | odd | 4 | 288.4.c.b.287.8 | yes | 8 | ||
16.13 | even | 4 | 576.4.c.f.575.1 | 8 | |||
24.5 | odd | 2 | 2304.4.f.h.1151.8 | 8 | |||
24.11 | even | 2 | inner | 2304.4.f.e.1151.7 | 8 | ||
48.5 | odd | 4 | 288.4.c.b.287.1 | ✓ | 8 | ||
48.11 | even | 4 | 288.4.c.b.287.2 | yes | 8 | ||
48.29 | odd | 4 | 576.4.c.f.575.7 | 8 | |||
48.35 | even | 4 | 576.4.c.f.575.8 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
288.4.c.b.287.1 | ✓ | 8 | 48.5 | odd | 4 | ||
288.4.c.b.287.2 | yes | 8 | 48.11 | even | 4 | ||
288.4.c.b.287.7 | yes | 8 | 16.5 | even | 4 | ||
288.4.c.b.287.8 | yes | 8 | 16.11 | odd | 4 | ||
576.4.c.f.575.1 | 8 | 16.13 | even | 4 | |||
576.4.c.f.575.2 | 8 | 16.3 | odd | 4 | |||
576.4.c.f.575.7 | 8 | 48.29 | odd | 4 | |||
576.4.c.f.575.8 | 8 | 48.35 | even | 4 | |||
2304.4.f.e.1151.1 | 8 | 8.3 | odd | 2 | inner | ||
2304.4.f.e.1151.2 | 8 | 3.2 | odd | 2 | inner | ||
2304.4.f.e.1151.7 | 8 | 24.11 | even | 2 | inner | ||
2304.4.f.e.1151.8 | 8 | 1.1 | even | 1 | trivial | ||
2304.4.f.h.1151.1 | 8 | 12.11 | even | 2 | |||
2304.4.f.h.1151.2 | 8 | 8.5 | even | 2 | |||
2304.4.f.h.1151.7 | 8 | 4.3 | odd | 2 | |||
2304.4.f.h.1151.8 | 8 | 24.5 | odd | 2 |