Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,3,Mod(127,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.127");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.m (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(27.4660106475\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-7})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - x^{2} - 2x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 336) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 127.4 | ||
Root | \(1.39564 - 0.228425i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1008.127 |
Dual form | 1008.3.m.e.127.1 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.00000 | 0.400000 | 0.200000 | − | 0.979796i | \(-0.435906\pi\) | ||||
0.200000 | + | 0.979796i | \(0.435906\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.64575i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 3.65480i | − 0.332255i | −0.986104 | − | 0.166127i | \(-0.946874\pi\) | ||||
0.986104 | − | 0.166127i | \(-0.0531263\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −16.3303 | −1.25618 | −0.628089 | − | 0.778142i | \(-0.716162\pi\) | ||||
−0.628089 | + | 0.778142i | \(0.716162\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.33030 | 0.254724 | 0.127362 | − | 0.991856i | \(-0.459349\pi\) | ||||
0.127362 | + | 0.991856i | \(0.459349\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 14.2378i | − 0.749358i | −0.927155 | − | 0.374679i | \(-0.877753\pi\) | ||||
0.927155 | − | 0.374679i | \(-0.122247\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 31.3676i | − 1.36381i | −0.731441 | − | 0.681905i | \(-0.761152\pi\) | ||||
0.731441 | − | 0.681905i | \(-0.238848\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −21.0000 | −0.840000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 50.6606 | 1.74692 | 0.873459 | − | 0.486898i | \(-0.161872\pi\) | ||||
0.873459 | + | 0.486898i | \(0.161872\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 27.7128i | − 0.893962i | −0.894544 | − | 0.446981i | \(-0.852499\pi\) | ||||
0.894544 | − | 0.446981i | \(-0.147501\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.29150i | 0.151186i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.6606 | −0.288124 | −0.144062 | − | 0.989569i | \(-0.546017\pi\) | ||||
−0.144062 | + | 0.989569i | \(0.546017\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.33030 | −0.203178 | −0.101589 | − | 0.994826i | \(-0.532393\pi\) | ||||
−0.101589 | + | 0.994826i | \(0.532393\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.54680i | 0.152251i | 0.997098 | + | 0.0761256i | \(0.0242550\pi\) | ||||
−0.997098 | + | 0.0761256i | \(0.975745\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 35.7852i | − 0.761388i | −0.924701 | − | 0.380694i | \(-0.875685\pi\) | ||||
0.924701 | − | 0.380694i | \(-0.124315\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 26.6606 | 0.503030 | 0.251515 | − | 0.967853i | \(-0.419071\pi\) | ||||
0.251515 | + | 0.967853i | \(0.419071\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 7.30960i | − 0.132902i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 0.381401i | − 0.00646442i | −0.999995 | − | 0.00323221i | \(-0.998971\pi\) | ||||
0.999995 | − | 0.00323221i | \(-0.00102885\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −24.3303 | −0.398857 | −0.199429 | − | 0.979912i | \(-0.563909\pi\) | ||||
−0.199429 | + | 0.979912i | \(0.563909\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −32.6606 | −0.502471 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 55.4256i | − 0.827248i | −0.910448 | − | 0.413624i | \(-0.864263\pi\) | ||||
0.910448 | − | 0.413624i | \(-0.135737\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 94.8656i | − 1.33614i | −0.744100 | − | 0.668068i | \(-0.767122\pi\) | ||||
0.744100 | − | 0.668068i | \(-0.232878\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 94.6606 | 1.29672 | 0.648360 | − | 0.761334i | \(-0.275455\pi\) | ||||
0.648360 | + | 0.761334i | \(0.275455\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9.66970 | 0.125580 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 96.9948i | 1.22778i | 0.789390 | + | 0.613891i | \(0.210397\pi\) | ||||
−0.789390 | + | 0.613891i | \(0.789603\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 105.449i | − 1.27047i | −0.772321 | − | 0.635233i | \(-0.780904\pi\) | ||||
0.772321 | − | 0.635233i | \(-0.219096\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.66061 | 0.101889 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −92.9909 | −1.04484 | −0.522421 | − | 0.852688i | \(-0.674971\pi\) | ||||
−0.522421 | + | 0.852688i | \(0.674971\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 43.2059i | − 0.474790i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 28.4756i | − 0.299743i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 51.3212 | 0.529085 | 0.264542 | − | 0.964374i | \(-0.414779\pi\) | ||||
0.264542 | + | 0.964374i | \(0.414779\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −74.6606 | −0.739214 | −0.369607 | − | 0.929188i | \(-0.620508\pi\) | ||||
−0.369607 | + | 0.929188i | \(0.620508\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 140.090i | − 1.36009i | −0.733169 | − | 0.680047i | \(-0.761959\pi\) | ||||
0.733169 | − | 0.680047i | \(-0.238041\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 198.407i | − 1.85427i | −0.374723 | − | 0.927137i | \(-0.622262\pi\) | ||||
0.374723 | − | 0.927137i | \(-0.377738\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −33.3394 | −0.305866 | −0.152933 | − | 0.988237i | \(-0.548872\pi\) | ||||
−0.152933 | + | 0.988237i | \(0.548872\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.3212 | −0.100188 | −0.0500939 | − | 0.998745i | \(-0.515952\pi\) | ||||
−0.0500939 | + | 0.998745i | \(0.515952\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 62.7352i | − 0.545524i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 11.4569i | 0.0962765i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 107.642 | 0.889607 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −92.0000 | −0.736000 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 84.6640i | − 0.666646i | −0.942813 | − | 0.333323i | \(-0.891830\pi\) | ||||
0.942813 | − | 0.333323i | \(-0.108170\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 160.111i | 1.22223i | 0.791544 | + | 0.611113i | \(0.209278\pi\) | ||||
−0.791544 | + | 0.611113i | \(0.790722\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 37.6697 | 0.283231 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −193.303 | −1.41097 | −0.705486 | − | 0.708724i | \(-0.749271\pi\) | ||||
−0.705486 | + | 0.708724i | \(0.749271\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 60.8282i | 0.437613i | 0.975768 | + | 0.218807i | \(0.0702164\pi\) | ||||
−0.975768 | + | 0.218807i | \(0.929784\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 59.6840i | 0.417371i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 101.321 | 0.698767 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 131.982 | 0.885784 | 0.442892 | − | 0.896575i | \(-0.353953\pi\) | ||||
0.442892 | + | 0.896575i | \(0.353953\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 62.7352i | − 0.415465i | −0.978186 | − | 0.207733i | \(-0.933392\pi\) | ||||
0.978186 | − | 0.207733i | \(-0.0666084\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 55.4256i | − 0.357585i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −86.3121 | −0.549759 | −0.274879 | − | 0.961479i | \(-0.588638\pi\) | ||||
−0.274879 | + | 0.961479i | \(0.588638\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 82.9909 | 0.515471 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 165.514i | 1.01542i | 0.861527 | + | 0.507712i | \(0.169509\pi\) | ||||
−0.861527 | + | 0.507712i | \(0.830491\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 270.581i | − 1.62025i | −0.586259 | − | 0.810124i | \(-0.699400\pi\) | ||||
0.586259 | − | 0.810124i | \(-0.300600\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 97.6788 | 0.577981 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 332.642 | 1.92279 | 0.961394 | − | 0.275175i | \(-0.0887356\pi\) | ||||
0.961394 | + | 0.275175i | \(0.0887356\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 55.5608i | − 0.317490i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 170.694i | 0.953600i | 0.879012 | + | 0.476800i | \(0.158203\pi\) | ||||
−0.879012 | + | 0.476800i | \(0.841797\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −169.652 | −0.937301 | −0.468651 | − | 0.883384i | \(-0.655260\pi\) | ||||
−0.468651 | + | 0.883384i | \(0.655260\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −21.3212 | −0.115250 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 15.8264i | − 0.0846332i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 301.949i | − 1.58088i | −0.612537 | − | 0.790442i | \(-0.709851\pi\) | ||||
0.612537 | − | 0.790442i | \(-0.290149\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −224.642 | −1.16395 | −0.581975 | − | 0.813207i | \(-0.697720\pi\) | ||||
−0.581975 | + | 0.813207i | \(0.697720\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.98182 | −0.0405168 | −0.0202584 | − | 0.999795i | \(-0.506449\pi\) | ||||
−0.0202584 | + | 0.999795i | \(0.506449\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 369.102i | − 1.85478i | −0.374093 | − | 0.927391i | \(-0.622046\pi\) | ||||
0.374093 | − | 0.927391i | \(-0.377954\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 134.035i | 0.660273i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −16.6606 | −0.0812712 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −52.0364 | −0.248978 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 344.440i | 1.63242i | 0.577757 | + | 0.816209i | \(0.303928\pi\) | ||||
−0.577757 | + | 0.816209i | \(0.696072\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 13.0936i | 0.0609005i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 73.3212 | 0.337886 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −70.7152 | −0.319978 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 386.009i | 1.73098i | 0.500923 | + | 0.865492i | \(0.332994\pi\) | ||||
−0.500923 | + | 0.865492i | \(0.667006\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 268.230i | 1.18163i | 0.806807 | + | 0.590815i | \(0.201194\pi\) | ||||
−0.806807 | + | 0.590815i | \(0.798806\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −89.6515 | −0.391491 | −0.195746 | − | 0.980655i | \(-0.562713\pi\) | ||||
−0.195746 | + | 0.980655i | \(0.562713\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 298.661 | 1.28181 | 0.640903 | − | 0.767622i | \(-0.278560\pi\) | ||||
0.640903 | + | 0.767622i | \(0.278560\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 71.5704i | − 0.304555i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 151.054i | 0.632025i | 0.948755 | + | 0.316013i | \(0.102344\pi\) | ||||
−0.948755 | + | 0.316013i | \(0.897656\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −326.000 | −1.35270 | −0.676349 | − | 0.736582i | \(-0.736439\pi\) | ||||
−0.676349 | + | 0.736582i | \(0.736439\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −14.0000 | −0.0571429 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 232.508i | 0.941327i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 379.844i | 1.51332i | 0.653807 | + | 0.756661i | \(0.273171\pi\) | ||||
−0.653807 | + | 0.756661i | \(0.726829\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −114.642 | −0.453132 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 53.6515 | 0.208761 | 0.104380 | − | 0.994537i | \(-0.466714\pi\) | ||||
0.104380 | + | 0.994537i | \(0.466714\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 28.2053i | − 0.108901i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 34.8632i | 0.132560i | 0.997801 | + | 0.0662799i | \(0.0211130\pi\) | ||||
−0.997801 | + | 0.0662799i | \(0.978887\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 53.3212 | 0.201212 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 191.982 | 0.713687 | 0.356844 | − | 0.934164i | \(-0.383853\pi\) | ||||
0.356844 | + | 0.934164i | \(0.383853\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 111.614i | − 0.411860i | −0.978567 | − | 0.205930i | \(-0.933978\pi\) | ||||
0.978567 | − | 0.205930i | \(-0.0660219\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 76.7508i | 0.279094i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 195.321 | 0.705131 | 0.352565 | − | 0.935787i | \(-0.385309\pi\) | ||||
0.352565 | + | 0.935787i | \(0.385309\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 253.303 | 0.901434 | 0.450717 | − | 0.892667i | \(-0.351168\pi\) | ||||
0.450717 | + | 0.892667i | \(0.351168\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 141.997i | 0.501755i | 0.968019 | + | 0.250878i | \(0.0807191\pi\) | ||||
−0.968019 | + | 0.250878i | \(0.919281\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 22.0399i | − 0.0767941i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −270.248 | −0.935116 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −518.624 | −1.77005 | −0.885024 | − | 0.465545i | \(-0.845858\pi\) | ||||
−0.885024 | + | 0.465545i | \(0.845858\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 0.762802i | − 0.00258577i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 512.243i | 1.71319i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −17.3212 | −0.0575456 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −48.6606 | −0.159543 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 139.708i | − 0.455076i | −0.973769 | − | 0.227538i | \(-0.926932\pi\) | ||||
0.973769 | − | 0.227538i | \(-0.0730676\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 299.057i | 0.961598i | 0.876831 | + | 0.480799i | \(0.159653\pi\) | ||||
−0.876831 | + | 0.480799i | \(0.840347\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −66.6606 | −0.212973 | −0.106487 | − | 0.994314i | \(-0.533960\pi\) | ||||
−0.106487 | + | 0.994314i | \(0.533960\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 85.3758 | 0.269324 | 0.134662 | − | 0.990892i | \(-0.457005\pi\) | ||||
0.134662 | + | 0.990892i | \(0.457005\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 185.154i | − 0.580422i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 61.6540i | − 0.190879i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 342.936 | 1.05519 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 94.6788 | 0.287777 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 612.289i | 1.84981i | 0.380192 | + | 0.924907i | \(0.375858\pi\) | ||||
−0.380192 | + | 0.924907i | \(0.624142\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 110.851i | − 0.330899i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 445.964 | 1.32333 | 0.661667 | − | 0.749798i | \(-0.269849\pi\) | ||||
0.661667 | + | 0.749798i | \(0.269849\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −101.285 | −0.297023 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 18.5203i | − 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 259.173i | 0.746895i | 0.927651 | + | 0.373447i | \(0.121824\pi\) | ||||
−0.927651 | + | 0.373447i | \(0.878176\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −332.991 | −0.954129 | −0.477064 | − | 0.878868i | \(-0.658299\pi\) | ||||
−0.477064 | + | 0.878868i | \(0.658299\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −75.0455 | −0.212593 | −0.106297 | − | 0.994334i | \(-0.533899\pi\) | ||||
−0.106297 | + | 0.994334i | \(0.533899\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 189.731i | − 0.534454i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 345.044i | − 0.961125i | −0.876961 | − | 0.480562i | \(-0.840433\pi\) | ||||
0.876961 | − | 0.480562i | \(-0.159567\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 158.285 | 0.438462 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 189.321 | 0.518688 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 177.400i | 0.483380i | 0.970354 | + | 0.241690i | \(0.0777017\pi\) | ||||
−0.970354 | + | 0.241690i | \(0.922298\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 70.5373i | 0.190128i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 635.248 | 1.70308 | 0.851540 | − | 0.524290i | \(-0.175669\pi\) | ||||
0.851540 | + | 0.524290i | \(0.175669\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −827.303 | −2.19444 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 31.2084i | 0.0823441i | 0.999152 | + | 0.0411720i | \(0.0131092\pi\) | ||||
−0.999152 | + | 0.0411720i | \(0.986891\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 28.4756i | − 0.0743489i | −0.999309 | − | 0.0371744i | \(-0.988164\pi\) | ||||
0.999309 | − | 0.0371744i | \(-0.0118357\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 19.3394 | 0.0502322 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −405.267 | −1.04182 | −0.520908 | − | 0.853613i | \(-0.674407\pi\) | ||||
−0.520908 | + | 0.853613i | \(0.674407\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 135.831i | − 0.347395i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 193.990i | 0.491113i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 490.936 | 1.23662 | 0.618308 | − | 0.785936i | \(-0.287819\pi\) | ||||
0.618308 | + | 0.785936i | \(0.287819\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 248.018 | 0.618499 | 0.309250 | − | 0.950981i | \(-0.399922\pi\) | ||||
0.309250 | + | 0.950981i | \(0.399922\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 452.559i | 1.12297i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 38.9624i | 0.0957307i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −369.964 | −0.904557 | −0.452278 | − | 0.891877i | \(-0.649389\pi\) | ||||
−0.452278 | + | 0.891877i | \(0.649389\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.00909 | 0.00244332 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 210.897i | − 0.508186i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 68.9006i | 0.164441i | 0.996614 | + | 0.0822203i | \(0.0262011\pi\) | ||||
−0.996614 | + | 0.0822203i | \(0.973799\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 296.606 | 0.704527 | 0.352264 | − | 0.935901i | \(-0.385412\pi\) | ||||
0.352264 | + | 0.935901i | \(0.385412\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −90.9364 | −0.213968 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 64.3719i | − 0.150754i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 373.075i | 0.865603i | 0.901489 | + | 0.432802i | \(0.142475\pi\) | ||||
−0.901489 | + | 0.432802i | \(0.857525\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −775.945 | −1.79202 | −0.896011 | − | 0.444032i | \(-0.853548\pi\) | ||||
−0.896011 | + | 0.444032i | \(0.853548\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −446.606 | −1.02198 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 744.750i | 1.69647i | 0.529620 | + | 0.848235i | \(0.322335\pi\) | ||||
−0.529620 | + | 0.848235i | \(0.677665\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 737.156i | 1.66401i | 0.554770 | + | 0.832004i | \(0.312806\pi\) | ||||
−0.554770 | + | 0.832004i | \(0.687194\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −185.982 | −0.417937 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 851.285 | 1.89596 | 0.947979 | − | 0.318334i | \(-0.103123\pi\) | ||||
0.947979 | + | 0.318334i | \(0.103123\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 30.4456i | 0.0675069i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 86.4118i | − 0.189916i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 601.927 | 1.31713 | 0.658564 | − | 0.752525i | \(-0.271164\pi\) | ||||
0.658564 | + | 0.752525i | \(0.271164\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −758.000 | −1.64425 | −0.822126 | − | 0.569306i | \(-0.807212\pi\) | ||||
−0.822126 | + | 0.569306i | \(0.807212\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 414.929i | − 0.896176i | −0.893990 | − | 0.448088i | \(-0.852105\pi\) | ||||
0.893990 | − | 0.448088i | \(-0.147895\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 45.7646i | − 0.0979971i | −0.998799 | − | 0.0489985i | \(-0.984397\pi\) | ||||
0.998799 | − | 0.0489985i | \(-0.0156030\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 146.642 | 0.312670 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 23.9273 | 0.0505862 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 298.994i | 0.629461i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 140.534i | − 0.293391i | −0.989182 | − | 0.146695i | \(-0.953136\pi\) | ||||
0.989182 | − | 0.146695i | \(-0.0468637\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 174.091 | 0.361935 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 102.642 | 0.211634 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 302.108i | − 0.620345i | −0.950680 | − | 0.310173i | \(-0.899613\pi\) | ||||
0.950680 | − | 0.310173i | \(-0.100387\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 78.7208i | − 0.160328i | −0.996782 | − | 0.0801638i | \(-0.974456\pi\) | ||||
0.996782 | − | 0.0801638i | \(-0.0255443\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 219.376 | 0.444981 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 250.991 | 0.505012 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 616.991i | − 1.23646i | −0.785999 | − | 0.618228i | \(-0.787851\pi\) | ||||
0.785999 | − | 0.618228i | \(-0.212149\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 309.418i | − 0.615145i | −0.951525 | − | 0.307572i | \(-0.900483\pi\) | ||||
0.951525 | − | 0.307572i | \(-0.0995166\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −149.321 | −0.295686 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 722.624 | 1.41969 | 0.709847 | − | 0.704356i | \(-0.248764\pi\) | ||||
0.709847 | + | 0.704356i | \(0.248764\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 250.448i | 0.490114i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 280.179i | − 0.544038i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −130.788 | −0.252975 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −743.633 | −1.42732 | −0.713660 | − | 0.700493i | \(-0.752964\pi\) | ||||
−0.713660 | + | 0.700493i | \(0.752964\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 694.283i | − 1.32750i | −0.747954 | − | 0.663750i | \(-0.768964\pi\) | ||||
0.747954 | − | 0.663750i | \(-0.231036\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 120.005i | − 0.227713i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −454.927 | −0.859976 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 136.036 | 0.255228 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 396.815i | − 0.741710i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 25.5836i | 0.0474650i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −480.570 | −0.888299 | −0.444149 | − | 0.895953i | \(-0.646494\pi\) | ||||
−0.444149 | + | 0.895953i | \(0.646494\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −66.6788 | −0.122346 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 724.347i | 1.32422i | 0.749408 | + | 0.662109i | \(0.230338\pi\) | ||||
−0.749408 | + | 0.662109i | \(0.769662\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 721.296i | − 1.30907i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −256.624 | −0.464058 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −449.303 | −0.806648 | −0.403324 | − | 0.915057i | \(-0.632145\pi\) | ||||
−0.403324 | + | 0.915057i | \(0.632145\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 106.911i | − 0.191255i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 964.101i | − 1.71244i | −0.516615 | − | 0.856218i | \(-0.672808\pi\) | ||||
0.516615 | − | 0.856218i | \(-0.327192\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −22.6424 | −0.0400751 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 843.909 | 1.48314 | 0.741572 | − | 0.670873i | \(-0.234081\pi\) | ||||
0.741572 | + | 0.670873i | \(0.234081\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 622.013i | 1.08934i | 0.838651 | + | 0.544670i | \(0.183345\pi\) | ||||
−0.838651 | + | 0.544670i | \(0.816655\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 658.720i | 1.14560i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −91.3576 | −0.158332 | −0.0791660 | − | 0.996861i | \(-0.525226\pi\) | ||||
−0.0791660 | + | 0.996861i | \(0.525226\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 278.991 | 0.480191 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 97.4392i | − 0.167134i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 471.499i | 0.803235i | 0.915807 | + | 0.401618i | \(0.131552\pi\) | ||||
−0.915807 | + | 0.401618i | \(0.868448\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −394.570 | −0.669898 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 863.524 | 1.45620 | 0.728098 | − | 0.685473i | \(-0.240405\pi\) | ||||
0.728098 | + | 0.685473i | \(0.240405\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 22.9138i | 0.0385106i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 842.223i | − 1.40605i | −0.711166 | − | 0.703024i | \(-0.751833\pi\) | ||||
0.711166 | − | 0.703024i | \(-0.248167\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −240.642 | −0.400403 | −0.200202 | − | 0.979755i | \(-0.564160\pi\) | ||||
−0.200202 | + | 0.979755i | \(0.564160\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 215.285 | 0.355843 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 85.1084i | 0.140212i | 0.997540 | + | 0.0701058i | \(0.0223337\pi\) | ||||
−0.997540 | + | 0.0701058i | \(0.977666\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 584.383i | 0.956438i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −147.982 | −0.241406 | −0.120703 | − | 0.992689i | \(-0.538515\pi\) | ||||
−0.120703 | + | 0.992689i | \(0.538515\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −73.2303 | −0.118688 | −0.0593438 | − | 0.998238i | \(-0.518901\pi\) | ||||
−0.0593438 | + | 0.998238i | \(0.518901\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 748.946i | 1.20993i | 0.796253 | + | 0.604964i | \(0.206813\pi\) | ||||
−0.796253 | + | 0.604964i | \(0.793187\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 246.031i | − 0.394913i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 341.000 | 0.545600 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −46.1636 | −0.0733921 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 1214.66i | − 1.92498i | −0.271321 | − | 0.962489i | \(-0.587461\pi\) | ||||
0.271321 | − | 0.962489i | \(-0.412539\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 169.328i | − 0.266658i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 114.312 | 0.179454 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 610.588 | 0.952555 | 0.476278 | − | 0.879295i | \(-0.341986\pi\) | ||||
0.476278 | + | 0.879295i | \(0.341986\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 734.008i | − 1.14154i | −0.821111 | − | 0.570768i | \(-0.806645\pi\) | ||||
0.821111 | − | 0.570768i | \(-0.193355\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 810.855i | − 1.25325i | −0.779319 | − | 0.626627i | \(-0.784435\pi\) | ||||
0.779319 | − | 0.626627i | \(-0.215565\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.39394 | −0.00214783 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 754.661 | 1.15568 | 0.577841 | − | 0.816149i | \(-0.303895\pi\) | ||||
0.577841 | + | 0.816149i | \(0.303895\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 320.223i | 0.488890i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 717.197i | − 1.08831i | −0.838984 | − | 0.544155i | \(-0.816850\pi\) | ||||
0.838984 | − | 0.544155i | \(-0.183150\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −461.615 | −0.698359 | −0.349179 | − | 0.937056i | \(-0.613540\pi\) | ||||
−0.349179 | + | 0.937056i | \(0.613540\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 75.3394 | 0.113292 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 1589.10i | − 2.38246i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 88.9224i | 0.132522i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −575.248 | −0.854753 | −0.427376 | − | 0.904074i | \(-0.640562\pi\) | ||||
−0.427376 | + | 0.904074i | \(0.640562\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −321.964 | −0.475574 | −0.237787 | − | 0.971317i | \(-0.576422\pi\) | ||||
−0.237787 | + | 0.971317i | \(0.576422\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 135.783i | 0.199975i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 1044.73i | − 1.52962i | −0.644257 | − | 0.764809i | \(-0.722833\pi\) | ||||
0.644257 | − | 0.764809i | \(-0.277167\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −386.606 | −0.564388 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −435.376 | −0.631895 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 544.914i | 0.788587i | 0.918985 | + | 0.394294i | \(0.129011\pi\) | ||||
−0.918985 | + | 0.394294i | \(0.870989\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 121.656i | 0.175045i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −36.0727 | −0.0517543 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 368.018 | 0.524990 | 0.262495 | − | 0.964933i | \(-0.415455\pi\) | ||||
0.262495 | + | 0.964933i | \(0.415455\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 151.784i | 0.215908i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 197.533i | − 0.279397i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 434.697 | 0.613113 | 0.306556 | − | 0.951852i | \(-0.400823\pi\) | ||||
0.306556 | + | 0.951852i | \(0.400823\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −869.285 | −1.21919 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 119.368i | 0.166948i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 752.060i | − 1.04598i | −0.852339 | − | 0.522990i | \(-0.824816\pi\) | ||||
0.852339 | − | 0.522990i | \(-0.175184\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 370.642 | 0.514067 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1063.87 | −1.46741 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 174.794i | − 0.240431i | −0.992748 | − | 0.120216i | \(-0.961641\pi\) | ||||
0.992748 | − | 0.120216i | \(-0.0383586\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 28.3496i | 0.0387820i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 416.294 | 0.567932 | 0.283966 | − | 0.958834i | \(-0.408350\pi\) | ||||
0.283966 | + | 0.958834i | \(0.408350\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −202.570 | −0.274857 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 1280.77i | − 1.73311i | −0.499084 | − | 0.866553i | \(-0.666330\pi\) | ||||
0.499084 | − | 0.866553i | \(-0.333670\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 57.8732i | − 0.0778913i | −0.999241 | − | 0.0389457i | \(-0.987600\pi\) | ||||
0.999241 | − | 0.0389457i | \(-0.0123999\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 263.964 | 0.354314 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 524.936 | 0.700850 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 399.866i | − 0.532444i | −0.963912 | − | 0.266222i | \(-0.914224\pi\) | ||||
0.963912 | − | 0.266222i | \(-0.0857755\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 125.470i | − 0.166186i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 846.661 | 1.11844 | 0.559221 | − | 0.829019i | \(-0.311100\pi\) | ||||
0.559221 | + | 0.829019i | \(0.311100\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 206.348 | 0.271154 | 0.135577 | − | 0.990767i | \(-0.456711\pi\) | ||||
0.135577 | + | 0.990767i | \(0.456711\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 88.2077i | − 0.115606i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.22839i | 0.00812046i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −203.982 | −0.265256 | −0.132628 | − | 0.991166i | \(-0.542342\pi\) | ||||
−0.132628 | + | 0.991166i | \(0.542342\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 466.697 | 0.603748 | 0.301874 | − | 0.953348i | \(-0.402388\pi\) | ||||
0.301874 | + | 0.953348i | \(0.402388\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 581.969i | 0.750928i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 118.605i | 0.152253i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −346.715 | −0.443937 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −172.624 | −0.219903 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 482.749i | 0.613404i | 0.951806 | + | 0.306702i | \(0.0992255\pi\) | ||||
−0.951806 | + | 0.306702i | \(0.900775\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 29.9531i | − 0.0378674i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 397.321 | 0.501036 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1387.28 | −1.74063 | −0.870317 | − | 0.492492i | \(-0.836086\pi\) | ||||
−0.870317 | + | 0.492492i | \(0.836086\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 154.961i | − 0.193943i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 345.966i | − 0.430842i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 165.982 | 0.206189 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −976.606 | −1.20718 | −0.603588 | − | 0.797296i | \(-0.706263\pi\) | ||||
−0.603588 | + | 0.797296i | \(0.706263\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 1258.58i | − 1.55189i | −0.630801 | − | 0.775944i | \(-0.717274\pi\) | ||||
0.630801 | − | 0.775944i | \(-0.282726\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 331.028i | 0.406170i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 93.2121 | 0.114091 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 984.018 | 1.19856 | 0.599280 | − | 0.800539i | \(-0.295454\pi\) | ||||
0.599280 | + | 0.800539i | \(0.295454\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 138.438i | − 0.168212i | −0.996457 | − | 0.0841058i | \(-0.973197\pi\) | ||||
0.996457 | − | 0.0841058i | \(-0.0268034\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 577.870i | − 0.698754i | −0.936982 | − | 0.349377i | \(-0.886393\pi\) | ||||
0.936982 | − | 0.349377i | \(-0.113607\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −45.0636 | −0.0543590 | −0.0271795 | − | 0.999631i | \(-0.508653\pi\) | ||||
−0.0271795 | + | 0.999631i | \(0.508653\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −30.3121 | −0.0363891 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 541.163i | − 0.648099i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 214.267i | − 0.255384i | −0.991814 | − | 0.127692i | \(-0.959243\pi\) | ||||
0.991814 | − | 0.127692i | \(-0.0407569\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1725.50 | 2.05172 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 195.358 | 0.231192 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 284.795i | 0.336240i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 334.398i | 0.392947i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −787.670 | −0.923411 | −0.461706 | − | 0.887033i | \(-0.652762\pi\) | ||||
−0.461706 | + | 0.887033i | \(0.652762\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1034.83 | −1.20750 | −0.603750 | − | 0.797174i | \(-0.706327\pi\) | ||||
−0.603750 | + | 0.797174i | \(0.706327\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 939.440i | 1.09364i | 0.837249 | + | 0.546822i | \(0.184162\pi\) | ||||
−0.837249 | + | 0.546822i | \(0.815838\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1259.44i | 1.45937i | 0.683781 | + | 0.729687i | \(0.260334\pi\) | ||||
−0.683781 | + | 0.729687i | \(0.739666\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 665.285 | 0.769115 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 354.497 | 0.407937 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 905.117i | 1.03917i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 243.409i | − 0.278182i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −309.376 | −0.352766 | −0.176383 | − | 0.984322i | \(-0.556440\pi\) | ||||
−0.176383 | + | 0.984322i | \(0.556440\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1365.47 | −1.54991 | −0.774954 | − | 0.632017i | \(-0.782227\pi\) | ||||
−0.774954 | + | 0.632017i | \(0.782227\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 190.620i | 0.215878i | 0.994158 | + | 0.107939i | \(0.0344251\pi\) | ||||
−0.994158 | + | 0.107939i | \(0.965575\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 1126.63i | − 1.27015i | −0.772449 | − | 0.635077i | \(-0.780968\pi\) | ||||
0.772449 | − | 0.635077i | \(-0.219032\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 224.000 | 0.251969 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −509.503 | −0.570552 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 341.389i | 0.381440i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 1403.95i | − 1.56168i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 115.448 | 0.128134 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −339.303 | −0.374920 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1526.69i | 1.68323i | 0.540081 | + | 0.841613i | \(0.318393\pi\) | ||||
−0.540081 | + | 0.841613i | \(0.681607\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1389.93i | 1.52572i | 0.646563 | + | 0.762861i | \(0.276206\pi\) | ||||
−0.646563 | + | 0.762861i | \(0.723794\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −385.394 | −0.422118 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −423.615 | −0.461958 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 140.534i | − 0.152921i | −0.997073 | − | 0.0764603i | \(-0.975638\pi\) | ||||
0.997073 | − | 0.0764603i | \(-0.0243619\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1549.18i | 1.67842i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 223.873 | 0.242025 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −290.900 | −0.313132 | −0.156566 | − | 0.987667i | \(-0.550042\pi\) | ||||
−0.156566 | + | 0.987667i | \(0.550042\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 99.6647i | 0.107051i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 31.6528i | − 0.0338533i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 805.891 | 0.860076 | 0.430038 | − | 0.902811i | \(-0.358500\pi\) | ||||
0.430038 | + | 0.902811i | \(0.358500\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1233.85 | 1.31122 | 0.655608 | − | 0.755101i | \(-0.272412\pi\) | ||||
0.655608 | + | 0.755101i | \(0.272412\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 261.302i | 0.277096i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 145.907i | − 0.154073i | −0.997028 | − | 0.0770364i | \(-0.975454\pi\) | ||||
0.997028 | − | 0.0770364i | \(-0.0245458\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1545.84 | −1.62891 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1833.96 | 1.92441 | 0.962205 | − | 0.272324i | \(-0.0877924\pi\) | ||||
0.962205 | + | 0.272324i | \(0.0877924\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 603.898i | − 0.632354i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 511.432i | − 0.533297i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 193.000 | 0.200832 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −449.285 | −0.465580 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 1255.34i | − 1.29818i | −0.760711 | − | 0.649091i | \(-0.775150\pi\) | ||||
0.760711 | − | 0.649091i | \(-0.224850\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1303.08i | 1.34199i | 0.741460 | + | 0.670997i | \(0.234134\pi\) | ||||
−0.741460 | + | 0.670997i | \(0.765866\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −160.936 | −0.165402 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −259.945 | −0.266065 | −0.133032 | − | 0.991112i | \(-0.542471\pi\) | ||||
−0.133032 | + | 0.991112i | \(0.542471\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 339.863i | 0.347154i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 153.946i | − 0.156608i | −0.996930 | − | 0.0783042i | \(-0.975049\pi\) | ||||
0.996930 | − | 0.0783042i | \(-0.0249505\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −15.9636 | −0.0162067 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 205.358 | 0.207642 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 577.585i | 0.582830i | 0.956597 | + | 0.291415i | \(0.0941261\pi\) | ||||
−0.956597 | + | 0.291415i | \(0.905874\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 738.204i | − 0.741913i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 567.670 | 0.569378 | 0.284689 | − | 0.958620i | \(-0.408110\pi\) | ||||
0.284689 | + | 0.958620i | \(0.408110\pi\) | |||||||
\(998\) | 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 | 1008.3.m.e.127.4 | 4 | ||
3.2 | odd | 2 | 336.3.m.b.127.4 | yes | 4 | ||
4.3 | odd | 2 | inner | 1008.3.m.e.127.1 | 4 | ||
12.11 | even | 2 | 336.3.m.b.127.1 | ✓ | 4 | ||
21.20 | even | 2 | 2352.3.m.i.1471.2 | 4 | |||
24.5 | odd | 2 | 1344.3.m.b.127.2 | 4 | |||
24.11 | even | 2 | 1344.3.m.b.127.3 | 4 | |||
84.83 | odd | 2 | 2352.3.m.i.1471.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
336.3.m.b.127.1 | ✓ | 4 | 12.11 | even | 2 | ||
336.3.m.b.127.4 | yes | 4 | 3.2 | odd | 2 | ||
1008.3.m.e.127.1 | 4 | 4.3 | odd | 2 | inner | ||
1008.3.m.e.127.4 | 4 | 1.1 | even | 1 | trivial | ||
1344.3.m.b.127.2 | 4 | 24.5 | odd | 2 | |||
1344.3.m.b.127.3 | 4 | 24.11 | even | 2 | |||
2352.3.m.i.1471.2 | 4 | 21.20 | even | 2 | |||
2352.3.m.i.1471.3 | 4 | 84.83 | odd | 2 |