Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [882,3,Mod(685,882)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(882, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("882.685");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 882.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(24.0327593166\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.0.2048.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 4x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 685.2 | ||
Root | \(1.84776i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 882.685 |
Dual form | 882.3.c.d.685.1 |
$q$-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 \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(785\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41421 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | 0.317025i | 0.0634051i | 0.999497 | + | 0.0317025i | \(0.0100929\pi\) | ||||
−0.999497 | + | 0.0317025i | \(0.989907\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.82843 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − 0.448342i | − 0.0448342i | ||||||||
\(11\) | −2.82843 | −0.257130 | −0.128565 | − | 0.991701i | \(-0.541037\pi\) | ||||
−0.128565 | + | 0.991701i | \(0.541037\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.11586i | 0.239682i | 0.992793 | + | 0.119841i | \(0.0382384\pi\) | ||||
−0.992793 | + | 0.119841i | \(0.961762\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | − 17.9749i | − 1.05734i | −0.848826 | − | 0.528672i | \(-0.822690\pi\) | ||||
0.848826 | − | 0.528672i | \(-0.177310\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 18.7402i | 0.986328i | 0.869936 | + | 0.493164i | \(0.164160\pi\) | ||||
−0.869936 | + | 0.493164i | \(0.835840\pi\) | |||||||
\(20\) | 0.634051i | 0.0317025i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.00000 | 0.181818 | ||||||||
\(23\) | −19.5147 | −0.848466 | −0.424233 | − | 0.905553i | \(-0.639456\pi\) | ||||
−0.424233 | + | 0.905553i | \(0.639456\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 24.8995 | 0.995980 | ||||||||
\(26\) | − 4.40649i | − 0.169480i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −43.5563 | −1.50194 | −0.750972 | − | 0.660335i | \(-0.770414\pi\) | ||||
−0.750972 | + | 0.660335i | \(0.770414\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 36.5838i | − 1.18012i | −0.807359 | − | 0.590061i | \(-0.799104\pi\) | ||||
0.807359 | − | 0.590061i | \(-0.200896\pi\) | |||||||
\(32\) | −5.65685 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 25.4203i | 0.747655i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −13.6985 | −0.370229 | −0.185115 | − | 0.982717i | \(-0.559266\pi\) | ||||
−0.185115 | + | 0.982717i | \(0.559266\pi\) | |||||||
\(38\) | − 26.5027i | − 0.697439i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − 0.896683i | − 0.0224171i | ||||||||
\(41\) | 53.9564i | 1.31601i | 0.753013 | + | 0.658005i | \(0.228600\pi\) | ||||
−0.753013 | + | 0.658005i | \(0.771400\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.59798 | 0.176697 | 0.0883486 | − | 0.996090i | \(-0.471841\pi\) | ||||
0.0883486 | + | 0.996090i | \(0.471841\pi\) | |||||||
\(44\) | −5.65685 | −0.128565 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 27.5980 | 0.599956 | ||||||||
\(47\) | − 56.7459i | − 1.20736i | −0.797227 | − | 0.603680i | \(-0.793700\pi\) | ||||
0.797227 | − | 0.603680i | \(-0.206300\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −35.2132 | −0.704264 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 6.23172i | 0.119841i | ||||||||
\(53\) | −20.2254 | −0.381611 | −0.190806 | − | 0.981628i | \(-0.561110\pi\) | ||||
−0.190806 | + | 0.981628i | \(0.561110\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 0.896683i | − 0.0163033i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 61.5980 | 1.06203 | ||||||||
\(59\) | − 89.5891i | − 1.51846i | −0.650823 | − | 0.759230i | \(-0.725576\pi\) | ||||
0.650823 | − | 0.759230i | \(-0.274424\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 74.4900i | 1.22115i | 0.791959 | + | 0.610574i | \(0.209061\pi\) | ||||
−0.791959 | + | 0.610574i | \(0.790939\pi\) | |||||||
\(62\) | 51.7373i | 0.834472i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | −0.987807 | −0.0151970 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.00000 | 0.0597015 | 0.0298507 | − | 0.999554i | \(-0.490497\pi\) | ||||
0.0298507 | + | 0.999554i | \(0.490497\pi\) | |||||||
\(68\) | − 35.9497i | − 0.528672i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −131.799 | −1.85632 | −0.928162 | − | 0.372177i | \(-0.878612\pi\) | ||||
−0.928162 | + | 0.372177i | \(0.878612\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 33.8712i | − 0.463989i | −0.972717 | − | 0.231994i | \(-0.925475\pi\) | ||||
0.972717 | − | 0.231994i | \(-0.0745251\pi\) | |||||||
\(74\) | 19.3726 | 0.261792 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 37.4804i | 0.493164i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −75.5980 | −0.956936 | −0.478468 | − | 0.878105i | \(-0.658808\pi\) | ||||
−0.478468 | + | 0.878105i | \(0.658808\pi\) | |||||||
\(80\) | 1.26810i | 0.0158513i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − 76.3059i | − 0.930560i | ||||||||
\(83\) | 131.245i | 1.58127i | 0.612289 | + | 0.790634i | \(0.290249\pi\) | ||||
−0.612289 | + | 0.790634i | \(0.709751\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.69848 | 0.0670410 | ||||||||
\(86\) | −10.7452 | −0.124944 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 8.00000 | 0.0909091 | ||||||||
\(89\) | − 111.305i | − 1.25061i | −0.780379 | − | 0.625306i | \(-0.784974\pi\) | ||||
0.780379 | − | 0.625306i | \(-0.215026\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −39.0294 | −0.424233 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 80.2509i | 0.853733i | ||||||||
\(95\) | −5.94113 | −0.0625382 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 148.106i | − 1.52686i | −0.645888 | − | 0.763432i | \(-0.723513\pi\) | ||||
0.645888 | − | 0.763432i | \(-0.276487\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 49.7990 | 0.497990 | ||||||||
\(101\) | − 100.019i | − 0.990288i | −0.868811 | − | 0.495144i | \(-0.835115\pi\) | ||||
0.868811 | − | 0.495144i | \(-0.164885\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 6.18666i | − 0.0600647i | −0.999549 | − | 0.0300323i | \(-0.990439\pi\) | ||||
0.999549 | − | 0.0300323i | \(-0.00956103\pi\) | |||||||
\(104\) | − 8.81298i | − 0.0847402i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 28.6030 | 0.269840 | ||||||||
\(107\) | −42.1421 | −0.393852 | −0.196926 | − | 0.980418i | \(-0.563096\pi\) | ||||
−0.196926 | + | 0.980418i | \(0.563096\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −120.693 | −1.10728 | −0.553640 | − | 0.832756i | \(-0.686761\pi\) | ||||
−0.553640 | + | 0.832756i | \(0.686761\pi\) | |||||||
\(110\) | 1.26810i | 0.0115282i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −104.794 | −0.927380 | −0.463690 | − | 0.885998i | \(-0.653475\pi\) | ||||
−0.463690 | + | 0.885998i | \(0.653475\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 6.18666i | − 0.0537970i | ||||||||
\(116\) | −87.1127 | −0.750972 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 126.698i | 1.07371i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −113.000 | −0.933884 | ||||||||
\(122\) | − 105.345i | − 0.863482i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − 73.1675i | − 0.590061i | ||||||||
\(125\) | 15.8194i | 0.126555i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −166.392 | −1.31017 | −0.655086 | − | 0.755554i | \(-0.727368\pi\) | ||||
−0.655086 | + | 0.755554i | \(0.727368\pi\) | |||||||
\(128\) | −11.3137 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.39697 | 0.0107459 | ||||||||
\(131\) | 65.6864i | 0.501423i | 0.968062 | + | 0.250711i | \(0.0806645\pi\) | ||||
−0.968062 | + | 0.250711i | \(0.919336\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −5.65685 | −0.0422153 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 50.8406i | 0.373828i | ||||||||
\(137\) | 3.95837 | 0.0288932 | 0.0144466 | − | 0.999896i | \(-0.495401\pi\) | ||||
0.0144466 | + | 0.999896i | \(0.495401\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 96.3010i | − 0.692813i | −0.938084 | − | 0.346407i | \(-0.887402\pi\) | ||||
0.938084 | − | 0.346407i | \(-0.112598\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 186.392 | 1.31262 | ||||||||
\(143\) | − 8.81298i | − 0.0616293i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − 13.8085i | − 0.0952308i | ||||||||
\(146\) | 47.9011i | 0.328090i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −27.3970 | −0.185115 | ||||||||
\(149\) | −120.912 | −0.811488 | −0.405744 | − | 0.913987i | \(-0.632988\pi\) | ||||
−0.405744 | + | 0.913987i | \(0.632988\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −162.392 | −1.07544 | −0.537722 | − | 0.843122i | \(-0.680715\pi\) | ||||
−0.537722 | + | 0.843122i | \(0.680715\pi\) | |||||||
\(152\) | − 53.0054i | − 0.348719i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 11.5980 | 0.0748257 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 66.0617i | 0.420775i | 0.977618 | + | 0.210387i | \(0.0674725\pi\) | ||||
−0.977618 | + | 0.210387i | \(0.932527\pi\) | |||||||
\(158\) | 106.912 | 0.676656 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − 1.79337i | − 0.0112085i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −209.990 | −1.28828 | −0.644141 | − | 0.764907i | \(-0.722785\pi\) | ||||
−0.644141 | + | 0.764907i | \(0.722785\pi\) | |||||||
\(164\) | 107.913i | 0.658005i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − 185.609i | − 1.11813i | ||||||||
\(167\) | − 152.739i | − 0.914606i | −0.889311 | − | 0.457303i | \(-0.848815\pi\) | ||||
0.889311 | − | 0.457303i | \(-0.151185\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 159.291 | 0.942553 | ||||||||
\(170\) | −8.05887 | −0.0474051 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 15.1960 | 0.0883486 | ||||||||
\(173\) | 35.5690i | 0.205601i | 0.994702 | + | 0.102800i | \(0.0327803\pi\) | ||||
−0.994702 | + | 0.102800i | \(0.967220\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −11.3137 | −0.0642824 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 157.408i | 0.884317i | ||||||||
\(179\) | −63.9167 | −0.357077 | −0.178538 | − | 0.983933i | \(-0.557137\pi\) | ||||
−0.178538 | + | 0.983933i | \(0.557137\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 183.748i | − 1.01518i | −0.861598 | − | 0.507591i | \(-0.830536\pi\) | ||||
0.861598 | − | 0.507591i | \(-0.169464\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 55.1960 | 0.299978 | ||||||||
\(185\) | − 4.34277i | − 0.0234744i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 50.8406i | 0.271875i | ||||||||
\(188\) | − 113.492i | − 0.603680i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 8.40202 | 0.0442212 | ||||||||
\(191\) | 154.426 | 0.808515 | 0.404258 | − | 0.914645i | \(-0.367530\pi\) | ||||
0.404258 | + | 0.914645i | \(0.367530\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −23.1960 | −0.120186 | −0.0600932 | − | 0.998193i | \(-0.519140\pi\) | ||||
−0.0600932 | + | 0.998193i | \(0.519140\pi\) | |||||||
\(194\) | 209.453i | 1.07966i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 202.510 | 1.02797 | 0.513984 | − | 0.857800i | \(-0.328169\pi\) | ||||
0.513984 | + | 0.857800i | \(0.328169\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 230.083i | − 1.15619i | −0.815968 | − | 0.578097i | \(-0.803796\pi\) | ||||
0.815968 | − | 0.578097i | \(-0.196204\pi\) | |||||||
\(200\) | −70.4264 | −0.352132 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 141.448i | 0.700239i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −17.1056 | −0.0834417 | ||||||||
\(206\) | 8.74926i | 0.0424721i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 12.4634i | 0.0599204i | ||||||||
\(209\) | − 53.0054i | − 0.253614i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −172.402 | −0.817071 | −0.408536 | − | 0.912742i | \(-0.633960\pi\) | ||||
−0.408536 | + | 0.912742i | \(0.633960\pi\) | |||||||
\(212\) | −40.4508 | −0.190806 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 59.5980 | 0.278495 | ||||||||
\(215\) | 2.40875i | 0.0112035i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 170.686 | 0.782965 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − 1.79337i | − 0.00815166i | ||||||||
\(221\) | 56.0071 | 0.253426 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 55.3240i | − 0.248090i | −0.992277 | − | 0.124045i | \(-0.960413\pi\) | ||||
0.992277 | − | 0.124045i | \(-0.0395867\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 148.201 | 0.655757 | ||||||||
\(227\) | 369.578i | 1.62810i | 0.580796 | + | 0.814049i | \(0.302741\pi\) | ||||
−0.580796 | + | 0.814049i | \(0.697259\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 294.396i | 1.28557i | 0.766046 | + | 0.642786i | \(0.222221\pi\) | ||||
−0.766046 | + | 0.642786i | \(0.777779\pi\) | |||||||
\(230\) | 8.74926i | 0.0380403i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 123.196 | 0.531017 | ||||||||
\(233\) | 174.787 | 0.750158 | 0.375079 | − | 0.926993i | \(-0.377616\pi\) | ||||
0.375079 | + | 0.926993i | \(0.377616\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 17.9899 | 0.0765528 | ||||||||
\(236\) | − 179.178i | − 0.759230i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 323.279 | 1.35263 | 0.676316 | − | 0.736611i | \(-0.263575\pi\) | ||||
0.676316 | + | 0.736611i | \(0.263575\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 165.501i | 0.686726i | 0.939203 | + | 0.343363i | \(0.111566\pi\) | ||||
−0.939203 | + | 0.343363i | \(0.888434\pi\) | |||||||
\(242\) | 159.806 | 0.660356 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 148.980i | 0.610574i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −58.3919 | −0.236405 | ||||||||
\(248\) | 103.475i | 0.417236i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − 22.3720i | − 0.0894881i | ||||||||
\(251\) | − 99.7339i | − 0.397346i | −0.980066 | − | 0.198673i | \(-0.936337\pi\) | ||||
0.980066 | − | 0.198673i | \(-0.0636632\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 55.1960 | 0.218166 | ||||||||
\(254\) | 235.314 | 0.926432 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 379.976i | 1.47851i | 0.673427 | + | 0.739254i | \(0.264821\pi\) | ||||
−0.673427 | + | 0.739254i | \(0.735179\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −1.97561 | −0.00759851 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − 92.8946i | − 0.354559i | ||||||||
\(263\) | 233.622 | 0.888298 | 0.444149 | − | 0.895953i | \(-0.353506\pi\) | ||||
0.444149 | + | 0.895953i | \(0.353506\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − 6.41196i | − 0.0241961i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 8.00000 | 0.0298507 | ||||||||
\(269\) | 465.286i | 1.72969i | 0.502040 | + | 0.864845i | \(0.332583\pi\) | ||||
−0.502040 | + | 0.864845i | \(0.667417\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 141.671i | − 0.522773i | −0.965234 | − | 0.261386i | \(-0.915820\pi\) | ||||
0.965234 | − | 0.261386i | \(-0.0841797\pi\) | |||||||
\(272\) | − 71.8994i | − 0.264336i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.59798 | −0.0204306 | ||||||||
\(275\) | −70.4264 | −0.256096 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 314.000 | 1.13357 | 0.566787 | − | 0.823864i | \(-0.308186\pi\) | ||||
0.566787 | + | 0.823864i | \(0.308186\pi\) | |||||||
\(278\) | 136.190i | 0.489893i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 323.002 | 1.14947 | 0.574737 | − | 0.818338i | \(-0.305104\pi\) | ||||
0.574737 | + | 0.818338i | \(0.305104\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 534.500i | − 1.88869i | −0.328955 | − | 0.944346i | \(-0.606696\pi\) | ||||
0.328955 | − | 0.944346i | \(-0.393304\pi\) | |||||||
\(284\) | −263.598 | −0.928162 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 12.4634i | 0.0435785i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −34.0955 | −0.117977 | ||||||||
\(290\) | 19.5281i | 0.0673383i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − 67.7424i | − 0.231994i | ||||||||
\(293\) | − 392.246i | − 1.33872i | −0.742936 | − | 0.669362i | \(-0.766567\pi\) | ||||
0.742936 | − | 0.669362i | \(-0.233433\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 28.4020 | 0.0962780 | ||||||||
\(296\) | 38.7452 | 0.130896 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 170.995 | 0.573809 | ||||||||
\(299\) | − 60.8051i | − 0.203362i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 229.657 | 0.760453 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 74.9609i | 0.246582i | ||||||||
\(305\) | −23.6152 | −0.0774270 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 541.583i | 1.76411i | 0.471143 | + | 0.882057i | \(0.343842\pi\) | ||||
−0.471143 | + | 0.882057i | \(0.656158\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −16.4020 | −0.0529097 | ||||||||
\(311\) | − 57.8866i | − 0.186130i | −0.995660 | − | 0.0930652i | \(-0.970333\pi\) | ||||
0.995660 | − | 0.0930652i | \(-0.0296665\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 461.981i | 1.47598i | 0.674813 | + | 0.737989i | \(0.264224\pi\) | ||||
−0.674813 | + | 0.737989i | \(0.735776\pi\) | |||||||
\(314\) | − 93.4253i | − 0.297533i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −151.196 | −0.478468 | ||||||||
\(317\) | 415.196 | 1.30977 | 0.654883 | − | 0.755730i | \(-0.272718\pi\) | ||||
0.654883 | + | 0.755730i | \(0.272718\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 123.196 | 0.386194 | ||||||||
\(320\) | 2.53620i | 0.00792563i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 336.853 | 1.04289 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 77.5834i | 0.238718i | ||||||||
\(326\) | 296.971 | 0.910953 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − 152.612i | − 0.465280i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 76.4020 | 0.230822 | 0.115411 | − | 0.993318i | \(-0.463182\pi\) | ||||
0.115411 | + | 0.993318i | \(0.463182\pi\) | |||||||
\(332\) | 262.491i | 0.790634i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 216.006i | 0.646724i | ||||||||
\(335\) | 1.26810i | 0.00378538i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 376.291 | 1.11659 | 0.558296 | − | 0.829642i | \(-0.311455\pi\) | ||||
0.558296 | + | 0.829642i | \(0.311455\pi\) | |||||||
\(338\) | −225.272 | −0.666485 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 11.3970 | 0.0335205 | ||||||||
\(341\) | 103.475i | 0.303444i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −21.4903 | −0.0624719 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − 50.3021i | − 0.145382i | ||||||||
\(347\) | −78.3289 | −0.225732 | −0.112866 | − | 0.993610i | \(-0.536003\pi\) | ||||
−0.112866 | + | 0.993610i | \(0.536003\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 376.710i | − 1.07940i | −0.841858 | − | 0.539700i | \(-0.818538\pi\) | ||||
0.841858 | − | 0.539700i | \(-0.181462\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 16.0000 | 0.0454545 | ||||||||
\(353\) | 213.352i | 0.604396i | 0.953245 | + | 0.302198i | \(0.0977203\pi\) | ||||
−0.953245 | + | 0.302198i | \(0.902280\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 41.7836i | − 0.117700i | ||||||||
\(356\) | − 222.609i | − 0.625306i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 90.3919 | 0.252491 | ||||||||
\(359\) | −28.0143 | −0.0780342 | −0.0390171 | − | 0.999239i | \(-0.512423\pi\) | ||||
−0.0390171 | + | 0.999239i | \(0.512423\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.80404 | 0.0271580 | ||||||||
\(362\) | 259.859i | 0.717842i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.7380 | 0.0294192 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 149.742i | 0.408015i | 0.978969 | + | 0.204008i | \(0.0653967\pi\) | ||||
−0.978969 | + | 0.204008i | \(0.934603\pi\) | |||||||
\(368\) | −78.0589 | −0.212117 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 6.14160i | 0.0165989i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 231.196 | 0.619828 | 0.309914 | − | 0.950765i | \(-0.399700\pi\) | ||||
0.309914 | + | 0.950765i | \(0.399700\pi\) | |||||||
\(374\) | − 71.8994i | − 0.192244i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 160.502i | 0.426866i | ||||||||
\(377\) | − 135.716i | − 0.359988i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −585.186 | −1.54403 | −0.772013 | − | 0.635607i | \(-0.780750\pi\) | ||||
−0.772013 | + | 0.635607i | \(0.780750\pi\) | |||||||
\(380\) | −11.8823 | −0.0312691 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −218.392 | −0.571707 | ||||||||
\(383\) | 533.858i | 1.39388i | 0.717127 | + | 0.696942i | \(0.245457\pi\) | ||||
−0.717127 | + | 0.696942i | \(0.754543\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 32.8040 | 0.0849846 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − 296.212i | − 0.763432i | ||||||||
\(389\) | −19.7918 | −0.0508788 | −0.0254394 | − | 0.999676i | \(-0.508098\pi\) | ||||
−0.0254394 | + | 0.999676i | \(0.508098\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 350.774i | 0.897121i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −286.392 | −0.726883 | ||||||||
\(395\) | − 23.9665i | − 0.0606746i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 367.340i | − 0.925291i | −0.886543 | − | 0.462645i | \(-0.846900\pi\) | ||||
0.886543 | − | 0.462645i | \(-0.153100\pi\) | |||||||
\(398\) | 325.386i | 0.817552i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 99.5980 | 0.248995 | ||||||||
\(401\) | −692.943 | −1.72804 | −0.864019 | − | 0.503459i | \(-0.832060\pi\) | ||||
−0.864019 | + | 0.503459i | \(0.832060\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 113.990 | 0.282853 | ||||||||
\(404\) | − 200.038i | − 0.495144i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 38.7452 | 0.0951970 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 290.899i | 0.711245i | 0.934630 | + | 0.355623i | \(0.115731\pi\) | ||||
−0.934630 | + | 0.355623i | \(0.884269\pi\) | |||||||
\(410\) | 24.1909 | 0.0590022 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − 12.3733i | − 0.0300323i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −41.6081 | −0.100260 | ||||||||
\(416\) | − 17.6260i | − 0.0423701i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 74.9609i | 0.179332i | ||||||||
\(419\) | − 624.333i | − 1.49005i | −0.667034 | − | 0.745027i | \(-0.732437\pi\) | ||||
0.667034 | − | 0.745027i | \(-0.267563\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 753.980 | 1.79093 | 0.895463 | − | 0.445136i | \(-0.146845\pi\) | ||||
0.895463 | + | 0.445136i | \(0.146845\pi\) | |||||||
\(422\) | 243.813 | 0.577757 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 57.2061 | 0.134920 | ||||||||
\(425\) | − 447.565i | − 1.05309i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −84.2843 | −0.196926 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − 3.40649i | − 0.00792207i | ||||||||
\(431\) | −1.15137 | −0.00267139 | −0.00133570 | − | 0.999999i | \(-0.500425\pi\) | ||||
−0.00133570 | + | 0.999999i | \(0.500425\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 193.834i | − 0.447655i | −0.974629 | − | 0.223827i | \(-0.928145\pi\) | ||||
0.974629 | − | 0.223827i | \(-0.0718552\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −241.387 | −0.553640 | ||||||||
\(437\) | − 365.710i | − 0.836865i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 444.295i | − 1.01206i | −0.862515 | − | 0.506031i | \(-0.831112\pi\) | ||||
0.862515 | − | 0.506031i | \(-0.168888\pi\) | |||||||
\(440\) | 2.53620i | 0.00576410i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −79.2061 | −0.179199 | ||||||||
\(443\) | 403.897 | 0.911730 | 0.455865 | − | 0.890049i | \(-0.349330\pi\) | ||||
0.455865 | + | 0.890049i | \(0.349330\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 35.2864 | 0.0792952 | ||||||||
\(446\) | 78.2399i | 0.175426i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −242.520 | −0.540133 | −0.270067 | − | 0.962842i | \(-0.587046\pi\) | ||||
−0.270067 | + | 0.962842i | \(0.587046\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 152.612i | − 0.338385i | ||||||||
\(452\) | −209.588 | −0.463690 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − 522.663i | − 1.15124i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 744.764 | 1.62968 | 0.814840 | − | 0.579686i | \(-0.196825\pi\) | ||||
0.814840 | + | 0.579686i | \(0.196825\pi\) | |||||||
\(458\) | − 416.339i | − 0.909036i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − 12.3733i | − 0.0268985i | ||||||||
\(461\) | 764.329i | 1.65798i | 0.559263 | + | 0.828990i | \(0.311084\pi\) | ||||
−0.559263 | + | 0.828990i | \(0.688916\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −658.774 | −1.42284 | −0.711419 | − | 0.702768i | \(-0.751947\pi\) | ||||
−0.711419 | + | 0.702768i | \(0.751947\pi\) | |||||||
\(464\) | −174.225 | −0.375486 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −247.186 | −0.530442 | ||||||||
\(467\) | − 65.6226i | − 0.140520i | −0.997529 | − | 0.0702598i | \(-0.977617\pi\) | ||||
0.997529 | − | 0.0702598i | \(-0.0223828\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −25.4416 | −0.0541310 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 253.396i | 0.536857i | ||||||||
\(473\) | −21.4903 | −0.0454341 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 466.622i | 0.982362i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −457.186 | −0.956456 | ||||||||
\(479\) | 248.478i | 0.518743i | 0.965778 | + | 0.259371i | \(0.0835153\pi\) | ||||
−0.965778 | + | 0.259371i | \(0.916485\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − 42.6826i | − 0.0887371i | ||||||||
\(482\) | − 234.054i | − 0.485589i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −226.000 | −0.466942 | ||||||||
\(485\) | 46.9533 | 0.0968110 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −764.402 | −1.56961 | −0.784807 | − | 0.619740i | \(-0.787238\pi\) | ||||
−0.784807 | + | 0.619740i | \(0.787238\pi\) | |||||||
\(488\) | − 210.690i | − 0.431741i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −782.621 | −1.59393 | −0.796967 | − | 0.604023i | \(-0.793564\pi\) | ||||
−0.796967 | + | 0.604023i | \(0.793564\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 782.919i | 1.58807i | ||||||||
\(494\) | 82.5786 | 0.167163 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − 146.335i | − 0.295030i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −131.980 | −0.264489 | −0.132244 | − | 0.991217i | \(-0.542218\pi\) | ||||
−0.132244 | + | 0.991217i | \(0.542218\pi\) | |||||||
\(500\) | 31.6388i | 0.0632776i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 141.045i | 0.280966i | ||||||||
\(503\) | 756.910i | 1.50479i | 0.658712 | + | 0.752395i | \(0.271102\pi\) | ||||
−0.658712 | + | 0.752395i | \(0.728898\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 31.7086 | 0.0627893 | ||||||||
\(506\) | −78.0589 | −0.154267 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −332.784 | −0.655086 | ||||||||
\(509\) | − 233.418i | − 0.458582i | −0.973358 | − | 0.229291i | \(-0.926359\pi\) | ||||
0.973358 | − | 0.229291i | \(-0.0736407\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −22.6274 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − 537.368i | − 1.04546i | ||||||||
\(515\) | 1.96133 | 0.00380840 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 160.502i | 0.310448i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.79394 | 0.00537296 | ||||||||
\(521\) | − 596.691i | − 1.14528i | −0.819807 | − | 0.572640i | \(-0.805919\pi\) | ||||
0.819807 | − | 0.572640i | \(-0.194081\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 815.152i | − 1.55861i | −0.626646 | − | 0.779304i | \(-0.715573\pi\) | ||||
0.626646 | − | 0.779304i | \(-0.284427\pi\) | |||||||
\(524\) | 131.373i | 0.250711i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −330.392 | −0.628122 | ||||||||
\(527\) | −657.588 | −1.24779 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −148.176 | −0.280105 | ||||||||
\(530\) | 9.06789i | 0.0171092i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −168.121 | −0.315423 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 13.3601i | − 0.0249722i | ||||||||
\(536\) | −11.3137 | −0.0211077 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − 658.014i | − 1.22307i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 233.568 | 0.431733 | 0.215867 | − | 0.976423i | \(-0.430742\pi\) | ||||
0.215867 | + | 0.976423i | \(0.430742\pi\) | |||||||
\(542\) | 200.354i | 0.369656i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 101.681i | 0.186914i | ||||||||
\(545\) | − 38.2629i | − 0.0702071i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −27.1758 | −0.0496815 | −0.0248407 | − | 0.999691i | \(-0.507908\pi\) | ||||
−0.0248407 | + | 0.999691i | \(0.507908\pi\) | |||||||
\(548\) | 7.91674 | 0.0144466 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 99.5980 | 0.181087 | ||||||||
\(551\) | − 816.256i | − 1.48141i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −444.063 | −0.801558 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − 192.602i | − 0.346407i | ||||||||
\(557\) | 290.745 | 0.521984 | 0.260992 | − | 0.965341i | \(-0.415950\pi\) | ||||
0.260992 | + | 0.965341i | \(0.415950\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 23.6742i | 0.0423511i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −456.794 | −0.812801 | ||||||||
\(563\) | − 976.476i | − 1.73442i | −0.497946 | − | 0.867208i | \(-0.665912\pi\) | ||||
0.497946 | − | 0.867208i | \(-0.334088\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 33.2223i | − 0.0588006i | ||||||||
\(566\) | 755.897i | 1.33551i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 372.784 | 0.656310 | ||||||||
\(569\) | 635.252 | 1.11644 | 0.558218 | − | 0.829694i | \(-0.311485\pi\) | ||||
0.558218 | + | 0.829694i | \(0.311485\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 453.186 | 0.793671 | 0.396835 | − | 0.917890i | \(-0.370108\pi\) | ||||
0.396835 | + | 0.917890i | \(0.370108\pi\) | |||||||
\(572\) | − 17.6260i | − 0.0308146i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −485.907 | −0.845055 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1093.00i | 1.89429i | 0.320807 | + | 0.947144i | \(0.396046\pi\) | ||||
−0.320807 | + | 0.947144i | \(0.603954\pi\) | |||||||
\(578\) | 48.2183 | 0.0834226 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − 27.6169i | − 0.0476154i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 57.2061 | 0.0981236 | ||||||||
\(584\) | 95.8022i | 0.164045i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 554.720i | 0.946621i | ||||||||
\(587\) | 883.401i | 1.50494i | 0.658625 | + | 0.752471i | \(0.271138\pi\) | ||||
−0.658625 | + | 0.752471i | \(0.728862\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 685.588 | 1.16399 | ||||||||
\(590\) | −40.1665 | −0.0680789 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −54.7939 | −0.0925573 | ||||||||
\(593\) | − 100.462i | − 0.169413i | −0.996406 | − | 0.0847065i | \(-0.973005\pi\) | ||||
0.996406 | − | 0.0847065i | \(-0.0269953\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −241.823 | −0.405744 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 85.9915i | 0.143798i | ||||||||
\(599\) | −1034.05 | −1.72630 | −0.863149 | − | 0.504949i | \(-0.831511\pi\) | ||||
−0.863149 | + | 0.504949i | \(0.831511\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − 401.682i | − 0.668357i | −0.942510 | − | 0.334178i | \(-0.891541\pi\) | ||||
0.942510 | − | 0.334178i | \(-0.108459\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −324.784 | −0.537722 | ||||||||
\(605\) | − 35.8239i | − 0.0592130i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 876.217i | − 1.44352i | −0.692143 | − | 0.721760i | \(-0.743333\pi\) | ||||
0.692143 | − | 0.721760i | \(-0.256667\pi\) | |||||||
\(608\) | − 106.011i | − 0.174360i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 33.3970 | 0.0547491 | ||||||||
\(611\) | 176.812 | 0.289382 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −85.4773 | −0.139441 | −0.0697205 | − | 0.997567i | \(-0.522211\pi\) | ||||
−0.0697205 | + | 0.997567i | \(0.522211\pi\) | |||||||
\(614\) | − 765.914i | − 1.24742i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −522.115 | −0.846215 | −0.423108 | − | 0.906079i | \(-0.639061\pi\) | ||||
−0.423108 | + | 0.906079i | \(0.639061\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 653.218i | − 1.05528i | −0.849468 | − | 0.527640i | \(-0.823077\pi\) | ||||
0.849468 | − | 0.527640i | \(-0.176923\pi\) | |||||||
\(620\) | 23.1960 | 0.0374128 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 81.8640i | 0.131614i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 617.472 | 0.987956 | ||||||||
\(626\) | − 653.340i | − 1.04367i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 132.123i | 0.210387i | ||||||||
\(629\) | 246.228i | 0.391460i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −728.764 | −1.15493 | −0.577467 | − | 0.816414i | \(-0.695959\pi\) | ||||
−0.577467 | + | 0.816414i | \(0.695959\pi\) | |||||||
\(632\) | 213.823 | 0.338328 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −587.176 | −0.926145 | ||||||||
\(635\) | − 52.7505i | − 0.0830716i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −174.225 | −0.273081 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − 3.58673i | − 0.00560427i | ||||||||
\(641\) | 190.606 | 0.297357 | 0.148679 | − | 0.988886i | \(-0.452498\pi\) | ||||
0.148679 | + | 0.988886i | \(0.452498\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 910.647i | 1.41625i | 0.706089 | + | 0.708124i | \(0.250458\pi\) | ||||
−0.706089 | + | 0.708124i | \(0.749542\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −476.382 | −0.737433 | ||||||||
\(647\) | − 355.757i | − 0.549856i | −0.961465 | − | 0.274928i | \(-0.911346\pi\) | ||||
0.961465 | − | 0.274928i | \(-0.0886539\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 253.396i | 0.390441i | ||||||||
\(650\) | − 109.719i | − 0.168799i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −419.980 | −0.644141 | ||||||||
\(653\) | −1130.75 | −1.73163 | −0.865813 | − | 0.500367i | \(-0.833198\pi\) | ||||
−0.865813 | + | 0.500367i | \(0.833198\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −20.8242 | −0.0317927 | ||||||||
\(656\) | 215.826i | 0.329003i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −520.388 | −0.789663 | −0.394831 | − | 0.918754i | \(-0.629197\pi\) | ||||
−0.394831 | + | 0.918754i | \(0.629197\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 351.243i | 0.531381i | 0.964058 | + | 0.265691i | \(0.0855999\pi\) | ||||
−0.964058 | + | 0.265691i | \(0.914400\pi\) | |||||||
\(662\) | −108.049 | −0.163216 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − 371.218i | − 0.559063i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 849.990 | 1.27435 | ||||||||
\(668\) | − 305.479i | − 0.457303i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − 1.79337i | − 0.00267667i | ||||||||
\(671\) | − 210.690i | − 0.313993i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 397.075 | 0.590008 | 0.295004 | − | 0.955496i | \(-0.404679\pi\) | ||||
0.295004 | + | 0.955496i | \(0.404679\pi\) | |||||||
\(674\) | −532.156 | −0.789550 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 318.583 | 0.471276 | ||||||||
\(677\) | − 361.210i | − 0.533545i | −0.963760 | − | 0.266772i | \(-0.914043\pi\) | ||||
0.963760 | − | 0.266772i | \(-0.0859572\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −16.1177 | −0.0237026 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − 146.335i | − 0.214568i | ||||||||
\(683\) | 938.455 | 1.37402 | 0.687010 | − | 0.726648i | \(-0.258923\pi\) | ||||
0.687010 | + | 0.726648i | \(0.258923\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.25490i | 0.00183198i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 30.3919 | 0.0441743 | ||||||||
\(689\) | − 63.0195i | − 0.0914652i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 381.888i | 0.552660i | 0.961063 | + | 0.276330i | \(0.0891182\pi\) | ||||
−0.961063 | + | 0.276330i | \(0.910882\pi\) | |||||||
\(692\) | 71.1379i | 0.102800i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 110.774 | 0.159616 | ||||||||
\(695\) | 30.5299 | 0.0439279 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 969.859 | 1.39148 | ||||||||
\(698\) | 532.749i | 0.763251i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −713.325 | −1.01758 | −0.508791 | − | 0.860890i | \(-0.669907\pi\) | ||||
−0.508791 | + | 0.860890i | \(0.669907\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 256.713i | − 0.365167i | ||||||||
\(704\) | −22.6274 | −0.0321412 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − 301.725i | − 0.427372i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −388.894 | −0.548511 | −0.274256 | − | 0.961657i | \(-0.588431\pi\) | ||||
−0.274256 | + | 0.961657i | \(0.588431\pi\) | |||||||
\(710\) | 59.0910i | 0.0832267i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 314.817i | 0.442158i | ||||||||
\(713\) | 713.922i | 1.00129i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.79394 | 0.00390761 | ||||||||
\(716\) | −127.833 | −0.178538 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 39.6182 | 0.0551785 | ||||||||
\(719\) | − 460.435i | − 0.640383i | −0.947353 | − | 0.320192i | \(-0.896253\pi\) | ||||
0.947353 | − | 0.320192i | \(-0.103747\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −13.8650 | −0.0192036 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − 367.496i | − 0.507591i | ||||||||
\(725\) | −1084.53 | −1.49590 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1005.79i | 1.38347i | 0.722150 | + | 0.691737i | \(0.243154\pi\) | ||||
−0.722150 | + | 0.691737i | \(0.756846\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −15.1859 | −0.0208025 | ||||||||
\(731\) | − 136.573i | − 0.186830i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 779.623i | 1.06361i | 0.846868 | + | 0.531803i | \(0.178485\pi\) | ||||
−0.846868 | + | 0.531803i | \(0.821515\pi\) | |||||||
\(734\) | − 211.767i | − 0.288510i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 110.392 | 0.149989 | ||||||||
\(737\) | −11.3137 | −0.0153510 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 72.3818 | 0.0979456 | 0.0489728 | − | 0.998800i | \(-0.484405\pi\) | ||||
0.0489728 | + | 0.998800i | \(0.484405\pi\) | |||||||
\(740\) | − 8.68553i | − 0.0117372i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 145.358 | 0.195637 | 0.0978185 | − | 0.995204i | \(-0.468814\pi\) | ||||
0.0978185 | + | 0.995204i | \(0.468814\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − 38.3321i | − 0.0514524i | ||||||||
\(746\) | −326.960 | −0.438285 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 101.681i | 0.135937i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.02020 | 0.00535313 | 0.00267657 | − | 0.999996i | \(-0.499148\pi\) | ||||
0.00267657 | + | 0.999996i | \(0.499148\pi\) | |||||||
\(752\) | − 226.984i | − 0.301840i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 191.931i | 0.254550i | ||||||||
\(755\) | − 51.4824i | − 0.0681885i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 705.678 | 0.932204 | 0.466102 | − | 0.884731i | \(-0.345658\pi\) | ||||
0.466102 | + | 0.884731i | \(0.345658\pi\) | |||||||
\(758\) | 827.578 | 1.09179 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 16.8040 | 0.0221106 | ||||||||
\(761\) | 883.814i | 1.16138i | 0.814123 | + | 0.580692i | \(0.197218\pi\) | ||||
−0.814123 | + | 0.580692i | \(0.802782\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 308.853 | 0.404258 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − 754.989i | − 0.985625i | ||||||||
\(767\) | 279.147 | 0.363947 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − 52.5686i | − 0.0683597i | −0.999416 | − | 0.0341799i | \(-0.989118\pi\) | ||||
0.999416 | − | 0.0341799i | \(-0.0108819\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −46.3919 | −0.0600932 | ||||||||
\(773\) | − 613.176i | − 0.793242i | −0.917982 | − | 0.396621i | \(-0.870183\pi\) | ||||
0.917982 | − | 0.396621i | \(-0.129817\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 910.917i | − 1.17538i | ||||||||
\(776\) | 418.907i | 0.539828i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 27.9899 | 0.0359767 | ||||||||
\(779\) | −1011.16 | −1.29802 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 372.784 | 0.477316 | ||||||||
\(782\) | − 496.070i | − 0.634360i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −20.9432 | −0.0266793 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 1058.60i | − 1.34511i | −0.740048 | − | 0.672554i | \(-0.765197\pi\) | ||||
0.740048 | − | 0.672554i | \(-0.234803\pi\) | |||||||
\(788\) | 405.019 | 0.513984 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 33.8937i | 0.0429034i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −232.101 | −0.292687 | ||||||||
\(794\) | 519.498i | 0.654279i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − 460.165i | − 0.578097i | ||||||||
\(797\) | − 1128.99i | − 1.41655i | −0.705934 | − | 0.708277i | \(-0.749473\pi\) | ||||
0.705934 | − | 0.708277i | \(-0.250527\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1020.00 | −1.27660 | ||||||||
\(800\) | −140.853 | −0.176066 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 979.970 | 1.22191 | ||||||||
\(803\) | 95.8022i | 0.119305i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −161.206 | −0.200008 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 282.897i | 0.350120i | ||||||||
\(809\) | −604.118 | −0.746746 | −0.373373 | − | 0.927681i | \(-0.621799\pi\) | ||||
−0.373373 | + | 0.927681i | \(0.621799\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 194.215i | 0.239476i | 0.992806 | + | 0.119738i | \(0.0382055\pi\) | ||||
−0.992806 | + | 0.119738i | \(0.961795\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −54.7939 | −0.0673144 | ||||||||
\(815\) | − 66.5721i | − 0.0816836i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 142.388i | 0.174281i | ||||||||
\(818\) | − 411.394i | − 0.502926i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −34.2111 | −0.0417209 | ||||||||
\(821\) | 776.098 | 0.945308 | 0.472654 | − | 0.881248i | \(-0.343296\pi\) | ||||
0.472654 | + | 0.881248i | \(0.343296\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −148.804 | −0.180807 | −0.0904034 | − | 0.995905i | \(-0.528816\pi\) | ||||
−0.0904034 | + | 0.995905i | \(0.528816\pi\) | |||||||
\(824\) | 17.4985i | 0.0212361i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1018.50 | 1.23156 | 0.615782 | − | 0.787916i | \(-0.288840\pi\) | ||||
0.615782 | + | 0.787916i | \(0.288840\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 310.313i | 0.374322i | 0.982329 | + | 0.187161i | \(0.0599286\pi\) | ||||
−0.982329 | + | 0.187161i | \(0.940071\pi\) | |||||||
\(830\) | 58.8427 | 0.0708948 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 24.9269i | 0.0299602i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 48.4222 | 0.0579907 | ||||||||
\(836\) | − 106.011i | − 0.126807i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 882.940i | 1.05363i | ||||||||
\(839\) | − 331.790i | − 0.395459i | −0.980257 | − | 0.197729i | \(-0.936643\pi\) | ||||
0.980257 | − | 0.197729i | \(-0.0633568\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1056.16 | 1.25583 | ||||||||
\(842\) | −1066.29 | −1.26638 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −344.804 | −0.408536 | ||||||||
\(845\) | 50.4994i | 0.0597626i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −80.9016 | −0.0954028 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 632.952i | 0.744650i | ||||||||
\(851\) | 267.322 | 0.314127 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 358.597i | − 0.420395i | −0.977659 | − | 0.210197i | \(-0.932589\pi\) | ||||
0.977659 | − | 0.210197i | \(-0.0674106\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 119.196 | 0.139248 | ||||||||
\(857\) | 832.835i | 0.971803i | 0.874014 | + | 0.485901i | \(0.161509\pi\) | ||||
−0.874014 | + | 0.485901i | \(0.838491\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1550.24i | 1.80470i | 0.431002 | + | 0.902351i | \(0.358160\pi\) | ||||
−0.431002 | + | 0.902351i | \(0.641840\pi\) | |||||||
\(860\) | 4.81750i | 0.00560175i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.62828 | 0.00188896 | ||||||||
\(863\) | 917.249 | 1.06286 | 0.531430 | − | 0.847102i | \(-0.321655\pi\) | ||||
0.531430 | + | 0.847102i | \(0.321655\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.2763 | −0.0130361 | ||||||||
\(866\) | 274.123i | 0.316540i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 213.823 | 0.246057 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.4634i | 0.0143093i | ||||||||
\(872\) | 341.373 | 0.391482 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 517.192i | 0.591753i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1490.26 | 1.69927 | 0.849636 | − | 0.527370i | \(-0.176822\pi\) | ||||
0.849636 | + | 0.527370i | \(0.176822\pi\) | |||||||
\(878\) | 628.328i | 0.715636i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | − 3.58673i | − 0.00407583i | ||||||||
\(881\) | 156.004i | 0.177076i | 0.996073 | + | 0.0885378i | \(0.0282194\pi\) | ||||
−0.996073 | + | 0.0885378i | \(0.971781\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −61.1859 | −0.0692932 | −0.0346466 | − | 0.999400i | \(-0.511031\pi\) | ||||
−0.0346466 | + | 0.999400i | \(0.511031\pi\) | |||||||
\(884\) | 112.014 | 0.126713 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −571.196 | −0.644691 | ||||||||
\(887\) | 880.738i | 0.992940i | 0.868054 | + | 0.496470i | \(0.165371\pi\) | ||||
−0.868054 | + | 0.496470i | \(0.834629\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −49.9025 | −0.0560702 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − 110.648i | − 0.124045i | ||||||||
\(893\) | 1063.43 | 1.19085 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 20.2632i | − 0.0226405i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 342.975 | 0.381932 | ||||||||
\(899\) | 1593.46i | 1.77248i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 363.549i | 0.403495i | ||||||||
\(902\) | 215.826i | 0.239275i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 296.402 | 0.327878 | ||||||||
\(905\) | 58.2527 | 0.0643677 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1288.76 | 1.42091 | 0.710454 | − | 0.703744i | \(-0.248490\pi\) | ||||
0.710454 | + | 0.703744i | \(0.248490\pi\) | |||||||
\(908\) | 739.156i | 0.814049i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 788.563 | 0.865601 | 0.432801 | − | 0.901490i | \(-0.357525\pi\) | ||||
0.432801 | + | 0.901490i | \(0.357525\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 371.218i | − 0.406591i | ||||||||
\(914\) | −1053.25 | −1.15236 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 588.792i | 0.642786i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1497.59 | −1.62958 | −0.814792 | − | 0.579753i | \(-0.803149\pi\) | ||||
−0.814792 | + | 0.579753i | \(0.803149\pi\) | |||||||
\(920\) | 17.4985i | 0.0190201i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − 1080.92i | − 1.17237i | ||||||||
\(923\) | − 410.667i | − 0.444927i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −341.085 | −0.368741 | ||||||||
\(926\) | 931.647 | 1.00610 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 246.392 | 0.265509 | ||||||||
\(929\) | − 1000.22i | − 1.07667i | −0.842732 | − | 0.538334i | \(-0.819054\pi\) | ||||
0.842732 | − | 0.538334i | \(-0.180946\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 349.574 | 0.375079 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 92.8044i | 0.0993623i | ||||||||
\(935\) | −16.1177 | −0.0172382 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 776.352i | − 0.828550i | −0.910152 | − | 0.414275i | \(-0.864035\pi\) | ||||
0.910152 | − | 0.414275i | \(-0.135965\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 35.9798 | 0.0382764 | ||||||||
\(941\) | − 3.45542i | − 0.00367207i | −0.999998 | − | 0.00183603i | \(-0.999416\pi\) | ||||
0.999998 | − | 0.00183603i | \(-0.000584428\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 1052.94i | − 1.11659i | ||||||||
\(944\) | − 358.356i | − 0.379615i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 30.3919 | 0.0321268 | ||||||||
\(947\) | 890.045 | 0.939857 | 0.469929 | − | 0.882704i | \(-0.344280\pi\) | ||||
0.469929 | + | 0.882704i | \(0.344280\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 105.538 | 0.111210 | ||||||||
\(950\) | − 659.903i | − 0.694635i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1399.43 | 1.46845 | 0.734224 | − | 0.678907i | \(-0.237546\pi\) | ||||
0.734224 | + | 0.678907i | \(0.237546\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 48.9571i | 0.0512640i | ||||||||
\(956\) | 646.558 | 0.676316 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − 351.401i | − 0.366806i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −377.372 | −0.392686 | ||||||||
\(962\) | 60.3623i | 0.0627466i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 331.002i | 0.343363i | ||||||||
\(965\) | − 7.35371i | − 0.00762042i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −404.382 | −0.418182 | −0.209091 | − | 0.977896i | \(-0.567050\pi\) | ||||
−0.209091 | + | 0.977896i | \(0.567050\pi\) | |||||||
\(968\) | 319.612 | 0.330178 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −66.4020 | −0.0684557 | ||||||||
\(971\) | 629.341i | 0.648137i | 0.946034 | + | 0.324069i | \(0.105051\pi\) | ||||
−0.946034 | + | 0.324069i | \(0.894949\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 1081.03 | 1.10988 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 297.960i | 0.305287i | ||||||||
\(977\) | 835.530 | 0.855200 | 0.427600 | − | 0.903968i | \(-0.359359\pi\) | ||||
0.427600 | + | 0.903968i | \(0.359359\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 314.817i | 0.321570i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1106.79 | 1.12708 | ||||||||
\(983\) | 585.085i | 0.595204i | 0.954690 | + | 0.297602i | \(0.0961868\pi\) | ||||
−0.954690 | + | 0.297602i | \(0.903813\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 64.2007i | 0.0651784i | ||||||||
\(986\) | − 1107.21i | − 1.12294i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −116.784 | −0.118202 | ||||||||
\(989\) | −148.272 | −0.149922 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1859.92 | −1.87681 | −0.938405 | − | 0.345537i | \(-0.887697\pi\) | ||||
−0.938405 | + | 0.345537i | \(0.887697\pi\) | |||||||
\(992\) | 206.949i | 0.208618i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 72.9420 | 0.0733085 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 137.481i | 0.137895i | 0.997620 | + | 0.0689473i | \(0.0219640\pi\) | ||||
−0.997620 | + | 0.0689473i | \(0.978036\pi\) | |||||||
\(998\) | 186.648 | 0.187022 | ||||||||
\(999\) | 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 | 882.3.c.d.685.2 | yes | 4 | |
3.2 | odd | 2 | 882.3.c.e.685.3 | yes | 4 | ||
7.2 | even | 3 | 882.3.n.h.325.4 | 8 | |||
7.3 | odd | 6 | 882.3.n.h.19.4 | 8 | |||
7.4 | even | 3 | 882.3.n.h.19.3 | 8 | |||
7.5 | odd | 6 | 882.3.n.h.325.3 | 8 | |||
7.6 | odd | 2 | inner | 882.3.c.d.685.1 | ✓ | 4 | |
21.2 | odd | 6 | 882.3.n.g.325.1 | 8 | |||
21.5 | even | 6 | 882.3.n.g.325.2 | 8 | |||
21.11 | odd | 6 | 882.3.n.g.19.2 | 8 | |||
21.17 | even | 6 | 882.3.n.g.19.1 | 8 | |||
21.20 | even | 2 | 882.3.c.e.685.4 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
882.3.c.d.685.1 | ✓ | 4 | 7.6 | odd | 2 | inner | |
882.3.c.d.685.2 | yes | 4 | 1.1 | even | 1 | trivial | |
882.3.c.e.685.3 | yes | 4 | 3.2 | odd | 2 | ||
882.3.c.e.685.4 | yes | 4 | 21.20 | even | 2 | ||
882.3.n.g.19.1 | 8 | 21.17 | even | 6 | |||
882.3.n.g.19.2 | 8 | 21.11 | odd | 6 | |||
882.3.n.g.325.1 | 8 | 21.2 | odd | 6 | |||
882.3.n.g.325.2 | 8 | 21.5 | even | 6 | |||
882.3.n.h.19.3 | 8 | 7.4 | even | 3 | |||
882.3.n.h.19.4 | 8 | 7.3 | odd | 6 | |||
882.3.n.h.325.3 | 8 | 7.5 | odd | 6 | |||
882.3.n.h.325.4 | 8 | 7.2 | even | 3 |