Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1680,2,Mod(1231,1680)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1680, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1680.1231");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1680.d (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: | \(13.4148675396\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1231.3 | ||
Root | \(1.22474 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1680.1231 |
Dual form | 1680.2.d.b.1231.1 |
$q$-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 \(\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(337\) | \(421\) | \(1121\) | \(1471\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.44949 | + | 1.00000i | −0.925820 | + | 0.377964i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 2.44949i | − | 0.738549i | −0.929320 | − | 0.369274i | \(-0.879606\pi\) | ||
0.929320 | − | 0.369274i | \(-0.120394\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 4.44949i | − | 1.23407i | −0.786937 | − | 0.617033i | \(-0.788334\pi\) | ||
0.786937 | − | 0.617033i | \(-0.211666\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000i | 0.258199i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 6.89898i | − | 1.67325i | −0.547777 | − | 0.836624i | \(-0.684526\pi\) | ||
0.547777 | − | 0.836624i | \(-0.315474\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.44949 | 1.02078 | 0.510391 | − | 0.859942i | \(-0.329501\pi\) | ||||
0.510391 | + | 0.859942i | \(0.329501\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.44949 | + | 1.00000i | −0.534522 | + | 0.218218i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.00000i | 0.417029i | 0.978019 | + | 0.208514i | \(0.0668628\pi\) | ||||
−0.978019 | + | 0.208514i | \(0.933137\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.89898 | −1.28111 | −0.640554 | − | 0.767913i | \(-0.721295\pi\) | ||||
−0.640554 | + | 0.767913i | \(0.721295\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.44949 | −1.51757 | −0.758787 | − | 0.651339i | \(-0.774207\pi\) | ||||
−0.758787 | + | 0.651339i | \(0.774207\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 2.44949i | − | 0.426401i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.00000 | − | 2.44949i | −0.169031 | − | 0.414039i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.89898 | 1.13419 | 0.567093 | − | 0.823654i | \(-0.308068\pi\) | ||||
0.567093 | + | 0.823654i | \(0.308068\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 4.44949i | − | 0.712489i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 0.898979i | − | 0.140397i | −0.997533 | − | 0.0701985i | \(-0.977637\pi\) | ||
0.997533 | − | 0.0701985i | \(-0.0223633\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 8.00000i | − | 1.21999i | −0.792406 | − | 0.609994i | \(-0.791172\pi\) | ||
0.792406 | − | 0.609994i | \(-0.208828\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000i | 0.149071i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.8990 | 1.58978 | 0.794890 | − | 0.606754i | \(-0.207529\pi\) | ||||
0.794890 | + | 0.606754i | \(0.207529\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.00000 | − | 4.89898i | 0.714286 | − | 0.699854i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 6.89898i | − | 0.966050i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.4495 | 1.43535 | 0.717674 | − | 0.696379i | \(-0.245207\pi\) | ||||
0.717674 | + | 0.696379i | \(0.245207\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.44949 | 0.330289 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.44949 | 0.589349 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.89898 | 0.637793 | 0.318896 | − | 0.947790i | \(-0.396688\pi\) | ||||
0.318896 | + | 0.947790i | \(0.396688\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 12.8990i | − | 1.65155i | −0.564003 | − | 0.825773i | \(-0.690739\pi\) | ||
0.564003 | − | 0.825773i | \(-0.309261\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.44949 | + | 1.00000i | −0.308607 | + | 0.125988i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.44949 | 0.551891 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 15.7980i | 1.93003i | 0.262199 | + | 0.965014i | \(0.415552\pi\) | ||||
−0.262199 | + | 0.965014i | \(0.584448\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.00000i | 0.240772i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 6.44949i | − | 0.765414i | −0.923870 | − | 0.382707i | \(-0.874992\pi\) | ||
0.923870 | − | 0.382707i | \(-0.125008\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 5.34847i | − | 0.625991i | −0.949755 | − | 0.312995i | \(-0.898668\pi\) | ||
0.949755 | − | 0.312995i | \(-0.101332\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.44949 | + | 6.00000i | 0.279145 | + | 0.683763i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.79796i | 1.10236i | 0.834388 | + | 0.551178i | \(0.185822\pi\) | ||||
−0.834388 | + | 0.551178i | \(0.814178\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.89898 | −0.318204 | −0.159102 | − | 0.987262i | \(-0.550860\pi\) | ||||
−0.159102 | + | 0.987262i | \(0.550860\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.89898 | 0.748299 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.89898 | −0.739648 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 15.7980i | − | 1.67458i | −0.546759 | − | 0.837290i | \(-0.684139\pi\) | ||
0.546759 | − | 0.837290i | \(-0.315861\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.44949 | + | 10.8990i | 0.466433 | + | 1.14252i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.44949 | −0.876171 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.44949i | 0.456508i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.65153i | 0.269222i | 0.990899 | + | 0.134611i | \(0.0429785\pi\) | ||||
−0.990899 | + | 0.134611i | \(0.957021\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 2.44949i | − | 0.246183i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 8.89898i | − | 0.885482i | −0.896650 | − | 0.442741i | \(-0.854006\pi\) | ||
0.896650 | − | 0.442741i | \(-0.145994\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.89898 | −0.876843 | −0.438421 | − | 0.898770i | \(-0.644462\pi\) | ||||
−0.438421 | + | 0.898770i | \(0.644462\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.00000 | − | 2.44949i | −0.0975900 | − | 0.239046i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 15.7980i | − | 1.52725i | −0.645662 | − | 0.763623i | \(-0.723419\pi\) | ||
0.645662 | − | 0.763623i | \(-0.276581\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.7980 | −1.32160 | −0.660802 | − | 0.750560i | \(-0.729784\pi\) | ||||
−0.660802 | + | 0.750560i | \(0.729784\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.89898 | 0.654822 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.34847 | −0.314997 | −0.157499 | − | 0.987519i | \(-0.550343\pi\) | ||||
−0.157499 | + | 0.987519i | \(0.550343\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.00000 | −0.186501 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 4.44949i | − | 0.411355i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.89898 | + | 16.8990i | 0.632428 | + | 1.54913i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | 0.454545 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 0.898979i | − | 0.0810583i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.79796i | 0.159543i | 0.996813 | + | 0.0797715i | \(0.0254191\pi\) | ||||
−0.996813 | + | 0.0797715i | \(0.974581\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 8.00000i | − | 0.704361i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.6969 | −1.63356 | −0.816780 | − | 0.576950i | \(-0.804243\pi\) | ||||
−0.816780 | + | 0.576950i | \(0.804243\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −10.8990 | + | 4.44949i | −0.945061 | + | 0.385820i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000i | 0.0860663i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 21.1464 | 1.80666 | 0.903331 | − | 0.428945i | \(-0.141115\pi\) | ||||
0.903331 | + | 0.428945i | \(0.141115\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.55051 | −0.640426 | −0.320213 | − | 0.947346i | \(-0.603754\pi\) | ||||
−0.320213 | + | 0.947346i | \(0.603754\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.8990 | 0.917860 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −10.8990 | −0.911418 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 6.89898i | − | 0.572929i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.00000 | − | 4.89898i | 0.412393 | − | 0.404061i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.79796 | −0.311141 | −0.155570 | − | 0.987825i | \(-0.549722\pi\) | ||||
−0.155570 | + | 0.987825i | \(0.549722\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.89898i | 0.724189i | 0.932141 | + | 0.362094i | \(0.117938\pi\) | ||||
−0.932141 | + | 0.362094i | \(0.882062\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 6.89898i | − | 0.557749i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 8.44949i | − | 0.678679i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.3485i | 1.38456i | 0.721630 | + | 0.692279i | \(0.243393\pi\) | ||||
−0.721630 | + | 0.692279i | \(0.756607\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 10.4495 | 0.828698 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.00000 | − | 4.89898i | −0.157622 | − | 0.386094i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 23.5959i | 1.84817i | 0.382181 | + | 0.924087i | \(0.375173\pi\) | ||||
−0.382181 | + | 0.924087i | \(0.624827\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.44949 | 0.190693 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.00000 | −0.619059 | −0.309529 | − | 0.950890i | \(-0.600171\pi\) | ||||
−0.309529 | + | 0.950890i | \(0.600171\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.79796 | −0.522920 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.44949 | 0.340261 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.79796i | 0.288753i | 0.989523 | + | 0.144377i | \(0.0461177\pi\) | ||||
−0.989523 | + | 0.144377i | \(0.953882\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.44949 | − | 1.00000i | 0.185164 | − | 0.0755929i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.89898 | 0.368230 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 0.247449i | − | 0.0184952i | −0.999957 | − | 0.00924759i | \(-0.997056\pi\) | ||
0.999957 | − | 0.00924759i | \(-0.00294364\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.7980i | 1.02559i | 0.858510 | + | 0.512797i | \(0.171391\pi\) | ||||
−0.858510 | + | 0.512797i | \(0.828609\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 12.8990i | − | 0.953520i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.89898i | 0.507223i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −16.8990 | −1.23578 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.44949 | + | 1.00000i | −0.178174 | + | 0.0727393i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 10.4495i | − | 0.756099i | −0.925785 | − | 0.378049i | \(-0.876595\pi\) | ||
0.925785 | − | 0.378049i | \(-0.123405\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.6969 | −0.913946 | −0.456973 | − | 0.889481i | \(-0.651066\pi\) | ||||
−0.456973 | + | 0.889481i | \(0.651066\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.44949 | 0.318635 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.247449 | 0.0176300 | 0.00881500 | − | 0.999961i | \(-0.497194\pi\) | ||||
0.00881500 | + | 0.999961i | \(0.497194\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.44949 | 0.315416 | 0.157708 | − | 0.987486i | \(-0.449590\pi\) | ||||
0.157708 | + | 0.987486i | \(0.449590\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 15.7980i | 1.11430i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 16.8990 | − | 6.89898i | 1.18608 | − | 0.484213i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.898979 | 0.0627875 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.00000i | 0.139010i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 10.8990i | − | 0.753898i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.69694i | 0.461036i | 0.973068 | + | 0.230518i | \(0.0740421\pi\) | ||||
−0.973068 | + | 0.230518i | \(0.925958\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 6.44949i | − | 0.441912i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.00000 | 0.545595 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 20.6969 | − | 8.44949i | 1.40500 | − | 0.573589i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 5.34847i | − | 0.361416i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −30.6969 | −2.06490 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.00000 | −0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 20.6969 | 1.37370 | 0.686852 | − | 0.726797i | \(-0.258992\pi\) | ||||
0.686852 | + | 0.726797i | \(0.258992\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 7.10102i | − | 0.469249i | −0.972086 | − | 0.234624i | \(-0.924614\pi\) | ||
0.972086 | − | 0.234624i | \(-0.0753860\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.44949 | + | 6.00000i | 0.161165 | + | 0.394771i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.2474 | −0.802357 | −0.401179 | − | 0.916000i | \(-0.631399\pi\) | ||||
−0.401179 | + | 0.916000i | \(0.631399\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.8990i | 0.710971i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 9.79796i | 0.636446i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 26.4495i | − | 1.71088i | −0.517906 | − | 0.855438i | \(-0.673288\pi\) | ||
0.517906 | − | 0.855438i | \(-0.326712\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 0.898979i | − | 0.0579084i | −0.999581 | − | 0.0289542i | \(-0.990782\pi\) | ||
0.999581 | − | 0.0289542i | \(-0.00921769\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.89898 | + | 5.00000i | 0.312984 | + | 0.319438i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 19.7980i | − | 1.25971i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.89898 | −0.183715 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.30306 | 0.0822485 | 0.0411243 | − | 0.999154i | \(-0.486906\pi\) | ||||
0.0411243 | + | 0.999154i | \(0.486906\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.89898 | 0.307996 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.89898 | 0.432031 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.10102i | 0.0686798i | 0.999410 | + | 0.0343399i | \(0.0109329\pi\) | ||||
−0.999410 | + | 0.0343399i | \(0.989067\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −16.8990 | + | 6.89898i | −1.05005 | + | 0.428682i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.89898 | −0.427036 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.10102i | 0.0678918i | 0.999424 | + | 0.0339459i | \(0.0108074\pi\) | ||||
−0.999424 | + | 0.0339459i | \(0.989193\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.4495i | 0.641907i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 15.7980i | − | 0.966819i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 20.4949i | 1.24960i | 0.780786 | + | 0.624798i | \(0.214819\pi\) | ||||
−0.780786 | + | 0.624798i | \(0.785181\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.1464 | 1.16306 | 0.581531 | − | 0.813524i | \(-0.302454\pi\) | ||||
0.581531 | + | 0.813524i | \(0.302454\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.44949 | + | 10.8990i | 0.269295 | + | 0.659636i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.44949i | 0.147710i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.5959 | 0.816900 | 0.408450 | − | 0.912781i | \(-0.366070\pi\) | ||||
0.408450 | + | 0.912781i | \(0.366070\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −8.44949 | −0.505858 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.10102 | −0.0656814 | −0.0328407 | − | 0.999461i | \(-0.510455\pi\) | ||||
−0.0328407 | + | 0.999461i | \(0.510455\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.00000 | −0.237775 | −0.118888 | − | 0.992908i | \(-0.537933\pi\) | ||||
−0.118888 | + | 0.992908i | \(0.537933\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.44949i | 0.263565i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.898979 | + | 2.20204i | 0.0530651 | + | 0.129982i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −30.5959 | −1.79976 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.65153i | 0.155435i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 24.6969i | 1.44281i | 0.692513 | + | 0.721405i | \(0.256503\pi\) | ||||
−0.692513 | + | 0.721405i | \(0.743497\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.89898i | 0.285230i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 2.44949i | − | 0.142134i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.89898 | 0.514641 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.00000 | + | 19.5959i | 0.461112 | + | 1.12949i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 8.89898i | − | 0.511233i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12.8990 | 0.738593 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.89898 | −0.507892 | −0.253946 | − | 0.967218i | \(-0.581728\pi\) | ||||
−0.253946 | + | 0.967218i | \(0.581728\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.89898 | −0.506245 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.10102 | 0.175843 | 0.0879214 | − | 0.996127i | \(-0.471978\pi\) | ||||
0.0879214 | + | 0.996127i | \(0.471978\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 14.6515i | − | 0.828153i | −0.910242 | − | 0.414077i | \(-0.864105\pi\) | ||
0.910242 | − | 0.414077i | \(-0.135895\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.00000 | − | 2.44949i | −0.0563436 | − | 0.138013i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 17.1464 | 0.963039 | 0.481520 | − | 0.876435i | \(-0.340085\pi\) | ||||
0.481520 | + | 0.876435i | \(0.340085\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 16.8990i | 0.946161i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 15.7980i | − | 0.881756i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 30.6969i | − | 1.70802i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.44949i | 0.246813i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −13.7980 | −0.763029 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −26.6969 | + | 10.8990i | −1.47185 | + | 0.600880i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 7.10102i | − | 0.390307i | −0.980773 | − | 0.195154i | \(-0.937479\pi\) | ||
0.980773 | − | 0.195154i | \(-0.0625206\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.89898 | 0.378062 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −15.7980 | −0.863135 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.6969 | 0.691646 | 0.345823 | − | 0.938300i | \(-0.387600\pi\) | ||||
0.345823 | + | 0.938300i | \(0.387600\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.34847 | −0.181864 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 20.6969i | 1.12080i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.34847 | + | 17.0000i | −0.396780 | + | 0.917914i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.00000 | −0.107676 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 34.8990i | 1.87348i | 0.350032 | + | 0.936738i | \(0.386171\pi\) | ||||
−0.350032 | + | 0.936738i | \(0.613829\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.6969i | 0.572594i | 0.958141 | + | 0.286297i | \(0.0924244\pi\) | ||||
−0.958141 | + | 0.286297i | \(0.907576\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 4.44949i | − | 0.237496i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 31.7980i | − | 1.69243i | −0.532838 | − | 0.846217i | \(-0.678874\pi\) | ||
0.532838 | − | 0.846217i | \(-0.321126\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.44949 | 0.342303 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.89898 | + | 16.8990i | 0.365133 | + | 0.894389i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 12.2474i | − | 0.646396i | −0.946331 | − | 0.323198i | \(-0.895242\pi\) | ||
0.946331 | − | 0.323198i | \(-0.104758\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.797959 | 0.0419978 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.00000 | 0.262432 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.34847 | 0.279952 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.79796 | −0.511449 | −0.255725 | − | 0.966750i | \(-0.582314\pi\) | ||||
−0.255725 | + | 0.966750i | \(0.582314\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 0.898979i | − | 0.0467990i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −25.5959 | + | 10.4495i | −1.32887 | + | 0.542510i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.0000 | −0.517780 | −0.258890 | − | 0.965907i | \(-0.583357\pi\) | ||||
−0.258890 | + | 0.965907i | \(0.583357\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 1.00000i | − | 0.0516398i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 30.6969i | 1.58097i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 11.1010i | − | 0.570221i | −0.958495 | − | 0.285111i | \(-0.907970\pi\) | ||
0.958495 | − | 0.285111i | \(-0.0920303\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.79796i | 0.0921122i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.20204 | −0.316909 | −0.158455 | − | 0.987366i | \(-0.550651\pi\) | ||||
−0.158455 | + | 0.987366i | \(0.550651\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.00000 | + | 2.44949i | −0.305788 | + | 0.124838i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 8.00000i | − | 0.406663i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −21.5959 | −1.09496 | −0.547478 | − | 0.836820i | \(-0.684412\pi\) | ||||
−0.547478 | + | 0.836820i | \(0.684412\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.7980 | 0.697793 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −18.6969 | −0.943136 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −9.79796 | −0.492989 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 37.8434i | 1.89930i | 0.313306 | + | 0.949652i | \(0.398563\pi\) | ||||
−0.313306 | + | 0.949652i | \(0.601437\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −10.8990 | + | 4.44949i | −0.545631 | + | 0.222753i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 27.7980 | 1.38816 | 0.694082 | − | 0.719896i | \(-0.255811\pi\) | ||||
0.694082 | + | 0.719896i | \(0.255811\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 37.5959i | 1.87279i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000i | 0.0496904i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 16.8990i | − | 0.837651i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.7980i | 0.880052i | 0.897985 | + | 0.440026i | \(0.145031\pi\) | ||||
−0.897985 | + | 0.440026i | \(0.854969\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 21.1464 | 1.04308 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −12.0000 | + | 4.89898i | −0.590481 | + | 0.241063i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 2.89898i | − | 0.142305i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.55051 | −0.369750 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.5959 | 0.761910 | 0.380955 | − | 0.924593i | \(-0.375595\pi\) | ||||
0.380955 | + | 0.924593i | \(0.375595\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −29.5959 | −1.44242 | −0.721208 | − | 0.692718i | \(-0.756413\pi\) | ||||
−0.721208 | + | 0.692718i | \(0.756413\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 10.8990 | 0.529927 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.89898i | 0.334650i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.8990 | + | 31.5959i | 0.624225 | + | 1.52903i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −10.8990 | −0.526208 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.55051i | 0.0746855i | 0.999303 | + | 0.0373427i | \(0.0118893\pi\) | ||||
−0.999303 | + | 0.0373427i | \(0.988111\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 0.449490i | − | 0.0216011i | −0.999942 | − | 0.0108005i | \(-0.996562\pi\) | ||
0.999942 | − | 0.0108005i | \(-0.00343799\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 6.89898i | − | 0.330781i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.89898i | 0.425696i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.75255 | 0.465464 | 0.232732 | − | 0.972541i | \(-0.425234\pi\) | ||||
0.232732 | + | 0.972541i | \(0.425234\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.00000 | − | 4.89898i | 0.238095 | − | 0.233285i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 1.10102i | − | 0.0523111i | −0.999658 | − | 0.0261555i | \(-0.991673\pi\) | ||
0.999658 | − | 0.0261555i | \(-0.00832651\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 15.7980 | 0.748895 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.79796 | −0.179637 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.202041 | 0.00953491 | 0.00476745 | − | 0.999989i | \(-0.498482\pi\) | ||||
0.00476745 | + | 0.999989i | \(0.498482\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.20204 | −0.103690 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.89898i | 0.418111i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −10.8990 | + | 4.44949i | −0.510952 | + | 0.208595i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.4949 | 1.05227 | 0.526133 | − | 0.850402i | \(-0.323641\pi\) | ||||
0.526133 | + | 0.850402i | \(0.323641\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 6.89898i | − | 0.322017i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 8.20204i | − | 0.382007i | −0.981589 | − | 0.191004i | \(-0.938826\pi\) | ||
0.981589 | − | 0.191004i | \(-0.0611742\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 24.0000i | − | 1.11537i | −0.830051 | − | 0.557687i | \(-0.811689\pi\) | ||
0.830051 | − | 0.557687i | \(-0.188311\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 8.44949i | − | 0.391836i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.6969 | 0.587544 | 0.293772 | − | 0.955875i | \(-0.405089\pi\) | ||||
0.293772 | + | 0.955875i | \(0.405089\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.7980 | − | 38.6969i | −0.729482 | − | 1.78686i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 17.3485i | 0.799375i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −19.5959 | −0.901021 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.44949 | −0.204157 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.4495 | 0.478449 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.10102 | 0.141689 | 0.0708446 | − | 0.997487i | \(-0.477431\pi\) | ||||
0.0708446 | + | 0.997487i | \(0.477431\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 30.6969i | − | 1.39966i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.00000 | − | 4.89898i | −0.0910032 | − | 0.222911i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.65153 | −0.120400 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 23.5959i | − | 1.06923i | −0.845095 | − | 0.534617i | \(-0.820456\pi\) | ||
0.845095 | − | 0.534617i | \(-0.179544\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 23.5959i | 1.06704i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 20.6515i | − | 0.931991i | −0.884787 | − | 0.465995i | \(-0.845696\pi\) | ||
0.884787 | − | 0.465995i | \(-0.154304\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 47.5959i | 2.14361i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.44949 | 0.110096 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.44949 | + | 15.7980i | 0.289299 | + | 0.708635i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 5.30306i | − | 0.237398i | −0.992930 | − | 0.118699i | \(-0.962128\pi\) | ||
0.992930 | − | 0.118699i | \(-0.0378723\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.00000 | −0.357414 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 43.5959 | 1.94385 | 0.971923 | − | 0.235299i | \(-0.0756070\pi\) | ||||
0.971923 | + | 0.235299i | \(0.0756070\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.89898 | 0.395999 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.79796 | −0.301908 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.89898i | 0.217143i | 0.994089 | + | 0.108572i | \(0.0346277\pi\) | ||||
−0.994089 | + | 0.108572i | \(0.965372\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.34847 | + | 13.1010i | 0.236602 | + | 0.579555i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.44949 | 0.196450 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 8.89898i | − | 0.392136i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 26.6969i | − | 1.17413i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.79796i | 0.166712i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 3.10102i | − | 0.135858i | −0.997690 | − | 0.0679291i | \(-0.978361\pi\) | ||
0.997690 | − | 0.0679291i | \(-0.0216392\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −27.1010 | −1.18504 | −0.592522 | − | 0.805554i | \(-0.701868\pi\) | ||||
−0.592522 | + | 0.805554i | \(0.701868\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.44949 | − | 1.00000i | 0.106904 | − | 0.0436436i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 58.2929i | 2.53928i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.0000 | 0.826087 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.89898 | 0.212598 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.00000 | −0.173259 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15.7980 | 0.683005 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 0.247449i | − | 0.0106782i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −12.0000 | − | 12.2474i | −0.516877 | − | 0.527535i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −25.5959 | −1.10045 | −0.550227 | − | 0.835015i | \(-0.685459\pi\) | ||||
−0.550227 | + | 0.835015i | \(0.685459\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 13.7980i | 0.592127i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 13.7980i | − | 0.591040i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 6.40408i | − | 0.273819i | −0.990584 | − | 0.136909i | \(-0.956283\pi\) | ||
0.990584 | − | 0.136909i | \(-0.0437169\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 12.8990i | − | 0.550515i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −30.6969 | −1.30773 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.79796 | − | 24.0000i | −0.416652 | − | 1.02058i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.89898i | 0.292845i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −10.4495 | −0.442759 | −0.221380 | − | 0.975188i | \(-0.571056\pi\) | ||||
−0.221380 | + | 0.975188i | \(0.571056\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −35.5959 | −1.50555 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −16.8990 | −0.713475 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.00000 | −0.168580 | −0.0842900 | − | 0.996441i | \(-0.526862\pi\) | ||||
−0.0842900 | + | 0.996441i | \(0.526862\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 3.34847i | − | 0.140871i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.44949 | + | 1.00000i | −0.102869 | + | 0.0419961i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11.7980 | −0.494596 | −0.247298 | − | 0.968939i | \(-0.579543\pi\) | ||||
−0.247298 | + | 0.968939i | \(0.579543\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 28.0000i | 1.17176i | 0.810397 | + | 0.585882i | \(0.199252\pi\) | ||||
−0.810397 | + | 0.585882i | \(0.800748\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 10.4495i | − | 0.436534i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 2.00000i | − | 0.0834058i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23.5505i | 0.980421i | 0.871604 | + | 0.490210i | \(0.163080\pi\) | ||||
−0.871604 | + | 0.490210i | \(0.836920\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −12.6969 | −0.527667 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.10102 | − | 2.89898i | 0.294600 | − | 0.120270i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 25.5959i | − | 1.06007i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.44949 | 0.183964 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 43.1918 | 1.78272 | 0.891359 | − | 0.453298i | \(-0.149753\pi\) | ||||
0.891359 | + | 0.453298i | \(0.149753\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −37.5959 | −1.54911 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.247449 | 0.0101787 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 20.2020i | 0.829598i | 0.909913 | + | 0.414799i | \(0.136148\pi\) | ||||
−0.909913 | + | 0.414799i | \(0.863852\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −16.8990 | + | 6.89898i | −0.692791 | + | 0.282831i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.44949 | 0.182105 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 22.0454i | 0.900751i | 0.892839 | + | 0.450375i | \(0.148710\pi\) | ||||
−0.892839 | + | 0.450375i | \(0.851290\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.8990i | 0.852487i | 0.904608 | + | 0.426244i | \(0.140163\pi\) | ||||
−0.904608 | + | 0.426244i | \(0.859837\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 15.7980i | 0.643343i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.00000i | 0.203279i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.5959 | −0.633019 | −0.316509 | − | 0.948589i | \(-0.602511\pi\) | ||||
−0.316509 | + | 0.948589i | \(0.602511\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 16.8990 | − | 6.89898i | 0.684781 | − | 0.279561i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 48.4949i | − | 1.96189i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 31.7980 | 1.28431 | 0.642154 | − | 0.766576i | \(-0.278041\pi\) | ||||
0.642154 | + | 0.766576i | \(0.278041\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.898979 | 0.0362504 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 31.8434 | 1.28197 | 0.640983 | − | 0.767555i | \(-0.278527\pi\) | ||||
0.640983 | + | 0.767555i | \(0.278527\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12.0454 | −0.484146 | −0.242073 | − | 0.970258i | \(-0.577827\pi\) | ||||
−0.242073 | + | 0.970258i | \(0.577827\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.00000i | 0.0802572i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 15.7980 | + | 38.6969i | 0.632932 | + | 1.55036i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 10.8990i | − | 0.435263i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 47.5959i | − | 1.89777i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 49.3939i | − | 1.96634i | −0.182695 | − | 0.983170i | \(-0.558482\pi\) | ||
0.182695 | − | 0.983170i | \(-0.441518\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.69694i | 0.266179i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.79796 | −0.0713498 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −21.7980 | − | 22.2474i | −0.863667 | − | 0.881476i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 6.44949i | − | 0.255138i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.6969 | 0.501499 | 0.250749 | − | 0.968052i | \(-0.419323\pi\) | ||||
0.250749 | + | 0.968052i | \(0.419323\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 28.8990 | 1.13966 | 0.569832 | − | 0.821761i | \(-0.307008\pi\) | ||||
0.569832 | + | 0.821761i | \(0.307008\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.00000 | 0.315000 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 27.5959 | 1.08491 | 0.542454 | − | 0.840086i | \(-0.317495\pi\) | ||||
0.542454 | + | 0.840086i | \(0.317495\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 12.0000i | − | 0.471041i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 20.6969 | − | 8.44949i | 0.811177 | − | 0.331162i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.14643 | 0.357927 | 0.178964 | − | 0.983856i | \(-0.442726\pi\) | ||||
0.178964 | + | 0.983856i | \(0.442726\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 18.6969i | − | 0.730550i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 5.34847i | − | 0.208664i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.2474i | 0.944546i | 0.881452 | + | 0.472273i | \(0.156566\pi\) | ||||
−0.881452 | + | 0.472273i | \(0.843434\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 35.1010i | 1.36527i | 0.730759 | + | 0.682636i | \(0.239166\pi\) | ||||
−0.730759 | + | 0.682636i | \(0.760834\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −30.6969 | −1.19217 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.44949 | − | 10.8990i | −0.172544 | − | 0.422644i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 13.7980i | − | 0.534259i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −31.5959 | −1.21975 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.30306 | 0.127324 | 0.0636618 | − | 0.997972i | \(-0.479722\pi\) | ||||
0.0636618 | + | 0.997972i | \(0.479722\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 8.69694i | − | 0.334250i | −0.985936 | − | 0.167125i | \(-0.946552\pi\) | ||
0.985936 | − | 0.167125i | \(-0.0534484\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.65153 | − | 6.49490i | −0.101756 | − | 0.249251i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 20.6969 | 0.793108 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 29.1010i | 1.11352i | 0.830674 | + | 0.556760i | \(0.187956\pi\) | ||||
−0.830674 | + | 0.556760i | \(0.812044\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 21.1464i | 0.807963i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 7.10102i | − | 0.270921i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 46.4949i | − | 1.77131i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23.5505 | −0.895904 | −0.447952 | − | 0.894058i | \(-0.647846\pi\) | ||||
−0.447952 | + | 0.894058i | \(0.647846\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.44949 | + | 6.00000i | 0.0930484 | + | 0.227921i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 7.55051i | − | 0.286407i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.20204 | −0.234919 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −12.2474 | −0.463241 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12.6969 | −0.479557 | −0.239778 | − | 0.970828i | \(-0.577075\pi\) | ||||
−0.239778 | + | 0.970828i | \(0.577075\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 30.6969 | 1.15776 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 10.8990i | 0.410479i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.89898 | + | 21.7980i | 0.334681 | + | 0.819797i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 35.7980 | 1.34442 | 0.672210 | − | 0.740360i | \(-0.265345\pi\) | ||||
0.672210 | + | 0.740360i | \(0.265345\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.79796i | 0.367452i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 16.8990i | − | 0.632872i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 10.8990i | − | 0.407599i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 26.4495i | − | 0.987774i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 31.1010 | 1.15987 | 0.579936 | − | 0.814662i | \(-0.303077\pi\) | ||||
0.579936 | + | 0.814662i | \(0.303077\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 21.7980 | − | 8.89898i | 0.811798 | − | 0.331415i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 0.898979i | − | 0.0334334i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.89898 | 0.256222 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.20204 | 0.230021 | 0.115010 | − | 0.993364i | \(-0.463310\pi\) | ||||
0.115010 | + | 0.993364i | \(0.463310\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −55.1918 | −2.04134 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.65153i | 0.0979365i | 0.998800 | + | 0.0489683i | \(0.0155933\pi\) | ||||
−0.998800 | + | 0.0489683i | \(0.984407\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.89898 | + | 5.00000i | 0.180702 | + | 0.184428i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 38.6969 | 1.42542 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 47.5959i | 1.75084i | 0.483359 | + | 0.875422i | \(0.339416\pi\) | ||||
−0.483359 | + | 0.875422i | \(0.660584\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 19.7980i | − | 0.727296i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 20.2929i | 0.744473i | 0.928138 | + | 0.372236i | \(0.121409\pi\) | ||||
−0.928138 | + | 0.372236i | \(0.878591\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 3.79796i | − | 0.139146i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.89898 | −0.106068 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 15.7980 | + | 38.6969i | 0.577245 | + | 1.41396i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 48.8990i | 1.78435i | 0.451691 | + | 0.892175i | \(0.350821\pi\) | ||||
−0.451691 | + | 0.892175i | \(0.649179\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.30306 | 0.0474862 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8.89898 | −0.323867 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 48.6969 | 1.76992 | 0.884960 | − | 0.465667i | \(-0.154185\pi\) | ||||
0.884960 | + | 0.465667i | \(0.154185\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.89898 | 0.177822 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 27.7980i | 1.00768i | 0.863798 | + | 0.503838i | \(0.168079\pi\) | ||||
−0.863798 | + | 0.503838i | \(0.831921\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 33.7980 | − | 13.7980i | 1.22357 | − | 0.499520i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6.89898 | 0.249433 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 21.7980i | − | 0.787079i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 8.49490i | − | 0.306334i | −0.988200 | − | 0.153167i | \(-0.951053\pi\) | ||
0.988200 | − | 0.153167i | \(-0.0489472\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.10102i | 0.0396523i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 43.3939i | − | 1.56077i | −0.625300 | − | 0.780385i | \(-0.715023\pi\) | ||
0.625300 | − | 0.780385i | \(-0.284977\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.44949 | 0.303515 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −16.8990 | + | 6.89898i | −0.606248 | + | 0.247500i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 4.00000i | − | 0.143315i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −15.7980 | −0.565295 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.89898 | −0.246549 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −17.3485 | −0.619193 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −18.6969 | −0.666474 | −0.333237 | − | 0.942843i | \(-0.608141\pi\) | ||||
−0.333237 | + | 0.942843i | \(0.608141\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.10102i | 0.0391974i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.20204 | − | 3.34847i | 0.291631 | − | 0.119058i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −57.3939 | −2.03812 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 10.4495i | 0.370605i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 15.7980i | − | 0.559592i | −0.960059 | − | 0.279796i | \(-0.909733\pi\) | ||
0.960059 | − | 0.279796i | \(-0.0902669\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 75.1918i | − | 2.66010i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 15.7980i | − | 0.558193i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13.1010 | −0.462325 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.89898 | − | 2.00000i | 0.172666 | − | 0.0704907i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 20.4949i | 0.721455i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −34.8990 | −1.22698 | −0.613491 | − | 0.789701i | \(-0.710235\pi\) | ||||
−0.613491 | + | 0.789701i | \(0.710235\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 35.1464 | 1.23416 | 0.617079 | − | 0.786901i | \(-0.288316\pi\) | ||||
0.617079 | + | 0.786901i | \(0.288316\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 19.1464 | 0.671495 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −23.5959 | −0.826529 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 35.5959i | − | 1.24534i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.44949 | + | 10.8990i | 0.155478 | + | 0.380841i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.49490 | −0.226673 | −0.113337 | − | 0.993557i | \(-0.536154\pi\) | ||||
−0.113337 | + | 0.993557i | \(0.536154\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 45.3939i | − | 1.58233i | −0.611602 | − | 0.791166i | \(-0.709475\pi\) | ||
0.611602 | − | 0.791166i | \(-0.290525\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.44949i | 0.0852803i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 43.3939i | − | 1.50895i | −0.656327 | − | 0.754476i | \(-0.727891\pi\) | ||
0.656327 | − | 0.754476i | \(-0.272109\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 5.39388i | − | 0.187337i | −0.995603 | − | 0.0936685i | \(-0.970141\pi\) | ||
0.995603 | − | 0.0936685i | \(-0.0298594\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 13.5959 | 0.471637 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −33.7980 | − | 34.4949i | −1.17103 | − | 1.19518i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 8.00000i | − | 0.276851i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.44949 | −0.292057 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −53.7980 | −1.85731 | −0.928656 | − | 0.370942i | \(-0.879035\pi\) | ||||
−0.928656 | + | 0.370942i | \(0.879035\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 18.5959 | 0.641239 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.10102 | −0.0379212 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 6.79796i | − | 0.233857i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −12.2474 | + | 5.00000i | −0.420827 | + | 0.171802i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.00000 | −0.137280 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 13.7980i | 0.472988i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 36.0454i | − | 1.23417i | −0.786896 | − | 0.617086i | \(-0.788313\pi\) | ||
0.786896 | − | 0.617086i | \(-0.211687\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.44949i | 0.152169i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 6.00000i | − | 0.204956i | −0.994735 | − | 0.102478i | \(-0.967323\pi\) | ||
0.994735 | − | 0.102478i | \(-0.0326771\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 35.5505 | 1.21297 | 0.606484 | − | 0.795096i | \(-0.292579\pi\) | ||||
0.606484 | + | 0.795096i | \(0.292579\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.898979 | + | 2.20204i | 0.0306371 | + | 0.0750454i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 31.3939i | − | 1.06866i | −0.845276 | − | 0.534330i | \(-0.820564\pi\) | ||
0.845276 | − | 0.534330i | \(-0.179436\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.79796 | −0.129134 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −30.5959 | −1.03909 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 24.0000 | 0.814144 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 70.2929 | 2.38178 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.65153i | 0.0897407i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.00000 | + | 2.44949i | 0.0338062 | + | 0.0828079i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13.5959 | −0.459102 | −0.229551 | − | 0.973297i | \(-0.573726\pi\) | ||||
−0.229551 | + | 0.973297i | \(0.573726\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 24.6969i | 0.833007i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.20204i | 0.276334i | 0.990409 | + | 0.138167i | \(0.0441210\pi\) | ||||
−0.990409 | + | 0.138167i | \(0.955879\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.202041i | 0.00679922i | 0.999994 | + | 0.00339961i | \(0.00108213\pi\) | ||||
−0.999994 | + | 0.00339961i | \(0.998918\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.89898i | 0.164677i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12.2929 | 0.412754 | 0.206377 | − | 0.978473i | \(-0.433833\pi\) | ||||
0.206377 | + | 0.978473i | \(0.433833\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.79796 | − | 4.40408i | −0.0603016 | − | 0.147708i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 2.44949i | − | 0.0820610i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 48.4949 | 1.62282 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.247449 | 0.00827130 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.89898 | 0.297128 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 58.2929 | 1.94418 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 72.0908i | − | 2.40169i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.00000 | + | 19.5959i | 0.266223 | + | 0.652111i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −13.7980 | −0.458660 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 1.59592i | − | 0.0529916i | −0.999649 | − | 0.0264958i | \(-0.991565\pi\) | ||
0.999649 | − | 0.0264958i | \(-0.00843486\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 8.89898i | − | 0.295161i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 32.6515i | − | 1.08179i | −0.841089 | − | 0.540897i | \(-0.818085\pi\) | ||
0.841089 | − | 0.540897i | \(-0.181915\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.10102i | 0.235009i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 12.8990 | 0.426427 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 45.7980 | − | 18.6969i | 1.51238 | − | 0.617427i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 28.4949i | − | 0.939960i | −0.882677 | − | 0.469980i | \(-0.844261\pi\) | ||
0.882677 | − | 0.469980i | \(-0.155739\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.89898 | −0.293231 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −28.6969 | −0.944571 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.89898 | −0.226837 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8.89898 | −0.292281 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 30.0000i | 0.984268i | 0.870519 | + | 0.492134i | \(0.163783\pi\) | ||||
−0.870519 | + | 0.492134i | \(0.836217\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 22.2474 | − | 21.7980i | 0.729131 | − | 0.714399i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.10102 | 0.101523 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 16.8990i | − | 0.552656i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18.2474i | 0.596118i | 0.954547 | + | 0.298059i | \(0.0963392\pi\) | ||||
−0.954547 | + | 0.298059i | \(0.903661\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 14.6515i | − | 0.478135i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 30.0000i | − | 0.977972i | −0.872292 | − | 0.488986i | \(-0.837367\pi\) | ||
0.872292 | − | 0.488986i | \(-0.162633\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.79796 | 0.0585496 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.00000 | − | 2.44949i | −0.0325300 | − | 0.0796819i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.69694i | 0.152630i | 0.997084 | + | 0.0763150i | \(0.0243155\pi\) | ||||
−0.997084 | + | 0.0763150i | \(0.975685\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −23.7980 | −0.772514 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 17.1464 | 0.556011 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.247449 | −0.00801565 | −0.00400783 | − | 0.999992i | \(-0.501276\pi\) | ||||
−0.00400783 | + | 0.999992i | \(0.501276\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10.4495 | 0.338138 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 16.8990i | 0.546266i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −51.7980 | + | 21.1464i | −1.67264 | + | 0.682854i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 40.3939 | 1.30303 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 15.7980i | − | 0.509082i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 12.6969i | − | 0.408729i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 31.3939i | − | 1.00956i | −0.863248 | − | 0.504780i | \(-0.831574\pi\) | ||
0.863248 | − | 0.504780i | \(-0.168426\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 30.6969i | − | 0.986128i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −39.1918 | −1.25773 | −0.628863 | − | 0.777516i | \(-0.716479\pi\) | ||||
−0.628863 | + | 0.777516i | \(0.716479\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 18.4949 | − | 7.55051i | 0.592919 | − | 0.242058i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.44949i | 0.142498i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 16.6515 | 0.532730 | 0.266365 | − | 0.963872i | \(-0.414177\pi\) | ||||
0.266365 | + | 0.963872i | \(0.414177\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −38.6969 | −1.23676 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13.7980 | −0.440535 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −30.8990 | −0.985524 | −0.492762 | − | 0.870164i | \(-0.664013\pi\) | ||||
−0.492762 | + | 0.870164i | \(0.664013\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.247449i | 0.00788437i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −26.6969 | + | 10.8990i | −0.849773 | + | 0.346918i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16.0000 | 0.508770 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 22.6969i | − | 0.720992i | −0.932761 | − | 0.360496i | \(-0.882607\pi\) | ||
0.932761 | − | 0.360496i | \(-0.117393\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 7.10102i | − | 0.225344i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.44949i | 0.141058i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.9546i | 0.378606i | 0.981919 | + | 0.189303i | \(0.0606228\pi\) | ||||
−0.981919 | + | 0.189303i | \(0.939377\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6.89898 | 0.218274 |
(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 | 1680.2.d.b.1231.3 | yes | 4 | |
3.2 | odd | 2 | 5040.2.d.b.4591.1 | 4 | |||
4.3 | odd | 2 | 1680.2.d.a.1231.4 | yes | 4 | ||
7.6 | odd | 2 | 1680.2.d.a.1231.2 | ✓ | 4 | ||
12.11 | even | 2 | 5040.2.d.a.4591.2 | 4 | |||
21.20 | even | 2 | 5040.2.d.a.4591.4 | 4 | |||
28.27 | even | 2 | inner | 1680.2.d.b.1231.1 | yes | 4 | |
84.83 | odd | 2 | 5040.2.d.b.4591.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1680.2.d.a.1231.2 | ✓ | 4 | 7.6 | odd | 2 | ||
1680.2.d.a.1231.4 | yes | 4 | 4.3 | odd | 2 | ||
1680.2.d.b.1231.1 | yes | 4 | 28.27 | even | 2 | inner | |
1680.2.d.b.1231.3 | yes | 4 | 1.1 | even | 1 | trivial | |
5040.2.d.a.4591.2 | 4 | 12.11 | even | 2 | |||
5040.2.d.a.4591.4 | 4 | 21.20 | even | 2 | |||
5040.2.d.b.4591.1 | 4 | 3.2 | odd | 2 | |||
5040.2.d.b.4591.3 | 4 | 84.83 | odd | 2 |