Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3584,2,Mod(897,3584)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3584, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3584.897");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3584 = 2^{9} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3584.m (of order \(4\), degree \(2\), 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: | \(28.6183840844\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 897.1 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3584.897 |
Dual form | 3584.2.m.g.2689.1 |
$q$-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 \(\left(\mathbb{Z}/3584\mathbb{Z}\right)^\times\).
\(n\) | \(1023\) | \(1025\) | \(1541\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 | + | 1.00000i | −0.577350 | + | 0.577350i | −0.934172 | − | 0.356822i | \(-0.883860\pi\) |
0.356822 | + | 0.934172i | \(0.383860\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.00000 | + | 2.00000i | 0.603023 | + | 0.603023i | 0.941113 | − | 0.338091i | \(-0.109781\pi\) |
−0.338091 | + | 0.941113i | \(0.609781\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.00000 | + | 2.00000i | −0.554700 | + | 0.554700i | −0.927794 | − | 0.373094i | \(-0.878297\pi\) |
0.373094 | + | 0.927794i | \(0.378297\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.00000 | −1.45521 | −0.727607 | − | 0.685994i | \(-0.759367\pi\) | ||||
−0.727607 | + | 0.685994i | \(0.759367\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.00000 | − | 3.00000i | 0.688247 | − | 0.688247i | −0.273597 | − | 0.961844i | \(-0.588214\pi\) |
0.961844 | + | 0.273597i | \(0.0882135\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | − | 1.00000i | −0.218218 | − | 0.218218i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 5.00000i | − | 1.00000i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.00000 | − | 4.00000i | −0.769800 | − | 0.769800i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.00000 | + | 1.00000i | −0.185695 | + | 0.185695i | −0.793832 | − | 0.608137i | \(-0.791917\pi\) |
0.608137 | + | 0.793832i | \(0.291917\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.0000 | −1.79605 | −0.898027 | − | 0.439941i | \(-0.854999\pi\) | ||||
−0.898027 | + | 0.439941i | \(0.854999\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.00000 | −0.696311 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.00000 | + | 3.00000i | 0.493197 | + | 0.493197i | 0.909312 | − | 0.416115i | \(-0.136609\pi\) |
−0.416115 | + | 0.909312i | \(0.636609\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 4.00000i | − | 0.640513i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.0000i | 1.56174i | 0.624695 | + | 0.780869i | \(0.285223\pi\) | ||||
−0.624695 | + | 0.780869i | \(0.714777\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.00000 | − | 6.00000i | −0.914991 | − | 0.914991i | 0.0816682 | − | 0.996660i | \(-0.473975\pi\) |
−0.996660 | + | 0.0816682i | \(0.973975\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.00000 | −0.291730 | −0.145865 | − | 0.989305i | \(-0.546597\pi\) | ||||
−0.145865 | + | 0.989305i | \(0.546597\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.00000 | − | 6.00000i | 0.840168 | − | 0.840168i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.00000 | + | 9.00000i | 1.23625 | + | 1.23625i | 0.961524 | + | 0.274721i | \(0.0885855\pi\) |
0.274721 | + | 0.961524i | \(0.411414\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.00000i | 0.794719i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.00000 | + | 1.00000i | 0.130189 | + | 0.130189i | 0.769199 | − | 0.639010i | \(-0.220656\pi\) |
−0.639010 | + | 0.769199i | \(0.720656\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.00000 | − | 8.00000i | 0.977356 | − | 0.977356i | −0.0223937 | − | 0.999749i | \(-0.507129\pi\) |
0.999749 | + | 0.0223937i | \(0.00712872\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 12.0000i | − | 1.42414i | −0.702109 | − | 0.712069i | \(-0.747758\pi\) | ||
0.702109 | − | 0.712069i | \(-0.252242\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 2.00000i | − | 0.234082i | −0.993127 | − | 0.117041i | \(-0.962659\pi\) | ||
0.993127 | − | 0.117041i | \(-0.0373409\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.00000 | + | 5.00000i | 0.577350 | + | 0.577350i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.00000 | + | 2.00000i | −0.227921 | + | 0.227921i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.00000 | −0.450035 | −0.225018 | − | 0.974355i | \(-0.572244\pi\) | ||||
−0.225018 | + | 0.974355i | \(0.572244\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.00000 | 0.555556 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.00000 | − | 5.00000i | 0.548821 | − | 0.548821i | −0.377279 | − | 0.926100i | \(-0.623140\pi\) |
0.926100 | + | 0.377279i | \(0.123140\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 2.00000i | − | 0.214423i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 2.00000i | − | 0.212000i | −0.994366 | − | 0.106000i | \(-0.966196\pi\) | ||
0.994366 | − | 0.106000i | \(-0.0338043\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.00000 | − | 2.00000i | −0.209657 | − | 0.209657i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 10.0000 | − | 10.0000i | 1.03695 | − | 1.03695i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.00000 | −0.203069 | −0.101535 | − | 0.994832i | \(-0.532375\pi\) | ||||
−0.101535 | + | 0.994832i | \(0.532375\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.00000 | + | 2.00000i | −0.201008 | + | 0.201008i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.00000 | − | 4.00000i | −0.398015 | − | 0.398015i | 0.479517 | − | 0.877532i | \(-0.340812\pi\) |
−0.877532 | + | 0.479517i | \(0.840812\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.00000i | 0.591198i | 0.955312 | + | 0.295599i | \(0.0955191\pi\) | ||||
−0.955312 | + | 0.295599i | \(0.904481\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.00000 | + | 3.00000i | −0.287348 | + | 0.287348i | −0.836031 | − | 0.548683i | \(-0.815129\pi\) |
0.548683 | + | 0.836031i | \(0.315129\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.00000 | −0.569495 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.0000 | −1.12887 | −0.564433 | − | 0.825479i | \(-0.690905\pi\) | ||||
−0.564433 | + | 0.825479i | \(0.690905\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.00000 | − | 2.00000i | −0.184900 | − | 0.184900i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 6.00000i | − | 0.550019i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 3.00000i | − | 0.272727i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −10.0000 | − | 10.0000i | −0.901670 | − | 0.901670i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.0000 | −1.06483 | −0.532414 | − | 0.846484i | \(-0.678715\pi\) | ||||
−0.532414 | + | 0.846484i | \(0.678715\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 12.0000 | 1.05654 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.00000 | − | 7.00000i | 0.611593 | − | 0.611593i | −0.331768 | − | 0.943361i | \(-0.607645\pi\) |
0.943361 | + | 0.331768i | \(0.107645\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.00000 | + | 3.00000i | 0.260133 | + | 0.260133i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 12.0000i | − | 1.02523i | −0.858619 | − | 0.512615i | \(-0.828677\pi\) | ||
0.858619 | − | 0.512615i | \(-0.171323\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.00000 | + | 3.00000i | 0.254457 | + | 0.254457i | 0.822795 | − | 0.568338i | \(-0.192414\pi\) |
−0.568338 | + | 0.822795i | \(0.692414\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.00000 | − | 2.00000i | 0.168430 | − | 0.168430i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.00000 | −0.668994 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00000 | − | 1.00000i | 0.0824786 | − | 0.0824786i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.00000 | + | 5.00000i | 0.409616 | + | 0.409616i | 0.881605 | − | 0.471989i | \(-0.156464\pi\) |
−0.471989 | + | 0.881605i | \(0.656464\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.0000i | 1.62758i | 0.581161 | + | 0.813788i | \(0.302599\pi\) | ||||
−0.581161 | + | 0.813788i | \(0.697401\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 6.00000i | − | 0.485071i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.0000 | + | 10.0000i | −0.798087 | + | 0.798087i | −0.982794 | − | 0.184707i | \(-0.940866\pi\) |
0.184707 | + | 0.982794i | \(0.440866\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −18.0000 | −1.42749 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.00000 | + | 2.00000i | −0.156652 | + | 0.156652i | −0.781081 | − | 0.624429i | \(-0.785332\pi\) |
0.624429 | + | 0.781081i | \(0.285332\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 22.0000i | − | 1.70241i | −0.524832 | − | 0.851206i | \(-0.675872\pi\) | ||
0.524832 | − | 0.851206i | \(-0.324128\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.00000i | 0.384615i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.00000 | + | 3.00000i | 0.229416 | + | 0.229416i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −10.0000 | + | 10.0000i | −0.760286 | + | 0.760286i | −0.976374 | − | 0.216088i | \(-0.930670\pi\) |
0.216088 | + | 0.976374i | \(0.430670\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.00000 | 0.377964 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.00000 | −0.150329 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 16.0000 | − | 16.0000i | 1.19590 | − | 1.19590i | 0.220512 | − | 0.975384i | \(-0.429227\pi\) |
0.975384 | − | 0.220512i | \(-0.0707728\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.00000 | − | 6.00000i | −0.445976 | − | 0.445976i | 0.448038 | − | 0.894015i | \(-0.352123\pi\) |
−0.894015 | + | 0.448038i | \(0.852123\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.0000 | − | 12.0000i | −0.877527 | − | 0.877527i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.00000 | − | 4.00000i | 0.290957 | − | 0.290957i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20.0000 | −1.44715 | −0.723575 | − | 0.690246i | \(-0.757502\pi\) | ||||
−0.723575 | + | 0.690246i | \(0.757502\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.00000 | 0.143963 | 0.0719816 | − | 0.997406i | \(-0.477068\pi\) | ||||
0.0719816 | + | 0.997406i | \(0.477068\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −13.0000 | − | 13.0000i | −0.926212 | − | 0.926212i | 0.0712470 | − | 0.997459i | \(-0.477302\pi\) |
−0.997459 | + | 0.0712470i | \(0.977302\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 22.0000i | − | 1.55954i | −0.626067 | − | 0.779769i | \(-0.715336\pi\) | ||
0.626067 | − | 0.779769i | \(-0.284664\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 16.0000i | 1.12855i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.00000 | − | 1.00000i | −0.0701862 | − | 0.0701862i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 12.0000 | 0.830057 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.0000 | − | 20.0000i | 1.37686 | − | 1.37686i | 0.526978 | − | 0.849879i | \(-0.323325\pi\) |
0.849879 | − | 0.526978i | \(-0.176675\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 12.0000 | + | 12.0000i | 0.822226 | + | 0.822226i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 10.0000i | − | 0.678844i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.00000 | + | 2.00000i | 0.135147 | + | 0.135147i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.0000 | − | 12.0000i | 0.807207 | − | 0.807207i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.0000 | −1.07144 | −0.535720 | − | 0.844396i | \(-0.679960\pi\) | ||||
−0.535720 | + | 0.844396i | \(0.679960\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.00000 | 0.333333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.00000 | + | 1.00000i | −0.0663723 | + | 0.0663723i | −0.739514 | − | 0.673141i | \(-0.764945\pi\) |
0.673141 | + | 0.739514i | \(0.264945\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.0000 | − | 18.0000i | −1.18947 | − | 1.18947i | −0.977213 | − | 0.212260i | \(-0.931918\pi\) |
−0.212260 | − | 0.977213i | \(-0.568082\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 4.00000i | − | 0.263181i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 10.0000i | − | 0.655122i | −0.944830 | − | 0.327561i | \(-0.893773\pi\) | ||
0.944830 | − | 0.327561i | \(-0.106227\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.00000 | − | 4.00000i | 0.259828 | − | 0.259828i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.00000 | 0.128831 | 0.0644157 | − | 0.997923i | \(-0.479482\pi\) | ||||
0.0644157 | + | 0.997923i | \(0.479482\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 7.00000 | − | 7.00000i | 0.449050 | − | 0.449050i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.0000i | 0.763542i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 10.0000i | 0.633724i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.0000 | − | 11.0000i | −0.694314 | − | 0.694314i | 0.268864 | − | 0.963178i | \(-0.413352\pi\) |
−0.963178 | + | 0.268864i | \(0.913352\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.00000 | −0.374270 | −0.187135 | − | 0.982334i | \(-0.559920\pi\) | ||||
−0.187135 | + | 0.982334i | \(0.559920\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.00000 | + | 3.00000i | −0.186411 | + | 0.186411i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.00000 | − | 1.00000i | −0.0618984 | − | 0.0618984i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.0000i | 0.739952i | 0.929041 | + | 0.369976i | \(0.120634\pi\) | ||||
−0.929041 | + | 0.369976i | \(0.879366\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.00000 | + | 2.00000i | 0.122398 | + | 0.122398i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.0000 | − | 14.0000i | 0.853595 | − | 0.853595i | −0.136979 | − | 0.990574i | \(-0.543739\pi\) |
0.990574 | + | 0.136979i | \(0.0437393\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.0000 | 1.45790 | 0.728948 | − | 0.684569i | \(-0.240010\pi\) | ||||
0.728948 | + | 0.684569i | \(0.240010\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.00000 | 0.242091 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 10.0000 | − | 10.0000i | 0.603023 | − | 0.603023i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −17.0000 | − | 17.0000i | −1.02143 | − | 1.02143i | −0.999765 | − | 0.0216657i | \(-0.993103\pi\) |
−0.0216657 | − | 0.999765i | \(-0.506897\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 10.0000i | − | 0.598684i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 10.0000i | − | 0.596550i | −0.954480 | − | 0.298275i | \(-0.903589\pi\) | ||
0.954480 | − | 0.298275i | \(-0.0964112\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.0000 | − | 15.0000i | −0.891657 | − | 0.891657i | 0.103022 | − | 0.994679i | \(-0.467149\pi\) |
−0.994679 | + | 0.103022i | \(0.967149\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.0000 | −0.590281 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 19.0000 | 1.11765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.00000 | − | 2.00000i | 0.117242 | − | 0.117242i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.00000 | + | 4.00000i | 0.233682 | + | 0.233682i | 0.814228 | − | 0.580545i | \(-0.197161\pi\) |
−0.580545 | + | 0.814228i | \(0.697161\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 16.0000i | − | 0.928414i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.00000 | − | 6.00000i | 0.345834 | − | 0.345834i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 8.00000 | 0.459588 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −23.0000 | + | 23.0000i | −1.31268 | + | 1.31268i | −0.393246 | + | 0.919433i | \(0.628648\pi\) |
−0.919433 | + | 0.393246i | \(0.871352\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.00000 | − | 6.00000i | −0.341328 | − | 0.341328i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.00000i | 0.453638i | 0.973937 | + | 0.226819i | \(0.0728326\pi\) | ||||
−0.973937 | + | 0.226819i | \(0.927167\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 30.0000i | 1.69570i | 0.530236 | + | 0.847850i | \(0.322103\pi\) | ||||
−0.530236 | + | 0.847850i | \(0.677897\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −17.0000 | + | 17.0000i | −0.954815 | + | 0.954815i | −0.999022 | − | 0.0442073i | \(-0.985924\pi\) |
0.0442073 | + | 0.999022i | \(0.485924\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.00000 | −0.223957 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −18.0000 | + | 18.0000i | −1.00155 | + | 1.00155i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.0000 | + | 10.0000i | 0.554700 | + | 0.554700i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 6.00000i | − | 0.331801i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 2.00000i | − | 0.110264i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.00000 | + | 6.00000i | 0.329790 | + | 0.329790i | 0.852506 | − | 0.522717i | \(-0.175081\pi\) |
−0.522717 | + | 0.852506i | \(0.675081\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.00000 | + | 3.00000i | −0.164399 | + | 0.164399i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.0000 | 0.871576 | 0.435788 | − | 0.900049i | \(-0.356470\pi\) | ||||
0.435788 | + | 0.900049i | \(0.356470\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 12.0000 | − | 12.0000i | 0.651751 | − | 0.651751i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −20.0000 | − | 20.0000i | −1.08306 | − | 1.08306i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 22.0000 | + | 22.0000i | 1.18102 | + | 1.18102i | 0.979480 | + | 0.201542i | \(0.0645953\pi\) |
0.201542 | + | 0.979480i | \(0.435405\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.00000 | + | 6.00000i | −0.321173 | + | 0.321173i | −0.849217 | − | 0.528044i | \(-0.822926\pi\) |
0.528044 | + | 0.849217i | \(0.322926\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 16.0000 | 0.854017 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.0000 | 0.532246 | 0.266123 | − | 0.963939i | \(-0.414257\pi\) | ||||
0.266123 | + | 0.963939i | \(0.414257\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.00000 | + | 6.00000i | 0.317554 | + | 0.317554i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 12.0000i | − | 0.633336i | −0.948536 | − | 0.316668i | \(-0.897436\pi\) | ||
0.948536 | − | 0.316668i | \(-0.102564\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000i | 0.0526316i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.00000 | + | 3.00000i | 0.157459 | + | 0.157459i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.00000 | −0.417597 | −0.208798 | − | 0.977959i | \(-0.566955\pi\) | ||||
−0.208798 | + | 0.977959i | \(0.566955\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −10.0000 | −0.520579 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9.00000 | + | 9.00000i | −0.467257 | + | 0.467257i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.00000 | + | 3.00000i | 0.155334 | + | 0.155334i | 0.780496 | − | 0.625161i | \(-0.214967\pi\) |
−0.625161 | + | 0.780496i | \(0.714967\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 4.00000i | − | 0.206010i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.00000 | − | 2.00000i | −0.102733 | − | 0.102733i | 0.653872 | − | 0.756605i | \(-0.273143\pi\) |
−0.756605 | + | 0.653872i | \(0.773143\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.0000 | − | 12.0000i | 0.614779 | − | 0.614779i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.00000 | −0.306586 | −0.153293 | − | 0.988181i | \(-0.548988\pi\) | ||||
−0.153293 | + | 0.988181i | \(0.548988\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.00000 | − | 6.00000i | 0.304997 | − | 0.304997i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 19.0000 | + | 19.0000i | 0.963338 | + | 0.963338i | 0.999351 | − | 0.0360131i | \(-0.0114658\pi\) |
−0.0360131 | + | 0.999351i | \(0.511466\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 14.0000i | 0.706207i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.0000 | − | 10.0000i | 0.501886 | − | 0.501886i | −0.410138 | − | 0.912024i | \(-0.634519\pi\) |
0.912024 | + | 0.410138i | \(0.134519\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.00000 | −0.300376 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.0000 | 0.499376 | 0.249688 | − | 0.968326i | \(-0.419672\pi\) | ||||
0.249688 | + | 0.968326i | \(0.419672\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 20.0000 | − | 20.0000i | 0.996271 | − | 0.996271i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12.0000i | 0.594818i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 6.00000i | − | 0.296681i | −0.988936 | − | 0.148340i | \(-0.952607\pi\) | ||
0.988936 | − | 0.148340i | \(-0.0473931\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.0000 | + | 12.0000i | 0.591916 | + | 0.591916i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.00000 | + | 1.00000i | −0.0492068 | + | 0.0492068i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.00000 | −0.293821 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.00000 | − | 3.00000i | 0.146560 | − | 0.146560i | −0.630020 | − | 0.776579i | \(-0.716953\pi\) |
0.776579 | + | 0.630020i | \(0.216953\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.0000 | + | 17.0000i | 0.828529 | + | 0.828529i | 0.987313 | − | 0.158784i | \(-0.0507574\pi\) |
−0.158784 | + | 0.987313i | \(0.550757\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 2.00000i | − | 0.0972433i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 30.0000i | 1.45521i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 8.00000 | − | 8.00000i | 0.386244 | − | 0.386244i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.0000 | 0.770693 | 0.385346 | − | 0.922772i | \(-0.374082\pi\) | ||||
0.385346 | + | 0.922772i | \(0.374082\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −26.0000 | −1.24948 | −0.624740 | − | 0.780833i | \(-0.714795\pi\) | ||||
−0.624740 | + | 0.780833i | \(0.714795\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.00000i | 0.381819i | 0.981608 | + | 0.190910i | \(0.0611437\pi\) | ||||
−0.981608 | + | 0.190910i | \(0.938856\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 1.00000i | − | 0.0476190i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −20.0000 | − | 20.0000i | −0.950229 | − | 0.950229i | 0.0485901 | − | 0.998819i | \(-0.484527\pi\) |
−0.998819 | + | 0.0485901i | \(0.984527\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −10.0000 | −0.472984 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −32.0000 | −1.51017 | −0.755087 | − | 0.655625i | \(-0.772405\pi\) | ||||
−0.755087 | + | 0.655625i | \(0.772405\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −20.0000 | + | 20.0000i | −0.941763 | + | 0.941763i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −20.0000 | − | 20.0000i | −0.939682 | − | 0.939682i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 42.0000i | − | 1.96468i | −0.187112 | − | 0.982339i | \(-0.559913\pi\) | ||
0.187112 | − | 0.982339i | \(-0.440087\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 24.0000 | + | 24.0000i | 1.12022 | + | 1.12022i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14.0000 | + | 14.0000i | −0.652045 | + | 0.652045i | −0.953485 | − | 0.301440i | \(-0.902533\pi\) |
0.301440 | + | 0.953485i | \(0.402533\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −40.0000 | −1.85896 | −0.929479 | − | 0.368875i | \(-0.879743\pi\) | ||||
−0.929479 | + | 0.368875i | \(0.879743\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.00000 | − | 5.00000i | 0.231372 | − | 0.231372i | −0.581893 | − | 0.813265i | \(-0.697688\pi\) |
0.813265 | + | 0.581893i | \(0.197688\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.00000 | + | 8.00000i | 0.369406 | + | 0.369406i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 20.0000i | − | 0.921551i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 24.0000i | − | 1.10352i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −15.0000 | − | 15.0000i | −0.688247 | − | 0.688247i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.00000 | + | 9.00000i | −0.412082 | + | 0.412082i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14.0000 | 0.639676 | 0.319838 | − | 0.947472i | \(-0.396371\pi\) | ||||
0.319838 | + | 0.947472i | \(0.396371\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.0000 | −0.547153 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.00000i | 0.362515i | 0.983436 | + | 0.181257i | \(0.0580167\pi\) | ||||
−0.983436 | + | 0.181257i | \(0.941983\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 4.00000i | − | 0.180886i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.00000 | − | 6.00000i | 0.270226 | − | 0.270226i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.0000 | 0.538274 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.0000 | + | 12.0000i | −0.537194 | + | 0.537194i | −0.922704 | − | 0.385510i | \(-0.874026\pi\) |
0.385510 | + | 0.922704i | \(0.374026\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 22.0000 | + | 22.0000i | 0.982888 | + | 0.982888i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16.0000i | 0.713405i | 0.934218 | + | 0.356702i | \(0.116099\pi\) | ||||
−0.934218 | + | 0.356702i | \(0.883901\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.00000 | − | 5.00000i | −0.222058 | − | 0.222058i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −26.0000 | + | 26.0000i | −1.15243 | + | 1.15243i | −0.166366 | + | 0.986064i | \(0.553203\pi\) |
−0.986064 | + | 0.166366i | \(0.946797\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.00000 | 0.0884748 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −24.0000 | −1.05963 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.00000 | − | 4.00000i | −0.175920 | − | 0.175920i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 20.0000i | − | 0.877903i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 30.0000i | − | 1.31432i | −0.753749 | − | 0.657162i | \(-0.771757\pi\) | ||
0.753749 | − | 0.657162i | \(-0.228243\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.0000 | + | 11.0000i | 0.480996 | + | 0.480996i | 0.905450 | − | 0.424453i | \(-0.139534\pi\) |
−0.424453 | + | 0.905450i | \(0.639534\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5.00000 | + | 5.00000i | −0.218218 | + | 0.218218i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 60.0000 | 2.61364 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 23.0000 | 1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.00000 | + | 1.00000i | −0.0433963 | + | 0.0433963i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −20.0000 | − | 20.0000i | −0.866296 | − | 0.866296i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 32.0000i | 1.38090i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.00000 | − | 2.00000i | −0.0861461 | − | 0.0861461i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.00000 | + | 1.00000i | −0.0429934 | + | 0.0429934i | −0.728277 | − | 0.685283i | \(-0.759678\pi\) |
0.685283 | + | 0.728277i | \(0.259678\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 12.0000 | 0.514969 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.0000 | + | 22.0000i | −0.940652 | + | 0.940652i | −0.998335 | − | 0.0576829i | \(-0.981629\pi\) |
0.0576829 | + | 0.998335i | \(0.481629\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.00000i | 0.255609i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 4.00000i | − | 0.170097i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.00000 | − | 1.00000i | 0.0423714 | − | 0.0423714i | −0.685604 | − | 0.727975i | \(-0.740462\pi\) |
0.727975 | + | 0.685604i | \(0.240462\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 24.0000 | 1.01509 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 24.0000 | 1.01328 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15.0000 | + | 15.0000i | −0.632175 | + | 0.632175i | −0.948613 | − | 0.316438i | \(-0.897513\pi\) |
0.316438 | + | 0.948613i | \(0.397513\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5.00000i | 0.209980i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 18.0000i | − | 0.754599i | −0.926091 | − | 0.377300i | \(-0.876853\pi\) | ||
0.926091 | − | 0.377300i | \(-0.123147\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.00000 | − | 6.00000i | −0.251092 | − | 0.251092i | 0.570326 | − | 0.821418i | \(-0.306817\pi\) |
−0.821418 | + | 0.570326i | \(0.806817\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 20.0000 | − | 20.0000i | 0.835512 | − | 0.835512i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.00000 | 0.0832611 | 0.0416305 | − | 0.999133i | \(-0.486745\pi\) | ||||
0.0416305 | + | 0.999133i | \(0.486745\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.00000 | + | 2.00000i | −0.0831172 | + | 0.0831172i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.00000 | + | 5.00000i | 0.207435 | + | 0.207435i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 36.0000i | 1.49097i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 21.0000 | + | 21.0000i | 0.866763 | + | 0.866763i | 0.992113 | − | 0.125350i | \(-0.0400053\pi\) |
−0.125350 | + | 0.992113i | \(0.540005\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −30.0000 | + | 30.0000i | −1.23613 | + | 1.23613i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 26.0000 | 1.06950 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.00000 | −0.246390 | −0.123195 | − | 0.992382i | \(-0.539314\pi\) | ||||
−0.123195 | + | 0.992382i | \(0.539314\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 22.0000 | + | 22.0000i | 0.900400 | + | 0.900400i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 40.0000i | 1.63436i | 0.576386 | + | 0.817178i | \(0.304463\pi\) | ||||
−0.576386 | + | 0.817178i | \(0.695537\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 30.0000i | 1.22373i | 0.790964 | + | 0.611863i | \(0.209580\pi\) | ||||
−0.790964 | + | 0.611863i | \(0.790420\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.00000 | + | 8.00000i | 0.325785 | + | 0.325785i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.00000 | 0.324710 | 0.162355 | − | 0.986732i | \(-0.448091\pi\) | ||||
0.162355 | + | 0.986732i | \(0.448091\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.00000 | 0.0810441 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.00000 | − | 4.00000i | 0.161823 | − | 0.161823i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.0000 | + | 19.0000i | 0.767403 | + | 0.767403i | 0.977649 | − | 0.210246i | \(-0.0674264\pi\) |
−0.210246 | + | 0.977649i | \(0.567426\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 40.0000i | 1.61034i | 0.593045 | + | 0.805170i | \(0.297926\pi\) | ||||
−0.593045 | + | 0.805170i | \(0.702074\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −27.0000 | − | 27.0000i | −1.08522 | − | 1.08522i | −0.996013 | − | 0.0892087i | \(-0.971566\pi\) |
−0.0892087 | − | 0.996013i | \(-0.528434\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.00000 | 0.0801283 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −25.0000 | −1.00000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −12.0000 | + | 12.0000i | −0.479234 | + | 0.479234i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −18.0000 | − | 18.0000i | −0.717707 | − | 0.717707i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.0000i | 0.796187i | 0.917345 | + | 0.398094i | \(0.130328\pi\) | ||||
−0.917345 | + | 0.398094i | \(0.869672\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 40.0000i | 1.58986i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.00000 | − | 2.00000i | 0.0792429 | − | 0.0792429i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12.0000 | 0.474713 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.00000 | 0.0789953 | 0.0394976 | − | 0.999220i | \(-0.487424\pi\) | ||||
0.0394976 | + | 0.999220i | \(0.487424\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17.0000 | + | 17.0000i | −0.670415 | + | 0.670415i | −0.957812 | − | 0.287397i | \(-0.907210\pi\) |
0.287397 | + | 0.957812i | \(0.407210\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 38.0000i | − | 1.49393i | −0.664861 | − | 0.746967i | \(-0.731509\pi\) | ||
0.664861 | − | 0.746967i | \(-0.268491\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.00000i | 0.157014i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10.0000 | + | 10.0000i | 0.391931 | + | 0.391931i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19.0000 | − | 19.0000i | 0.743527 | − | 0.743527i | −0.229728 | − | 0.973255i | \(-0.573784\pi\) |
0.973255 | + | 0.229728i | \(0.0737835\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.00000 | 0.0780274 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14.0000 | + | 14.0000i | −0.545363 | + | 0.545363i | −0.925096 | − | 0.379733i | \(-0.876016\pi\) |
0.379733 | + | 0.925096i | \(0.376016\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 28.0000 | + | 28.0000i | 1.08907 | + | 1.08907i | 0.995624 | + | 0.0934498i | \(0.0297895\pi\) |
0.0934498 | + | 0.995624i | \(0.470211\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 24.0000i | 0.932083i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 16.0000 | − | 16.0000i | 0.618596 | − | 0.618596i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −36.0000 | −1.38770 | −0.693849 | − | 0.720121i | \(-0.744086\pi\) | ||||
−0.693849 | + | 0.720121i | \(0.744086\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −20.0000 | + | 20.0000i | −0.769800 | + | 0.769800i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.00000 | + | 2.00000i | 0.0768662 | + | 0.0768662i | 0.744495 | − | 0.667628i | \(-0.232690\pi\) |
−0.667628 | + | 0.744495i | \(0.732690\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 2.00000i | − | 0.0767530i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 2.00000i | − | 0.0766402i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −16.0000 | − | 16.0000i | −0.612223 | − | 0.612223i | 0.331302 | − | 0.943525i | \(-0.392512\pi\) |
−0.943525 | + | 0.331302i | \(0.892512\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 36.0000 | 1.37349 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −36.0000 | −1.37149 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15.0000 | + | 15.0000i | −0.570627 | + | 0.570627i | −0.932304 | − | 0.361677i | \(-0.882204\pi\) |
0.361677 | + | 0.932304i | \(0.382204\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.00000 | − | 2.00000i | −0.0759737 | − | 0.0759737i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 60.0000i | − | 2.27266i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 10.0000 | + | 10.0000i | 0.378235 | + | 0.378235i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21.0000 | − | 21.0000i | 0.793159 | − | 0.793159i | −0.188847 | − | 0.982006i | \(-0.560475\pi\) |
0.982006 | + | 0.188847i | \(0.0604752\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18.0000 | 0.678883 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.00000 | − | 4.00000i | 0.150435 | − | 0.150435i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 27.0000 | + | 27.0000i | 1.01401 | + | 1.01401i | 0.999901 | + | 0.0141058i | \(0.00449016\pi\) |
0.0141058 | + | 0.999901i | \(0.495510\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 4.00000i | − | 0.150012i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 26.0000 | 0.969636 | 0.484818 | − | 0.874615i | \(-0.338886\pi\) | ||||
0.484818 | + | 0.874615i | \(0.338886\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.00000 | −0.223452 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.00000 | + | 2.00000i | −0.0743808 | + | 0.0743808i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.00000 | + | 5.00000i | 0.185695 | + | 0.185695i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 30.0000i | − | 1.11264i | −0.830969 | − | 0.556319i | \(-0.812213\pi\) | ||
0.830969 | − | 0.556319i | \(-0.187787\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.0000i | 1.07407i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 36.0000 | + | 36.0000i | 1.33151 | + | 1.33151i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −24.0000 | + | 24.0000i | −0.886460 | + | 0.886460i | −0.994181 | − | 0.107721i | \(-0.965645\pi\) |
0.107721 | + | 0.994181i | \(0.465645\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 32.0000 | 1.17874 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −22.0000 | + | 22.0000i | −0.809283 | + | 0.809283i | −0.984525 | − | 0.175242i | \(-0.943929\pi\) |
0.175242 | + | 0.984525i | \(0.443929\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −12.0000 | − | 12.0000i | −0.440831 | − | 0.440831i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 44.0000i | − | 1.61420i | −0.590412 | − | 0.807102i | \(-0.701035\pi\) | ||
0.590412 | − | 0.807102i | \(-0.298965\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.00000 | + | 5.00000i | 0.182940 | + | 0.182940i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −32.0000 | −1.16770 | −0.583848 | − | 0.811863i | \(-0.698454\pi\) | ||||
−0.583848 | + | 0.811863i | \(0.698454\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 22.0000 | 0.801725 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −37.0000 | − | 37.0000i | −1.34479 | − | 1.34479i | −0.891224 | − | 0.453564i | \(-0.850152\pi\) |
−0.453564 | − | 0.891224i | \(-0.649848\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 42.0000i | 1.52250i | 0.648459 | + | 0.761249i | \(0.275414\pi\) | ||||
−0.648459 | + | 0.761249i | \(0.724586\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.00000 | − | 3.00000i | −0.108607 | − | 0.108607i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.00000 | −0.144432 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −38.0000 | −1.37032 | −0.685158 | − | 0.728395i | \(-0.740267\pi\) | ||||
−0.685158 | + | 0.728395i | \(0.740267\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.00000 | − | 6.00000i | 0.216085 | − | 0.216085i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −12.0000 | − | 12.0000i | −0.431610 | − | 0.431610i | 0.457566 | − | 0.889176i | \(-0.348721\pi\) |
−0.889176 | + | 0.457566i | \(0.848721\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 50.0000i | 1.79605i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 6.00000i | − | 0.215249i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 30.0000 | + | 30.0000i | 1.07486 | + | 1.07486i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 24.0000 | − | 24.0000i | 0.858788 | − | 0.858788i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.00000 | 0.285897 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.0000 | − | 13.0000i | 0.463400 | − | 0.463400i | −0.436368 | − | 0.899768i | \(-0.643735\pi\) |
0.899768 | + | 0.436368i | \(0.143735\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −12.0000 | − | 12.0000i | −0.427211 | − | 0.427211i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 12.0000i | − | 0.426671i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −22.0000 | + | 22.0000i | −0.779280 | + | 0.779280i | −0.979708 | − | 0.200428i | \(-0.935767\pi\) |
0.200428 | + | 0.979708i | \(0.435767\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.0000 | 0.424529 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.00000 | 0.0706665 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.00000 | − | 4.00000i | 0.141157 | − | 0.141157i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 28.0000i | 0.985647i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 22.0000i | − | 0.773479i | −0.922189 | − | 0.386739i | \(-0.873601\pi\) | ||
0.922189 | − | 0.386739i | \(-0.126399\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.00000 | − | 7.00000i | −0.245803 | − | 0.245803i | 0.573443 | − | 0.819246i | \(-0.305608\pi\) |
−0.819246 | + | 0.573443i | \(0.805608\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −24.0000 | + | 24.0000i | −0.841717 | + | 0.841717i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −36.0000 | −1.25948 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.00000 | − | 2.00000i | 0.0698857 | − | 0.0698857i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 31.0000 | + | 31.0000i | 1.08191 | + | 1.08191i | 0.996332 | + | 0.0855758i | \(0.0272730\pi\) |
0.0855758 | + | 0.996332i | \(0.472727\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.00000i | 0.278862i | 0.990232 | + | 0.139431i | \(0.0445274\pi\) | ||||
−0.990232 | + | 0.139431i | \(0.955473\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 20.0000i | 0.696311i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 20.0000 | + | 20.0000i | 0.695468 | + | 0.695468i | 0.963430 | − | 0.267961i | \(-0.0863500\pi\) |
−0.267961 | + | 0.963430i | \(0.586350\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −32.0000 | + | 32.0000i | −1.11141 | + | 1.11141i | −0.118445 | + | 0.992961i | \(0.537791\pi\) |
−0.992961 | + | 0.118445i | \(0.962209\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 34.0000 | 1.17945 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.00000 | 0.207888 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 40.0000 | + | 40.0000i | 1.38260 | + | 1.38260i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 30.0000i | 1.03572i | 0.855467 | + | 0.517858i | \(0.173270\pi\) | ||||
−0.855467 | + | 0.517858i | \(0.826730\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.0000i | 0.931034i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 10.0000 | + | 10.0000i | 0.344418 | + | 0.344418i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.00000 | 0.103081 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 30.0000 | 1.02960 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.0000 | − | 10.0000i | −0.342393 | − | 0.342393i | 0.514873 | − | 0.857266i | \(-0.327839\pi\) |
−0.857266 | + | 0.514873i | \(0.827839\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 22.0000i | − | 0.751506i | −0.926720 | − | 0.375753i | \(-0.877384\pi\) | ||
0.926720 | − | 0.375753i | \(-0.122616\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −33.0000 | − | 33.0000i | −1.12595 | − | 1.12595i | −0.990830 | − | 0.135116i | \(-0.956859\pi\) |
−0.135116 | − | 0.990830i | \(-0.543141\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 10.0000 | − | 10.0000i | 0.340799 | − | 0.340799i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −4.00000 | −0.136162 | −0.0680808 | − | 0.997680i | \(-0.521688\pi\) | ||||
−0.0680808 | + | 0.997680i | \(0.521688\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −19.0000 | + | 19.0000i | −0.645274 | + | 0.645274i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.00000 | − | 8.00000i | −0.271381 | − | 0.271381i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 32.0000i | 1.08428i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 2.00000i | − | 0.0676897i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.00000 | − | 1.00000i | 0.0337676 | − | 0.0337676i | −0.690021 | − | 0.723789i | \(-0.742399\pi\) |
0.723789 | + | 0.690021i | \(0.242399\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −8.00000 | −0.269833 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 26.0000 | 0.875962 | 0.437981 | − | 0.898984i | \(-0.355694\pi\) | ||||
0.437981 | + | 0.898984i | \(0.355694\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −28.0000 | + | 28.0000i | −0.942275 | + | 0.942275i | −0.998422 | − | 0.0561475i | \(-0.982118\pi\) |
0.0561475 | + | 0.998422i | \(0.482118\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 38.0000i | − | 1.27592i | −0.770072 | − | 0.637958i | \(-0.779780\pi\) | ||
0.770072 | − | 0.637958i | \(-0.220220\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 12.0000i | − | 0.402467i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 10.0000 | + | 10.0000i | 0.335013 | + | 0.335013i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.00000 | + | 6.00000i | −0.200782 | + | 0.200782i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 10.0000 | − | 10.0000i | 0.333519 | − | 0.333519i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −54.0000 | − | 54.0000i | −1.79900 | − | 1.79900i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 12.0000i | 0.399335i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16.0000 | − | 16.0000i | −0.531271 | − | 0.531271i | 0.389679 | − | 0.920951i | \(-0.372586\pi\) |
−0.920951 | + | 0.389679i | \(0.872586\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.00000 | − | 4.00000i | 0.132672 | − | 0.132672i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12.0000 | −0.397578 | −0.198789 | − | 0.980042i | \(-0.563701\pi\) | ||||
−0.198789 | + | 0.980042i | \(0.563701\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 20.0000 | 0.661903 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.00000 | + | 7.00000i | 0.231160 | + | 0.231160i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 32.0000i | 1.05558i | 0.849374 | + | 0.527791i | \(0.176980\pi\) | ||||
−0.849374 | + | 0.527791i | \(0.823020\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 46.0000i | − | 1.51575i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 24.0000 | + | 24.0000i | 0.789970 | + | 0.789970i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15.0000 | − | 15.0000i | 0.493197 | − | 0.493197i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −6.00000 | −0.197066 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.00000 | 0.196854 | 0.0984268 | − | 0.995144i | \(-0.468619\pi\) | ||||
0.0984268 | + | 0.995144i | \(0.468619\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.00000 | + | 3.00000i | −0.0983210 | + | 0.0983210i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8.00000 | − | 8.00000i | −0.261908 | − | 0.261908i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30.0000i | 0.980057i | 0.871706 | + | 0.490029i | \(0.163014\pi\) | ||||
−0.871706 | + | 0.490029i | \(0.836986\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −30.0000 | − | 30.0000i | −0.979013 | − | 0.979013i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 28.0000 | − | 28.0000i | 0.912774 | − | 0.912774i | −0.0837158 | − | 0.996490i | \(-0.526679\pi\) |
0.996490 | + | 0.0837158i | \(0.0266788\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −38.0000 | + | 38.0000i | −1.23483 | + | 1.23483i | −0.272749 | + | 0.962085i | \(0.587933\pi\) |
−0.962085 | + | 0.272749i | \(0.912067\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.00000 | + | 4.00000i | 0.129845 | + | 0.129845i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 34.0000i | − | 1.10253i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 16.0000i | − | 0.518291i | −0.965838 | − | 0.259145i | \(-0.916559\pi\) | ||
0.965838 | − | 0.259145i | \(-0.0834409\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.00000 | − | 4.00000i | 0.129302 | − | 0.129302i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 12.0000 | 0.387500 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 69.0000 | 2.22581 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24.0000i | 0.771788i | 0.922543 | + | 0.385894i | \(0.126107\pi\) | ||||
−0.922543 | + | 0.385894i | \(0.873893\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 36.0000i | − | 1.15649i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15.0000 | + | 15.0000i | 0.481373 | + | 0.481373i | 0.905570 | − | 0.424197i | \(-0.139444\pi\) |
−0.424197 | + | 0.905570i | \(0.639444\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.00000 | + | 3.00000i | −0.0961756 | + | 0.0961756i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −20.0000 | −0.640513 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −20.0000 | −0.639857 | −0.319928 | − | 0.947442i | \(-0.603659\pi\) | ||||
−0.319928 | + | 0.947442i | \(0.603659\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.00000 | − | 4.00000i | 0.127841 | − | 0.127841i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.00000 | − | 3.00000i | −0.0957826 | − | 0.0957826i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 6.00000i | − | 0.191370i | −0.995412 | − | 0.0956851i | \(-0.969496\pi\) | ||
0.995412 | − | 0.0956851i | \(-0.0305042\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.00000 | + | 2.00000i | 0.0636607 | + | 0.0636607i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 48.0000 | 1.52477 | 0.762385 | − | 0.647124i | \(-0.224028\pi\) | ||||
0.762385 | + | 0.647124i | \(0.224028\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −12.0000 | −0.380808 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −20.0000 | − | 20.0000i | −0.633406 | − | 0.633406i | 0.315514 | − | 0.948921i | \(-0.397823\pi\) |
−0.948921 | + | 0.315514i | \(0.897823\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 24.0000i | − | 0.759326i |
(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 | 3584.2.m.g.897.1 | ✓ | 2 | |
4.3 | odd | 2 | 3584.2.m.u.897.1 | yes | 2 | ||
8.3 | odd | 2 | 3584.2.m.h.897.1 | yes | 2 | ||
8.5 | even | 2 | 3584.2.m.v.897.1 | yes | 2 | ||
16.3 | odd | 4 | 3584.2.m.u.2689.1 | yes | 2 | ||
16.5 | even | 4 | 3584.2.m.v.2689.1 | yes | 2 | ||
16.11 | odd | 4 | 3584.2.m.h.2689.1 | yes | 2 | ||
16.13 | even | 4 | inner | 3584.2.m.g.2689.1 | yes | 2 | |
32.3 | odd | 8 | 7168.2.a.e.1.2 | 2 | |||
32.13 | even | 8 | 7168.2.a.n.1.2 | 2 | |||
32.19 | odd | 8 | 7168.2.a.e.1.1 | 2 | |||
32.29 | even | 8 | 7168.2.a.n.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3584.2.m.g.897.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
3584.2.m.g.2689.1 | yes | 2 | 16.13 | even | 4 | inner | |
3584.2.m.h.897.1 | yes | 2 | 8.3 | odd | 2 | ||
3584.2.m.h.2689.1 | yes | 2 | 16.11 | odd | 4 | ||
3584.2.m.u.897.1 | yes | 2 | 4.3 | odd | 2 | ||
3584.2.m.u.2689.1 | yes | 2 | 16.3 | odd | 4 | ||
3584.2.m.v.897.1 | yes | 2 | 8.5 | even | 2 | ||
3584.2.m.v.2689.1 | yes | 2 | 16.5 | even | 4 | ||
7168.2.a.e.1.1 | 2 | 32.19 | odd | 8 | |||
7168.2.a.e.1.2 | 2 | 32.3 | odd | 8 | |||
7168.2.a.n.1.1 | 2 | 32.29 | even | 8 | |||
7168.2.a.n.1.2 | 2 | 32.13 | even | 8 |