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 | 2689.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3584.2689 |
Dual form | 3584.2.m.e.897.1 |
$q$-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 \(\left(\mathbb{Z}/3584\mathbb{Z}\right)^\times\).
\(n\) | \(1023\) | \(1025\) | \(1541\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 | 0.356822 | − | 0.934172i | \(-0.383860\pi\) |
−0.934172 | + | 0.356822i | \(0.883860\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.00000 | + | 2.00000i | −0.894427 | + | 0.894427i | −0.994936 | − | 0.100509i | \(-0.967953\pi\) |
0.100509 | + | 0.994936i | \(0.467953\pi\) | |||||||
\(6\) | 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 | −0.338091 | − | 0.941113i | \(-0.609781\pi\) |
0.941113 | + | 0.338091i | \(0.109781\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.00000 | − | 4.00000i | −1.10940 | − | 1.10940i | −0.993229 | − | 0.116171i | \(-0.962938\pi\) |
−0.116171 | − | 0.993229i | \(-0.537062\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.00000 | 1.03280 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.00000 | −0.485071 | −0.242536 | − | 0.970143i | \(-0.577979\pi\) | ||||
−0.242536 | + | 0.970143i | \(0.577979\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.00000 | − | 5.00000i | −1.14708 | − | 1.14708i | −0.987124 | − | 0.159954i | \(-0.948865\pi\) |
−0.159954 | − | 0.987124i | \(-0.551135\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | + | 1.00000i | −0.218218 | + | 0.218218i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.00000i | 0.834058i | 0.908893 | + | 0.417029i | \(0.136929\pi\) | ||||
−0.908893 | + | 0.417029i | \(0.863071\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 3.00000i | − | 0.600000i | ||||||
\(26\) | 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 | \(-0.208083\pi\) |
−0.608137 | + | 0.793832i | \(0.708083\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.0000 | 1.79605 | 0.898027 | − | 0.439941i | \(-0.145001\pi\) | ||||
0.898027 | + | 0.439941i | \(0.145001\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.00000 | −0.696311 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.00000 | + | 2.00000i | 0.338062 | + | 0.338062i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.00000 | − | 5.00000i | 0.821995 | − | 0.821995i | −0.164399 | − | 0.986394i | \(-0.552568\pi\) |
0.986394 | + | 0.164399i | \(0.0525685\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 8.00000i | 1.28103i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 6.00000i | − | 0.937043i | −0.883452 | − | 0.468521i | \(-0.844787\pi\) | ||
0.883452 | − | 0.468521i | \(-0.155213\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.00000 | − | 6.00000i | 0.914991 | − | 0.914991i | −0.0816682 | − | 0.996660i | \(-0.526025\pi\) |
0.996660 | + | 0.0816682i | \(0.0260248\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.00000 | + | 2.00000i | 0.298142 | + | 0.298142i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.00000 | −0.875190 | −0.437595 | − | 0.899172i | \(-0.644170\pi\) | ||||
−0.437595 | + | 0.899172i | \(0.644170\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.00000 | + | 2.00000i | 0.280056 | + | 0.280056i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.00000 | + | 5.00000i | −0.686803 | + | 0.686803i | −0.961524 | − | 0.274721i | \(-0.911414\pi\) |
0.274721 | + | 0.961524i | \(0.411414\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.00000i | 1.07872i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 10.0000i | 1.32453i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.00000 | + | 7.00000i | −0.911322 | + | 0.911322i | −0.996376 | − | 0.0850540i | \(-0.972894\pi\) |
0.0850540 | + | 0.996376i | \(0.472894\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.00000 | − | 6.00000i | −0.768221 | − | 0.768221i | 0.209572 | − | 0.977793i | \(-0.432793\pi\) |
−0.977793 | + | 0.209572i | \(0.932793\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 16.0000 | 1.98456 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.00000 | − | 4.00000i | −0.488678 | − | 0.488678i | 0.419211 | − | 0.907889i | \(-0.362307\pi\) |
−0.907889 | + | 0.419211i | \(0.862307\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.00000 | − | 4.00000i | 0.481543 | − | 0.481543i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.0000i | 1.42414i | 0.702109 | + | 0.712069i | \(0.252242\pi\) | ||||
−0.702109 | + | 0.712069i | \(0.747758\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 6.00000i | − | 0.702247i | −0.936329 | − | 0.351123i | \(-0.885800\pi\) | ||
0.936329 | − | 0.351123i | \(-0.114200\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.00000 | + | 3.00000i | −0.346410 | + | 0.346410i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.00000 | − | 2.00000i | −0.227921 | − | 0.227921i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.00000 | 0.450035 | 0.225018 | − | 0.974355i | \(-0.427756\pi\) | ||||
0.225018 | + | 0.974355i | \(0.427756\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.00000 | 0.555556 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.00000 | + | 5.00000i | 0.548821 | + | 0.548821i | 0.926100 | − | 0.377279i | \(-0.123140\pi\) |
−0.377279 | + | 0.926100i | \(0.623140\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.00000 | − | 4.00000i | 0.433861 | − | 0.433861i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 2.00000i | − | 0.214423i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 14.0000i | − | 1.48400i | −0.670402 | − | 0.741999i | \(-0.733878\pi\) | ||
0.670402 | − | 0.741999i | \(-0.266122\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.00000 | + | 4.00000i | −0.419314 | + | 0.419314i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −10.0000 | − | 10.0000i | −1.03695 | − | 1.03695i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 20.0000 | 2.05196 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.0000 | 1.01535 | 0.507673 | − | 0.861550i | \(-0.330506\pi\) | ||||
0.507673 | + | 0.861550i | \(0.330506\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.00000 | − | 2.00000i | −0.201008 | − | 0.201008i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.00000 | + | 6.00000i | −0.597022 | + | 0.597022i | −0.939519 | − | 0.342497i | \(-0.888727\pi\) |
0.342497 | + | 0.939519i | \(0.388727\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.00000i | 0.591198i | 0.955312 | + | 0.295599i | \(0.0955191\pi\) | ||||
−0.955312 | + | 0.295599i | \(0.904481\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 4.00000i | − | 0.390360i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.00000 | + | 8.00000i | −0.773389 | + | 0.773389i | −0.978697 | − | 0.205308i | \(-0.934180\pi\) |
0.205308 | + | 0.978697i | \(0.434180\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.0000 | + | 11.0000i | 1.05361 | + | 1.05361i | 0.998479 | + | 0.0551297i | \(0.0175572\pi\) |
0.0551297 | + | 0.998479i | \(0.482443\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.0000 | −0.949158 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.0000 | −1.12887 | −0.564433 | − | 0.825479i | \(-0.690905\pi\) | ||||
−0.564433 | + | 0.825479i | \(0.690905\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.00000 | − | 8.00000i | −0.746004 | − | 0.746004i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.00000 | + | 4.00000i | −0.369800 | + | 0.369800i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.00000i | 0.183340i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.00000i | 0.272727i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.00000 | + | 6.00000i | −0.541002 | + | 0.541002i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.00000 | − | 4.00000i | −0.357771 | − | 0.357771i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.00000 | −0.709885 | −0.354943 | − | 0.934888i | \(-0.615500\pi\) | ||||
−0.354943 | + | 0.934888i | \(0.615500\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −12.0000 | −1.05654 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.00000 | − | 1.00000i | −0.0873704 | − | 0.0873704i | 0.662071 | − | 0.749441i | \(-0.269678\pi\) |
−0.749441 | + | 0.662071i | \(0.769678\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.00000 | + | 5.00000i | −0.433555 | + | 0.433555i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 16.0000i | − | 1.37706i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.00000i | 0.341743i | 0.985293 | + | 0.170872i | \(0.0546583\pi\) | ||||
−0.985293 | + | 0.170872i | \(0.945342\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.0000 | + | 13.0000i | −1.10265 | + | 1.10265i | −0.108555 | + | 0.994090i | \(0.534622\pi\) |
−0.994090 | + | 0.108555i | \(0.965378\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.00000 | + | 6.00000i | 0.505291 | + | 0.505291i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −16.0000 | −1.33799 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.00000 | −0.332182 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00000 | + | 1.00000i | 0.0824786 | + | 0.0824786i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.00000 | + | 9.00000i | −0.737309 | + | 0.737309i | −0.972056 | − | 0.234748i | \(-0.924574\pi\) |
0.234748 | + | 0.972056i | \(0.424574\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.00000i | 0.651031i | 0.945537 | + | 0.325515i | \(0.105538\pi\) | ||||
−0.945537 | + | 0.325515i | \(0.894462\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.00000i | 0.161690i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −20.0000 | + | 20.0000i | −1.60644 | + | 1.60644i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.0000 | + | 12.0000i | 0.957704 | + | 0.957704i | 0.999141 | − | 0.0414369i | \(-0.0131935\pi\) |
−0.0414369 | + | 0.999141i | \(0.513194\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 10.0000 | 0.793052 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.00000 | 0.315244 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.0000 | − | 10.0000i | −0.783260 | − | 0.783260i | 0.197119 | − | 0.980380i | \(-0.436841\pi\) |
−0.980380 | + | 0.197119i | \(0.936841\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 8.00000 | − | 8.00000i | 0.622799 | − | 0.622799i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.00000i | 0.154765i | 0.997001 | + | 0.0773823i | \(0.0246562\pi\) | ||||
−0.997001 | + | 0.0773823i | \(0.975344\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 19.0000i | 1.46154i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.00000 | + | 5.00000i | −0.382360 | + | 0.382360i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −12.0000 | − | 12.0000i | −0.912343 | − | 0.912343i | 0.0841131 | − | 0.996456i | \(-0.473194\pi\) |
−0.996456 | + | 0.0841131i | \(0.973194\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.00000 | −0.226779 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 14.0000 | 1.05230 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.0000 | + | 12.0000i | 0.896922 | + | 0.896922i | 0.995163 | − | 0.0982406i | \(-0.0313215\pi\) |
−0.0982406 | + | 0.995163i | \(0.531321\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 12.0000i | 0.887066i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 20.0000i | 1.47043i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.00000 | + | 4.00000i | −0.292509 | + | 0.292509i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.00000 | + | 4.00000i | 0.290957 | + | 0.290957i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.0000 | 0.868290 | 0.434145 | − | 0.900843i | \(-0.357051\pi\) | ||||
0.434145 | + | 0.900843i | \(0.357051\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.0000 | −1.00774 | −0.503871 | − | 0.863779i | \(-0.668091\pi\) | ||||
−0.503871 | + | 0.863779i | \(0.668091\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −16.0000 | − | 16.0000i | −1.14578 | − | 1.14578i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.00000 | − | 9.00000i | 0.641223 | − | 0.641223i | −0.309633 | − | 0.950856i | \(-0.600206\pi\) |
0.950856 | + | 0.309633i | \(0.100206\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 6.00000i | − | 0.425329i | −0.977125 | − | 0.212664i | \(-0.931786\pi\) | ||
0.977125 | − | 0.212664i | \(-0.0682141\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.00000i | 0.564276i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.00000 | − | 1.00000i | 0.0701862 | − | 0.0701862i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12.0000 | + | 12.0000i | 0.838116 | + | 0.838116i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.00000 | 0.278019 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −20.0000 | −1.38343 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 12.0000 | − | 12.0000i | 0.822226 | − | 0.822226i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 24.0000i | 1.63679i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 10.0000i | − | 0.678844i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.00000 | + | 6.00000i | −0.405442 | + | 0.405442i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.00000 | + | 8.00000i | 0.538138 | + | 0.538138i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.00000 | −0.535720 | −0.267860 | − | 0.963458i | \(-0.586316\pi\) | ||||
−0.267860 | + | 0.963458i | \(0.586316\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.00000 | −0.200000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.00000 | + | 7.00000i | 0.464606 | + | 0.464606i | 0.900162 | − | 0.435556i | \(-0.143448\pi\) |
−0.435556 | + | 0.900162i | \(0.643448\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.00000i | 0.263181i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 22.0000i | − | 1.44127i | −0.693316 | − | 0.720634i | \(-0.743851\pi\) | ||
0.693316 | − | 0.720634i | \(-0.256149\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.0000 | − | 12.0000i | 0.782794 | − | 0.782794i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.00000 | − | 4.00000i | −0.259828 | − | 0.259828i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −20.0000 | −1.29369 | −0.646846 | − | 0.762620i | \(-0.723912\pi\) | ||||
−0.646846 | + | 0.762620i | \(0.723912\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.0000 | 0.901819 | 0.450910 | − | 0.892570i | \(-0.351100\pi\) | ||||
0.450910 | + | 0.892570i | \(0.351100\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 7.00000 | + | 7.00000i | 0.449050 | + | 0.449050i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.00000 | − | 2.00000i | 0.127775 | − | 0.127775i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 40.0000i | 2.54514i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 10.0000i | − | 0.633724i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.00000 | − | 5.00000i | 0.315597 | − | 0.315597i | −0.531476 | − | 0.847073i | \(-0.678362\pi\) |
0.847073 | + | 0.531476i | \(0.178362\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.00000 | + | 8.00000i | 0.502956 | + | 0.502956i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −8.00000 | −0.500979 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −14.0000 | −0.873296 | −0.436648 | − | 0.899632i | \(-0.643834\pi\) | ||||
−0.436648 | + | 0.899632i | \(0.643834\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.00000 | − | 5.00000i | −0.310685 | − | 0.310685i | ||||
\(260\) | 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 | ||||||||
\(265\) | − | 20.0000i | − | 1.22859i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −14.0000 | + | 14.0000i | −0.856786 | + | 0.856786i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.00000 | + | 8.00000i | 0.487769 | + | 0.487769i | 0.907601 | − | 0.419833i | \(-0.137911\pi\) |
−0.419833 | + | 0.907601i | \(0.637911\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 32.0000 | 1.94386 | 0.971931 | − | 0.235267i | \(-0.0755965\pi\) | ||||
0.971931 | + | 0.235267i | \(0.0755965\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 8.00000 | 0.484182 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.00000 | − | 6.00000i | −0.361814 | − | 0.361814i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.00000 | + | 3.00000i | −0.180253 | + | 0.180253i | −0.791466 | − | 0.611213i | \(-0.790682\pi\) |
0.611213 | + | 0.791466i | \(0.290682\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 10.0000i | − | 0.598684i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26.0000i | 1.55103i | 0.631329 | + | 0.775515i | \(0.282510\pi\) | ||||
−0.631329 | + | 0.775515i | \(0.717490\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.0000 | + | 15.0000i | −0.891657 | + | 0.891657i | −0.994679 | − | 0.103022i | \(-0.967149\pi\) |
0.103022 | + | 0.994679i | \(0.467149\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −20.0000 | − | 20.0000i | −1.18470 | − | 1.18470i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.00000 | −0.354169 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −10.0000 | − | 10.0000i | −0.586210 | − | 0.586210i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.00000 | + | 2.00000i | −0.116841 | + | 0.116841i | −0.763110 | − | 0.646269i | \(-0.776329\pi\) |
0.646269 | + | 0.763110i | \(0.276329\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 28.0000i | − | 1.63022i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 16.0000i | 0.928414i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 16.0000 | − | 16.0000i | 0.925304 | − | 0.925304i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.00000 | − | 6.00000i | −0.345834 | − | 0.345834i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 12.0000 | 0.689382 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 24.0000 | 1.37424 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.0000 | + | 17.0000i | 0.970241 | + | 0.970241i | 0.999570 | − | 0.0293286i | \(-0.00933691\pi\) |
−0.0293286 | + | 0.999570i | \(0.509337\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.00000 | − | 6.00000i | 0.341328 | − | 0.341328i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 24.0000i | 1.36092i | 0.732787 | + | 0.680458i | \(0.238219\pi\) | ||||
−0.732787 | + | 0.680458i | \(0.761781\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.0000i | 0.791327i | 0.918396 | + | 0.395663i | \(0.129485\pi\) | ||||
−0.918396 | + | 0.395663i | \(0.870515\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.00000 | − | 2.00000i | 0.112687 | − | 0.112687i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.00000 | + | 5.00000i | 0.280828 | + | 0.280828i | 0.833439 | − | 0.552611i | \(-0.186369\pi\) |
−0.552611 | + | 0.833439i | \(0.686369\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.00000 | 0.223957 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 16.0000 | 0.893033 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.0000 | + | 10.0000i | 0.556415 | + | 0.556415i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −12.0000 | + | 12.0000i | −0.665640 | + | 0.665640i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 22.0000i | − | 1.21660i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.00000i | 0.330791i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.0000 | − | 18.0000i | 0.989369 | − | 0.989369i | −0.0105746 | − | 0.999944i | \(-0.503366\pi\) |
0.999944 | + | 0.0105746i | \(0.00336607\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5.00000 | − | 5.00000i | −0.273998 | − | 0.273998i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 16.0000 | 0.874173 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −32.0000 | −1.74315 | −0.871576 | − | 0.490261i | \(-0.836901\pi\) | ||||
−0.871576 | + | 0.490261i | \(0.836901\pi\) | |||||||
\(338\) | 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 | ||||||||
\(345\) | 16.0000i | 0.861411i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 18.0000 | − | 18.0000i | 0.966291 | − | 0.966291i | −0.0331594 | − | 0.999450i | \(-0.510557\pi\) |
0.999450 | + | 0.0331594i | \(0.0105569\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.00000 | − | 8.00000i | −0.428230 | − | 0.428230i | 0.459795 | − | 0.888025i | \(-0.347923\pi\) |
−0.888025 | + | 0.459795i | \(0.847923\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 32.0000 | 1.70803 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.0000 | 0.958043 | 0.479022 | − | 0.877803i | \(-0.340992\pi\) | ||||
0.479022 | + | 0.877803i | \(0.340992\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −24.0000 | − | 24.0000i | −1.27379 | − | 1.27379i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.00000 | − | 2.00000i | 0.105851 | − | 0.105851i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.00000i | 0.422224i | 0.977462 | + | 0.211112i | \(0.0677085\pi\) | ||||
−0.977462 | + | 0.211112i | \(0.932292\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 31.0000i | 1.63158i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.00000 | − | 3.00000i | 0.157459 | − | 0.157459i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12.0000 | + | 12.0000i | 0.628109 | + | 0.628109i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.0000 | −0.835193 | −0.417597 | − | 0.908633i | \(-0.637127\pi\) | ||||
−0.417597 | + | 0.908633i | \(0.637127\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.00000 | −0.312348 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.00000 | + | 5.00000i | 0.259587 | + | 0.259587i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.0000 | + | 15.0000i | −0.776671 | + | 0.776671i | −0.979263 | − | 0.202593i | \(-0.935063\pi\) |
0.202593 | + | 0.979263i | \(0.435063\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 8.00000i | 0.413118i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 8.00000i | − | 0.412021i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.00000 | + | 6.00000i | −0.308199 | + | 0.308199i | −0.844211 | − | 0.536011i | \(-0.819930\pi\) |
0.536011 | + | 0.844211i | \(0.319930\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.00000 | + | 8.00000i | 0.409852 | + | 0.409852i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 14.0000 | 0.715367 | 0.357683 | − | 0.933843i | \(-0.383567\pi\) | ||||
0.357683 | + | 0.933843i | \(0.383567\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.00000 | 0.407718 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.00000 | − | 6.00000i | −0.304997 | − | 0.304997i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.00000 | + | 3.00000i | −0.152106 | + | 0.152106i | −0.779058 | − | 0.626952i | \(-0.784302\pi\) |
0.626952 | + | 0.779058i | \(0.284302\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 8.00000i | − | 0.404577i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.00000i | 0.100887i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.00000 | + | 8.00000i | −0.402524 | + | 0.402524i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −24.0000 | − | 24.0000i | −1.20453 | − | 1.20453i | −0.972775 | − | 0.231750i | \(-0.925555\pi\) |
−0.231750 | − | 0.972775i | \(-0.574445\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 10.0000 | 0.500626 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −30.0000 | −1.49813 | −0.749064 | − | 0.662497i | \(-0.769497\pi\) | ||||
−0.749064 | + | 0.662497i | \(0.769497\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −40.0000 | − | 40.0000i | −1.99254 | − | 1.99254i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −10.0000 | + | 10.0000i | −0.496904 | + | 0.496904i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 20.0000i | − | 0.991363i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 22.0000i | − | 1.08783i | −0.839140 | − | 0.543915i | \(-0.816941\pi\) | ||
0.839140 | − | 0.543915i | \(-0.183059\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.00000 | − | 4.00000i | 0.197305 | − | 0.197305i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.00000 | + | 7.00000i | 0.344447 | + | 0.344447i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −20.0000 | −0.981761 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 26.0000 | 1.27323 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.00000 | + | 3.00000i | 0.146560 | + | 0.146560i | 0.776579 | − | 0.630020i | \(-0.216953\pi\) |
−0.630020 | + | 0.776579i | \(0.716953\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.00000 | − | 3.00000i | 0.146211 | − | 0.146211i | −0.630212 | − | 0.776423i | \(-0.717032\pi\) |
0.776423 | + | 0.630212i | \(0.217032\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.00000i | 0.291730i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.00000i | 0.291043i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.00000 | + | 6.00000i | −0.290360 | + | 0.290360i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 16.0000 | + | 16.0000i | 0.772487 | + | 0.772487i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.0000 | 0.578020 | 0.289010 | − | 0.957326i | \(-0.406674\pi\) | ||||
0.289010 | + | 0.957326i | \(0.406674\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.00000 | −0.288342 | −0.144171 | − | 0.989553i | \(-0.546051\pi\) | ||||
−0.144171 | + | 0.989553i | \(0.546051\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.00000 | + | 4.00000i | 0.191785 | + | 0.191785i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 20.0000 | − | 20.0000i | 0.956730 | − | 0.956730i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.0000i | 0.763638i | 0.924237 | + | 0.381819i | \(0.124702\pi\) | ||||
−0.924237 | + | 0.381819i | \(0.875298\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000i | 0.0476190i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.00000 | − | 8.00000i | 0.380091 | − | 0.380091i | −0.491044 | − | 0.871135i | \(-0.663384\pi\) |
0.871135 | + | 0.491044i | \(0.163384\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 28.0000 | + | 28.0000i | 1.32733 | + | 1.32733i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 18.0000 | 0.851371 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −16.0000 | −0.755087 | −0.377543 | − | 0.925992i | \(-0.623231\pi\) | ||||
−0.377543 | + | 0.925992i | \(0.623231\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.0000 | − | 12.0000i | −0.565058 | − | 0.565058i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.00000 | − | 8.00000i | 0.375873 | − | 0.375873i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 16.0000i | − | 0.750092i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 38.0000i | − | 1.77757i | −0.458329 | − | 0.888783i | \(-0.651552\pi\) | ||
0.458329 | − | 0.888783i | \(-0.348448\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 8.00000 | − | 8.00000i | 0.373408 | − | 0.373408i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −32.0000 | −1.48717 | −0.743583 | − | 0.668644i | \(-0.766875\pi\) | ||||
−0.743583 | + | 0.668644i | \(0.766875\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 40.0000 | 1.85496 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 21.0000 | + | 21.0000i | 0.971764 | + | 0.971764i | 0.999612 | − | 0.0278481i | \(-0.00886546\pi\) |
−0.0278481 | + | 0.999612i | \(0.508865\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.00000 | + | 4.00000i | −0.184703 | + | 0.184703i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 24.0000i | − | 1.10586i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 24.0000i | − | 1.10352i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −15.0000 | + | 15.0000i | −0.688247 | + | 0.688247i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.00000 | + | 5.00000i | 0.228934 | + | 0.228934i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 18.0000 | 0.822441 | 0.411220 | − | 0.911536i | \(-0.365103\pi\) | ||||
0.411220 | + | 0.911536i | \(0.365103\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −40.0000 | −1.82384 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.00000 | − | 4.00000i | −0.182006 | − | 0.182006i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −20.0000 | + | 20.0000i | −0.908153 | + | 0.908153i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 28.0000i | − | 1.26880i | −0.773004 | − | 0.634401i | \(-0.781247\pi\) | ||
0.773004 | − | 0.634401i | \(-0.218753\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 20.0000i | 0.904431i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.0000 | − | 20.0000i | 0.902587 | − | 0.902587i | −0.0930720 | − | 0.995659i | \(-0.529669\pi\) |
0.995659 | + | 0.0930720i | \(0.0296687\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.00000 | − | 2.00000i | −0.0900755 | − | 0.0900755i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8.00000 | 0.359573 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.0000 | 0.538274 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.0000 | + | 20.0000i | 0.895323 | + | 0.895323i | 0.995018 | − | 0.0996951i | \(-0.0317867\pi\) |
−0.0996951 | + | 0.995018i | \(0.531787\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.00000 | − | 2.00000i | 0.0893534 | − | 0.0893534i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.00000i | 0.356702i | 0.983967 | + | 0.178351i | \(0.0570763\pi\) | ||||
−0.983967 | + | 0.178351i | \(0.942924\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 24.0000i | − | 1.06799i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 19.0000 | − | 19.0000i | 0.843820 | − | 0.843820i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −16.0000 | − | 16.0000i | −0.709188 | − | 0.709188i | 0.257177 | − | 0.966364i | \(-0.417208\pi\) |
−0.966364 | + | 0.257177i | \(0.917208\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.00000 | −0.265424 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 40.0000 | 1.76604 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −12.0000 | − | 12.0000i | −0.528783 | − | 0.528783i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12.0000 | + | 12.0000i | −0.527759 | + | 0.527759i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 24.0000i | 1.05348i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 6.00000i | − | 0.262865i | −0.991325 | − | 0.131432i | \(-0.958042\pi\) | ||
0.991325 | − | 0.131432i | \(-0.0419576\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.00000 | + | 5.00000i | −0.218635 | + | 0.218635i | −0.807923 | − | 0.589288i | \(-0.799408\pi\) |
0.589288 | + | 0.807923i | \(0.299408\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.00000 | + | 3.00000i | 0.130931 | + | 0.130931i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −20.0000 | −0.871214 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.00000 | 0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.00000 | + | 7.00000i | 0.303774 | + | 0.303774i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −24.0000 | + | 24.0000i | −1.03956 | + | 1.03956i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 32.0000i | − | 1.38348i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 24.0000i | − | 1.03568i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.00000 | + | 2.00000i | −0.0861461 | + | 0.0861461i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.00000 | − | 3.00000i | −0.128980 | − | 0.128980i | 0.639670 | − | 0.768650i | \(-0.279071\pi\) |
−0.768650 | + | 0.639670i | \(0.779071\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −44.0000 | −1.88475 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.00000 | + | 2.00000i | 0.0855138 | + | 0.0855138i | 0.748570 | − | 0.663056i | \(-0.230741\pi\) |
−0.663056 | + | 0.748570i | \(0.730741\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.00000 | + | 6.00000i | −0.256074 | + | 0.256074i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 10.0000i | − | 0.426014i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 4.00000i | − | 0.170097i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 20.0000 | − | 20.0000i | 0.848953 | − | 0.848953i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −13.0000 | − | 13.0000i | −0.550828 | − | 0.550828i | 0.375852 | − | 0.926680i | \(-0.377350\pi\) |
−0.926680 | + | 0.375852i | \(0.877350\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −48.0000 | −2.03018 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.00000 | 0.337760 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 25.0000 | + | 25.0000i | 1.05362 | + | 1.05362i | 0.998478 | + | 0.0551461i | \(0.0175625\pi\) |
0.0551461 | + | 0.998478i | \(0.482438\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 24.0000 | − | 24.0000i | 1.00969 | − | 1.00969i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 5.00000i | − | 0.209980i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 22.0000i | − | 0.922288i | −0.887325 | − | 0.461144i | \(-0.847439\pi\) | ||
0.887325 | − | 0.461144i | \(-0.152561\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.00000 | − | 6.00000i | 0.251092 | − | 0.251092i | −0.570326 | − | 0.821418i | \(-0.693183\pi\) |
0.821418 | + | 0.570326i | \(0.193183\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12.0000 | − | 12.0000i | −0.501307 | − | 0.501307i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 12.0000 | 0.500435 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −38.0000 | −1.58196 | −0.790980 | − | 0.611842i | \(-0.790429\pi\) | ||||
−0.790980 | + | 0.611842i | \(0.790429\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 14.0000 | + | 14.0000i | 0.581820 | + | 0.581820i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.00000 | − | 5.00000i | 0.207435 | − | 0.207435i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 20.0000i | 0.828315i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 16.0000i | − | 0.661519i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −11.0000 | + | 11.0000i | −0.454019 | + | 0.454019i | −0.896686 | − | 0.442667i | \(-0.854032\pi\) |
0.442667 | + | 0.896686i | \(0.354032\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −50.0000 | − | 50.0000i | −2.06021 | − | 2.06021i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −18.0000 | −0.740421 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.00000 | 0.0821302 | 0.0410651 | − | 0.999156i | \(-0.486925\pi\) | ||||
0.0410651 | + | 0.999156i | \(0.486925\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.00000 | − | 4.00000i | −0.163984 | − | 0.163984i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6.00000 | + | 6.00000i | −0.245564 | + | 0.245564i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 16.0000i | 0.653742i | 0.945069 | + | 0.326871i | \(0.105994\pi\) | ||||
−0.945069 | + | 0.326871i | \(0.894006\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.00000i | 0.0815817i | 0.999168 | + | 0.0407909i | \(0.0129877\pi\) | ||||
−0.999168 | + | 0.0407909i | \(0.987012\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.00000 | + | 4.00000i | −0.162893 | + | 0.162893i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6.00000 | − | 6.00000i | −0.243935 | − | 0.243935i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −40.0000 | −1.62355 | −0.811775 | − | 0.583970i | \(-0.801498\pi\) | ||||
−0.811775 | + | 0.583970i | \(0.801498\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.00000 | −0.0810441 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 24.0000 | + | 24.0000i | 0.970936 | + | 0.970936i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.0000 | + | 11.0000i | −0.444286 | + | 0.444286i | −0.893449 | − | 0.449164i | \(-0.851722\pi\) |
0.449164 | + | 0.893449i | \(0.351722\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 24.0000i | − | 0.967773i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 24.0000i | 0.966204i | 0.875564 | + | 0.483102i | \(0.160490\pi\) | ||||
−0.875564 | + | 0.483102i | \(0.839510\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21.0000 | − | 21.0000i | 0.844061 | − | 0.844061i | −0.145323 | − | 0.989384i | \(-0.546422\pi\) |
0.989384 | + | 0.145323i | \(0.0464221\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −16.0000 | − | 16.0000i | −0.642058 | − | 0.642058i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −14.0000 | −0.560898 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 31.0000 | 1.24000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 20.0000 | + | 20.0000i | 0.798723 | + | 0.798723i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −10.0000 | + | 10.0000i | −0.398726 | + | 0.398726i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 20.0000i | − | 0.796187i | −0.917345 | − | 0.398094i | \(-0.869672\pi\) | ||
0.917345 | − | 0.398094i | \(-0.130328\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 16.0000 | − | 16.0000i | 0.634941 | − | 0.634941i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.00000 | + | 4.00000i | 0.158486 | + | 0.158486i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12.0000 | 0.474713 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 42.0000 | 1.65890 | 0.829450 | − | 0.558581i | \(-0.188654\pi\) | ||||
0.829450 | + | 0.558581i | \(0.188654\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.00000 | − | 1.00000i | −0.0394362 | − | 0.0394362i | 0.687114 | − | 0.726550i | \(-0.258877\pi\) |
−0.726550 | + | 0.687114i | \(0.758877\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 24.0000 | − | 24.0000i | 0.944999 | − | 0.944999i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 6.00000i | − | 0.235884i | −0.993020 | − | 0.117942i | \(-0.962370\pi\) | ||
0.993020 | − | 0.117942i | \(-0.0376297\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 28.0000i | 1.09910i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10.0000 | + | 10.0000i | −0.391931 | + | 0.391931i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 29.0000 | + | 29.0000i | 1.13486 | + | 1.13486i | 0.989358 | + | 0.145499i | \(0.0464789\pi\) |
0.145499 | + | 0.989358i | \(0.453521\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.00000 | 0.156293 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6.00000 | −0.234082 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −30.0000 | − | 30.0000i | −1.16863 | − | 1.16863i | −0.982530 | − | 0.186104i | \(-0.940414\pi\) |
−0.186104 | − | 0.982530i | \(-0.559586\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.00000 | − | 6.00000i | 0.233373 | − | 0.233373i | −0.580726 | − | 0.814099i | \(-0.697231\pi\) |
0.814099 | + | 0.580726i | \(0.197231\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 16.0000i | − | 0.621389i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 20.0000i | − | 0.775567i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.00000 | + | 4.00000i | −0.154881 | + | 0.154881i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8.00000 | + | 8.00000i | 0.309298 | + | 0.309298i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −24.0000 | −0.926510 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.0000 | 0.770943 | 0.385472 | − | 0.922720i | \(-0.374039\pi\) | ||||
0.385472 | + | 0.922720i | \(0.374039\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 12.0000 | + | 12.0000i | 0.461880 | + | 0.461880i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −20.0000 | + | 20.0000i | −0.768662 | + | 0.768662i | −0.977871 | − | 0.209209i | \(-0.932911\pi\) |
0.209209 | + | 0.977871i | \(0.432911\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 10.0000i | − | 0.383765i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 14.0000i | − | 0.536481i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.00000 | − | 8.00000i | 0.306111 | − | 0.306111i | −0.537288 | − | 0.843399i | \(-0.680551\pi\) |
0.843399 | + | 0.537288i | \(0.180551\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.00000 | − | 8.00000i | −0.305664 | − | 0.305664i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 40.0000 | 1.52388 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.00000 | + | 9.00000i | 0.342376 | + | 0.342376i | 0.857260 | − | 0.514884i | \(-0.172165\pi\) |
−0.514884 | + | 0.857260i | \(0.672165\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.00000 | + | 2.00000i | −0.0759737 | + | 0.0759737i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 52.0000i | − | 1.97247i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12.0000i | 0.454532i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −22.0000 | + | 22.0000i | −0.832116 | + | 0.832116i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −29.0000 | − | 29.0000i | −1.09531 | − | 1.09531i | −0.994951 | − | 0.100364i | \(-0.967999\pi\) |
−0.100364 | − | 0.994951i | \(-0.532001\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −50.0000 | −1.88579 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −24.0000 | −0.903892 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.00000 | + | 6.00000i | 0.225653 | + | 0.225653i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.0000 | − | 13.0000i | 0.488225 | − | 0.488225i | −0.419521 | − | 0.907746i | \(-0.637802\pi\) |
0.907746 | + | 0.419521i | \(0.137802\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 4.00000i | − | 0.150012i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 40.0000i | 1.49801i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 32.0000 | − | 32.0000i | 1.19673 | − | 1.19673i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 20.0000 | + | 20.0000i | 0.746914 | + | 0.746914i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −50.0000 | −1.86469 | −0.932343 | − | 0.361576i | \(-0.882239\pi\) | ||||
−0.932343 | + | 0.361576i | \(0.882239\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.00000 | 0.223452 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −14.0000 | − | 14.0000i | −0.520666 | − | 0.520666i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.00000 | − | 3.00000i | 0.111417 | − | 0.111417i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.0000i | 0.370879i | 0.982656 | + | 0.185440i | \(0.0593710\pi\) | ||||
−0.982656 | + | 0.185440i | \(0.940629\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 29.0000i | − | 1.07407i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.0000 | + | 12.0000i | −0.443836 | + | 0.443836i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.00000 | + | 6.00000i | 0.221615 | + | 0.221615i | 0.809178 | − | 0.587563i | \(-0.199913\pi\) |
−0.587563 | + | 0.809178i | \(0.699913\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4.00000 | −0.147542 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −16.0000 | −0.589368 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 34.0000 | + | 34.0000i | 1.25071 | + | 1.25071i | 0.955402 | + | 0.295308i | \(0.0954223\pi\) |
0.295308 | + | 0.955402i | \(0.404578\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 40.0000 | − | 40.0000i | 1.46944 | − | 1.46944i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 16.0000i | − | 0.586983i | −0.955962 | − | 0.293492i | \(-0.905183\pi\) | ||
0.955962 | − | 0.293492i | \(-0.0948173\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 36.0000i | − | 1.31894i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.00000 | − | 5.00000i | 0.182940 | − | 0.182940i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.00000 | + | 8.00000i | 0.292314 | + | 0.292314i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.0000 | −0.729810 | −0.364905 | − | 0.931045i | \(-0.618899\pi\) | ||||
−0.364905 | + | 0.931045i | \(0.618899\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −10.0000 | −0.364420 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −16.0000 | − | 16.0000i | −0.582300 | − | 0.582300i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.00000 | + | 3.00000i | −0.109037 | + | 0.109037i | −0.759520 | − | 0.650484i | \(-0.774566\pi\) |
0.650484 | + | 0.759520i | \(0.274566\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 16.0000i | − | 0.580763i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 50.0000i | 1.81250i | 0.422744 | + | 0.906249i | \(0.361067\pi\) | ||||
−0.422744 | + | 0.906249i | \(0.638933\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11.0000 | − | 11.0000i | 0.398227 | − | 0.398227i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.00000 | − | 4.00000i | −0.144620 | − | 0.144620i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 56.0000 | 2.02204 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 38.0000 | 1.37032 | 0.685158 | − | 0.728395i | \(-0.259733\pi\) | ||||
0.685158 | + | 0.728395i | \(0.259733\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.0000 | + | 14.0000i | 0.504198 | + | 0.504198i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −18.0000 | + | 18.0000i | −0.647415 | + | 0.647415i | −0.952368 | − | 0.304953i | \(-0.901359\pi\) |
0.304953 | + | 0.952368i | \(0.401359\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 30.0000i | − | 1.07763i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 10.0000i | 0.358748i | ||||||||
\(778\) | 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 | ||||||||
\(785\) | −48.0000 | −1.71319 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −27.0000 | − | 27.0000i | −0.962446 | − | 0.962446i | 0.0368739 | − | 0.999320i | \(-0.488260\pi\) |
−0.999320 | + | 0.0368739i | \(0.988260\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 12.0000 | − | 12.0000i | 0.427211 | − | 0.427211i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 12.0000i | 0.426671i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 48.0000i | 1.70453i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −20.0000 | + | 20.0000i | −0.709327 | + | 0.709327i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 16.0000 | + | 16.0000i | 0.566749 | + | 0.566749i | 0.931216 | − | 0.364467i | \(-0.118749\pi\) |
−0.364467 | + | 0.931216i | \(0.618749\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.0000 | 0.424529 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −14.0000 | −0.494666 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −12.0000 | − | 12.0000i | −0.423471 | − | 0.423471i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.00000 | + | 8.00000i | −0.281963 | + | 0.281963i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 16.0000i | − | 0.563227i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 42.0000i | − | 1.47664i | −0.674450 | − | 0.738321i | \(-0.735619\pi\) | ||
0.674450 | − | 0.738321i | \(-0.264381\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 25.0000 | − | 25.0000i | 0.877869 | − | 0.877869i | −0.115445 | − | 0.993314i | \(-0.536829\pi\) |
0.993314 | + | 0.115445i | \(0.0368294\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −32.0000 | − | 32.0000i | −1.12229 | − | 1.12229i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 40.0000 | 1.40114 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −60.0000 | −2.09913 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.00000 | + | 4.00000i | 0.139771 | + | 0.139771i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.00000 | − | 5.00000i | 0.174501 | − | 0.174501i | −0.614453 | − | 0.788954i | \(-0.710623\pi\) |
0.788954 | + | 0.614453i | \(0.210623\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 48.0000i | − | 1.67317i | −0.547833 | − | 0.836587i | \(-0.684547\pi\) | ||
0.547833 | − | 0.836587i | \(-0.315453\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 12.0000i | 0.417786i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.00000 | − | 4.00000i | 0.139094 | − | 0.139094i | −0.634132 | − | 0.773225i | \(-0.718642\pi\) |
0.773225 | + | 0.634132i | \(0.218642\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −22.0000 | − | 22.0000i | −0.764092 | − | 0.764092i | 0.212968 | − | 0.977059i | \(-0.431687\pi\) |
−0.977059 | + | 0.212968i | \(0.931687\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.00000 | 0.208138 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.00000 | 0.0692959 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.00000 | − | 4.00000i | −0.138426 | − | 0.138426i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −40.0000 | + | 40.0000i | −1.38260 | + | 1.38260i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 50.0000i | − | 1.72619i | −0.505040 | − | 0.863096i | \(-0.668522\pi\) | ||
0.505040 | − | 0.863096i | \(-0.331478\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 27.0000i | − | 0.931034i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 26.0000 | − | 26.0000i | 0.895488 | − | 0.895488i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −38.0000 | − | 38.0000i | −1.30724 | − | 1.30724i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.00000 | 0.103081 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 30.0000 | 1.02960 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 20.0000 | + | 20.0000i | 0.685591 | + | 0.685591i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.00000 | + | 4.00000i | −0.136957 | + | 0.136957i | −0.772262 | − | 0.635304i | \(-0.780875\pi\) |
0.635304 | + | 0.772262i | \(0.280875\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 20.0000i | − | 0.683986i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 18.0000i | 0.614868i | 0.951569 | + | 0.307434i | \(0.0994704\pi\) | ||||
−0.951569 | + | 0.307434i | \(0.900530\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.0000 | − | 15.0000i | 0.511793 | − | 0.511793i | −0.403282 | − | 0.915076i | \(-0.632131\pi\) |
0.915076 | + | 0.403282i | \(0.132131\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.00000 | + | 6.00000i | 0.204479 | + | 0.204479i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 20.0000 | 0.680808 | 0.340404 | − | 0.940279i | \(-0.389436\pi\) | ||||
0.340404 | + | 0.940279i | \(0.389436\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 48.0000 | 1.63205 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13.0000 | + | 13.0000i | 0.441503 | + | 0.441503i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.00000 | − | 8.00000i | 0.271381 | − | 0.271381i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 32.0000i | 1.08428i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 10.0000i | − | 0.338449i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.00000 | + | 4.00000i | −0.135225 | + | 0.135225i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.0000 | + | 15.0000i | 0.506514 | + | 0.506514i | 0.913455 | − | 0.406941i | \(-0.133404\pi\) |
−0.406941 | + | 0.913455i | \(0.633404\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.00000 | 0.134917 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.00000 | 0.0673817 | 0.0336909 | − | 0.999432i | \(-0.489274\pi\) | ||||
0.0336909 | + | 0.999432i | \(0.489274\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12.0000 | − | 12.0000i | −0.403832 | − | 0.403832i | 0.475749 | − | 0.879581i | \(-0.342177\pi\) |
−0.879581 | + | 0.475749i | \(0.842177\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −28.0000 | + | 28.0000i | −0.941210 | + | 0.941210i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 14.0000i | − | 0.470074i | −0.971986 | − | 0.235037i | \(-0.924479\pi\) | ||
0.971986 | − | 0.235037i | \(-0.0755211\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.00000i | 0.268311i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 10.0000 | − | 10.0000i | 0.335013 | − | 0.335013i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 30.0000 | + | 30.0000i | 1.00391 | + | 1.00391i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −48.0000 | −1.60446 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −32.0000 | −1.06845 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 10.0000 | + | 10.0000i | 0.333519 | + | 0.333519i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.0000 | − | 10.0000i | 0.333148 | − | 0.333148i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 12.0000i | 0.399335i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20.0000 | − | 20.0000i | 0.664089 | − | 0.664089i | −0.292252 | − | 0.956341i | \(-0.594405\pi\) |
0.956341 | + | 0.292252i | \(0.0944047\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.00000 | + | 6.00000i | 0.199007 | + | 0.199007i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 20.0000 | 0.661903 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −24.0000 | − | 24.0000i | −0.793416 | − | 0.793416i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.00000 | + | 1.00000i | −0.0330229 | + | 0.0330229i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16.0000i | 0.527791i | 0.964551 | + | 0.263896i | \(0.0850075\pi\) | ||||
−0.964551 | + | 0.263896i | \(0.914993\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 34.0000i | − | 1.12034i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 48.0000 | − | 48.0000i | 1.57994 | − | 1.57994i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15.0000 | − | 15.0000i | −0.493197 | − | 0.493197i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.00000 | 0.197066 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −54.0000 | −1.77168 | −0.885841 | − | 0.463988i | \(-0.846418\pi\) | ||||
−0.885841 | + | 0.463988i | \(0.846418\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.00000 | + | 5.00000i | 0.163868 | + | 0.163868i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 24.0000 | − | 24.0000i | 0.785725 | − | 0.785725i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 16.0000i | − | 0.523256i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 14.0000i | − | 0.457360i | −0.973502 | − | 0.228680i | \(-0.926559\pi\) | ||
0.973502 | − | 0.228680i | \(-0.0734410\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14.0000 | − | 14.0000i | 0.456873 | − | 0.456873i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14.0000 | + | 14.0000i | 0.456387 | + | 0.456387i | 0.897468 | − | 0.441081i | \(-0.145405\pi\) |
−0.441081 | + | 0.897468i | \(0.645405\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 24.0000 | 0.781548 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −16.0000 | −0.520480 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 18.0000 | + | 18.0000i | 0.584921 | + | 0.584921i | 0.936252 | − | 0.351330i | \(-0.114271\pi\) |
−0.351330 | + | 0.936252i | \(0.614271\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −24.0000 | + | 24.0000i | −0.779073 | + | 0.779073i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 10.0000i | − | 0.324272i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 48.0000i | − | 1.55487i | −0.628962 | − | 0.777436i | \(-0.716520\pi\) | ||
0.628962 | − | 0.777436i | \(-0.283480\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −24.0000 | + | 24.0000i | −0.776622 | + | 0.776622i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.00000 | − | 4.00000i | −0.129302 | − | 0.129302i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.00000 | 0.129167 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 69.0000 | 2.22581 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.00000 | + | 8.00000i | 0.257796 | + | 0.257796i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 28.0000 | − | 28.0000i | 0.901352 | − | 0.901352i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 44.0000i | 1.41494i | 0.706741 | + | 0.707472i | \(0.250165\pi\) | ||||
−0.706741 | + | 0.707472i | \(0.749835\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 20.0000i | − | 0.642493i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −41.0000 | + | 41.0000i | −1.31575 | + | 1.31575i | −0.398649 | + | 0.917104i | \(0.630521\pi\) |
−0.917104 | + | 0.398649i | \(0.869479\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 13.0000 | + | 13.0000i | 0.416761 | + | 0.416761i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 24.0000 | 0.768615 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −12.0000 | −0.383914 | −0.191957 | − | 0.981403i | \(-0.561483\pi\) | ||||
−0.191957 | + | 0.981403i | \(0.561483\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −28.0000 | − | 28.0000i | −0.894884 | − | 0.894884i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11.0000 | − | 11.0000i | 0.351203 | − | 0.351203i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 6.00000i | − | 0.191370i | −0.995412 | − | 0.0956851i | \(-0.969496\pi\) | ||
0.995412 | − | 0.0956851i | \(-0.0305042\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 36.0000i | 1.14706i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.00000 | − | 6.00000i | 0.190982 | − | 0.190982i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 24.0000 | + | 24.0000i | 0.763156 | + | 0.763156i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −40.0000 | −1.27064 | −0.635321 | − | 0.772248i | \(-0.719132\pi\) | ||||
−0.635321 | + | 0.772248i | \(0.719132\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −36.0000 | −1.14243 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 12.0000 | + | 12.0000i | 0.380426 | + | 0.380426i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −34.0000 | + | 34.0000i | −1.07679 | + | 1.07679i | −0.0799956 | + | 0.996795i | \(0.525491\pi\) |
−0.996795 | + | 0.0799956i | \(0.974509\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 40.0000i | 1.26554i |
(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.e.2689.1 | yes | 2 | |
4.3 | odd | 2 | 3584.2.m.q.2689.1 | yes | 2 | ||
8.3 | odd | 2 | 3584.2.m.l.2689.1 | yes | 2 | ||
8.5 | even | 2 | 3584.2.m.x.2689.1 | yes | 2 | ||
16.3 | odd | 4 | 3584.2.m.l.897.1 | yes | 2 | ||
16.5 | even | 4 | inner | 3584.2.m.e.897.1 | ✓ | 2 | |
16.11 | odd | 4 | 3584.2.m.q.897.1 | yes | 2 | ||
16.13 | even | 4 | 3584.2.m.x.897.1 | yes | 2 | ||
32.5 | even | 8 | 7168.2.a.m.1.2 | 2 | |||
32.11 | odd | 8 | 7168.2.a.g.1.2 | 2 | |||
32.21 | even | 8 | 7168.2.a.m.1.1 | 2 | |||
32.27 | odd | 8 | 7168.2.a.g.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3584.2.m.e.897.1 | ✓ | 2 | 16.5 | even | 4 | inner | |
3584.2.m.e.2689.1 | yes | 2 | 1.1 | even | 1 | trivial | |
3584.2.m.l.897.1 | yes | 2 | 16.3 | odd | 4 | ||
3584.2.m.l.2689.1 | yes | 2 | 8.3 | odd | 2 | ||
3584.2.m.q.897.1 | yes | 2 | 16.11 | odd | 4 | ||
3584.2.m.q.2689.1 | yes | 2 | 4.3 | odd | 2 | ||
3584.2.m.x.897.1 | yes | 2 | 16.13 | even | 4 | ||
3584.2.m.x.2689.1 | yes | 2 | 8.5 | even | 2 | ||
7168.2.a.g.1.1 | 2 | 32.27 | odd | 8 | |||
7168.2.a.g.1.2 | 2 | 32.11 | odd | 8 | |||
7168.2.a.m.1.1 | 2 | 32.21 | even | 8 | |||
7168.2.a.m.1.2 | 2 | 32.5 | even | 8 |