Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [28,3,Mod(13,28)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(28, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("28.13");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 28 = 2^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 28.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.762944740209\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-6}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 6 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 13.1 | ||
Root | \(-2.44949i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 28.13 |
Dual form | 28.3.b.a.13.2 |
$q$-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 \(\left(\mathbb{Z}/28\mathbb{Z}\right)^\times\).
\(n\) | \(15\) | \(17\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 4.89898i | − | 1.63299i | −0.577350 | − | 0.816497i | \(-0.695913\pi\) | ||
0.577350 | − | 0.816497i | \(-0.304087\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.89898i | 0.979796i | 0.871780 | + | 0.489898i | \(0.162966\pi\) | ||||
−0.871780 | + | 0.489898i | \(0.837034\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.00000 | + | 4.89898i | 0.714286 | + | 0.699854i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −15.0000 | −1.66667 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6.00000 | −0.545455 | −0.272727 | − | 0.962091i | \(-0.587926\pi\) | ||||
−0.272727 | + | 0.962091i | \(0.587926\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 4.89898i | − | 0.376845i | −0.982088 | − | 0.188422i | \(-0.939663\pi\) | ||
0.982088 | − | 0.188422i | \(-0.0603374\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 24.0000 | 1.60000 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 19.5959i | 1.15270i | 0.817203 | + | 0.576351i | \(0.195524\pi\) | ||||
−0.817203 | + | 0.576351i | \(0.804476\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 24.4949i | − | 1.28921i | −0.764518 | − | 0.644603i | \(-0.777023\pi\) | ||
0.764518 | − | 0.644603i | \(-0.222977\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 24.0000 | − | 24.4949i | 1.14286 | − | 1.16642i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −30.0000 | −1.30435 | −0.652174 | − | 0.758069i | \(-0.726143\pi\) | ||||
−0.652174 | + | 0.758069i | \(0.726143\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.0400000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 29.3939i | 1.08866i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.00000 | −0.206897 | −0.103448 | − | 0.994635i | \(-0.532988\pi\) | ||||
−0.103448 | + | 0.994635i | \(0.532988\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 29.3939i | 0.890724i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −24.0000 | + | 24.4949i | −0.685714 | + | 0.699854i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.0000 | 0.270270 | 0.135135 | − | 0.990827i | \(-0.456853\pi\) | ||||
0.135135 | + | 0.990827i | \(0.456853\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −24.0000 | −0.615385 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 48.9898i | − | 1.19487i | −0.801916 | − | 0.597437i | \(-0.796186\pi\) | ||
0.801916 | − | 0.597437i | \(-0.203814\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.0000 | 0.232558 | 0.116279 | − | 0.993217i | \(-0.462903\pi\) | ||||
0.116279 | + | 0.993217i | \(0.462903\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 73.4847i | − | 1.63299i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 19.5959i | 0.416934i | 0.978029 | + | 0.208467i | \(0.0668475\pi\) | ||||
−0.978029 | + | 0.208467i | \(0.933153\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | + | 48.9898i | 0.0204082 | + | 0.999792i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 96.0000 | 1.88235 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 90.0000 | 1.69811 | 0.849057 | − | 0.528302i | \(-0.177171\pi\) | ||||
0.849057 | + | 0.528302i | \(0.177171\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 29.3939i | − | 0.534434i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −120.000 | −2.10526 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 24.4949i | 0.415168i | 0.978217 | + | 0.207584i | \(0.0665600\pi\) | ||||
−0.978217 | + | 0.207584i | \(0.933440\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 24.4949i | − | 0.401556i | −0.979637 | − | 0.200778i | \(-0.935653\pi\) | ||
0.979637 | − | 0.200778i | \(-0.0643469\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −75.0000 | − | 73.4847i | −1.19048 | − | 1.16642i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 24.0000 | 0.369231 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −70.0000 | −1.04478 | −0.522388 | − | 0.852708i | \(-0.674959\pi\) | ||||
−0.522388 | + | 0.852708i | \(0.674959\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 146.969i | 2.12999i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 42.0000 | 0.591549 | 0.295775 | − | 0.955258i | \(-0.404422\pi\) | ||||
0.295775 | + | 0.955258i | \(0.404422\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 107.778i | 1.47640i | 0.674579 | + | 0.738202i | \(0.264325\pi\) | ||||
−0.674579 | + | 0.738202i | \(0.735675\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 4.89898i | − | 0.0653197i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −30.0000 | − | 29.3939i | −0.389610 | − | 0.381739i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 74.0000 | 0.936709 | 0.468354 | − | 0.883541i | \(-0.344847\pi\) | ||||
0.468354 | + | 0.883541i | \(0.344847\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 63.6867i | − | 0.767310i | −0.923476 | − | 0.383655i | \(-0.874665\pi\) | ||
0.923476 | − | 0.383655i | \(-0.125335\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −96.0000 | −1.12941 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 29.3939i | 0.337861i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 146.969i | − | 1.65134i | −0.564152 | − | 0.825671i | \(-0.690797\pi\) | ||
0.564152 | − | 0.825671i | \(-0.309203\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 24.0000 | − | 24.4949i | 0.263736 | − | 0.269175i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 120.000 | 1.26316 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 78.3837i | − | 0.808079i | −0.914742 | − | 0.404040i | \(-0.867606\pi\) | ||
0.914742 | − | 0.404040i | \(-0.132394\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 90.0000 | 0.909091 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 73.4847i | − | 0.727571i | −0.931483 | − | 0.363786i | \(-0.881484\pi\) | ||
0.931483 | − | 0.363786i | \(-0.118516\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 166.565i | 1.61714i | 0.588401 | + | 0.808569i | \(0.299758\pi\) | ||||
−0.588401 | + | 0.808569i | \(0.700242\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 120.000 | + | 117.576i | 1.14286 | + | 1.11977i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −150.000 | −1.40187 | −0.700935 | − | 0.713226i | \(-0.747234\pi\) | ||||
−0.700935 | + | 0.713226i | \(0.747234\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −86.0000 | −0.788991 | −0.394495 | − | 0.918898i | \(-0.629081\pi\) | ||||
−0.394495 | + | 0.918898i | \(0.629081\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 48.9898i | − | 0.441350i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 90.0000 | 0.796460 | 0.398230 | − | 0.917286i | \(-0.369625\pi\) | ||||
0.398230 | + | 0.917286i | \(0.369625\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 146.969i | − | 1.27799i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 73.4847i | 0.628074i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −96.0000 | + | 97.9796i | −0.806723 | + | 0.823358i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −85.0000 | −0.702479 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −240.000 | −1.95122 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 127.373i | 1.01899i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 50.0000 | 0.393701 | 0.196850 | − | 0.980434i | \(-0.436929\pi\) | ||||
0.196850 | + | 0.980434i | \(0.436929\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 48.9898i | − | 0.379766i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 73.4847i | 0.560952i | 0.959861 | + | 0.280476i | \(0.0904923\pi\) | ||||
−0.959861 | + | 0.280476i | \(0.909508\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 120.000 | − | 122.474i | 0.902256 | − | 0.920861i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −144.000 | −1.06667 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 210.000 | 1.53285 | 0.766423 | − | 0.642336i | \(-0.222035\pi\) | ||||
0.766423 | + | 0.642336i | \(0.222035\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 122.474i | 0.881111i | 0.897725 | + | 0.440556i | \(0.145219\pi\) | ||||
−0.897725 | + | 0.440556i | \(0.854781\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 96.0000 | 0.680851 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 29.3939i | 0.205552i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 29.3939i | − | 0.202716i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 240.000 | − | 4.89898i | 1.63265 | − | 0.0333264i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −198.000 | −1.32886 | −0.664430 | − | 0.747351i | \(-0.731325\pi\) | ||||
−0.664430 | + | 0.747351i | \(0.731325\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 34.0000 | 0.225166 | 0.112583 | − | 0.993642i | \(-0.464088\pi\) | ||||
0.112583 | + | 0.993642i | \(0.464088\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 293.939i | − | 1.92117i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 132.272i | 0.842500i | 0.906945 | + | 0.421250i | \(0.138408\pi\) | ||||
−0.906945 | + | 0.421250i | \(0.861592\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 440.908i | − | 2.77301i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −150.000 | − | 146.969i | −0.931677 | − | 0.912853i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 170.000 | 1.04294 | 0.521472 | − | 0.853268i | \(-0.325383\pi\) | ||||
0.521472 | + | 0.853268i | \(0.325383\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −144.000 | −0.872727 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 166.565i | 0.997397i | 0.866776 | + | 0.498699i | \(0.166189\pi\) | ||||
−0.866776 | + | 0.498699i | \(0.833811\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 145.000 | 0.857988 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 367.423i | 2.14868i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 191.060i | 1.10439i | 0.833714 | + | 0.552197i | \(0.186210\pi\) | ||||
−0.833714 | + | 0.552197i | \(0.813790\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.00000 | + | 4.89898i | 0.0285714 | + | 0.0279942i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 120.000 | 0.677966 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 42.0000 | 0.234637 | 0.117318 | − | 0.993094i | \(-0.462570\pi\) | ||||
0.117318 | + | 0.993094i | \(0.462570\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 24.4949i | 0.135331i | 0.997708 | + | 0.0676655i | \(0.0215551\pi\) | ||||
−0.997708 | + | 0.0676655i | \(0.978445\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −120.000 | −0.655738 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 48.9898i | 0.264810i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 117.576i | − | 0.628746i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −144.000 | + | 146.969i | −0.761905 | + | 0.777616i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −246.000 | −1.28796 | −0.643979 | − | 0.765043i | \(-0.722718\pi\) | ||||
−0.643979 | + | 0.765043i | \(0.722718\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −230.000 | −1.19171 | −0.595855 | − | 0.803092i | \(-0.703187\pi\) | ||||
−0.595855 | + | 0.803092i | \(0.703187\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 117.576i | − | 0.602951i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −150.000 | −0.761421 | −0.380711 | − | 0.924694i | \(-0.624321\pi\) | ||||
−0.380711 | + | 0.924694i | \(0.624321\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 342.929i | − | 1.72326i | −0.507538 | − | 0.861630i | \(-0.669444\pi\) | ||
0.507538 | − | 0.861630i | \(-0.330556\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 342.929i | 1.70611i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −30.0000 | − | 29.3939i | −0.147783 | − | 0.144797i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 240.000 | 1.17073 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 450.000 | 2.17391 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 146.969i | 0.703203i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −326.000 | −1.54502 | −0.772512 | − | 0.635000i | \(-0.781000\pi\) | ||||
−0.772512 | + | 0.635000i | \(0.781000\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 205.757i | − | 0.965996i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 48.9898i | 0.227860i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 528.000 | 2.41096 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 96.0000 | 0.434389 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 117.576i | 0.527244i | 0.964626 | + | 0.263622i | \(0.0849172\pi\) | ||||
−0.964626 | + | 0.263622i | \(0.915083\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −15.0000 | −0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 396.817i | − | 1.74809i | −0.485841 | − | 0.874047i | \(-0.661487\pi\) | ||
0.485841 | − | 0.874047i | \(-0.338513\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 73.4847i | − | 0.320894i | −0.987044 | − | 0.160447i | \(-0.948706\pi\) | ||
0.987044 | − | 0.160447i | \(-0.0512935\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −144.000 | + | 146.969i | −0.623377 | + | 0.636231i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 210.000 | 0.901288 | 0.450644 | − | 0.892704i | \(-0.351194\pi\) | ||||
0.450644 | + | 0.892704i | \(0.351194\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −96.0000 | −0.408511 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 362.524i | − | 1.52964i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 114.000 | 0.476987 | 0.238494 | − | 0.971144i | \(-0.423346\pi\) | ||||
0.238494 | + | 0.971144i | \(0.423346\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 97.9796i | − | 0.406554i | −0.979121 | − | 0.203277i | \(-0.934841\pi\) | ||
0.979121 | − | 0.203277i | \(-0.0651592\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 220.454i | 0.907218i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −240.000 | + | 4.89898i | −0.979592 | + | 0.0199958i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −120.000 | −0.485830 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −312.000 | −1.25301 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 171.464i | − | 0.683125i | −0.939859 | − | 0.341562i | \(-0.889044\pi\) | ||
0.939859 | − | 0.341562i | \(-0.110956\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 180.000 | 0.711462 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 470.302i | 1.84432i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 235.151i | − | 0.914984i | −0.889214 | − | 0.457492i | \(-0.848748\pi\) | ||
0.889214 | − | 0.457492i | \(-0.151252\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 50.0000 | + | 48.9898i | 0.193050 | + | 0.189150i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 90.0000 | 0.344828 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 330.000 | 1.25475 | 0.627376 | − | 0.778716i | \(-0.284129\pi\) | ||||
0.627376 | + | 0.778716i | \(0.284129\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 440.908i | 1.66380i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −720.000 | −2.69663 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 465.403i | 1.73012i | 0.501666 | + | 0.865061i | \(0.332721\pi\) | ||||
−0.501666 | + | 0.865061i | \(0.667279\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 97.9796i | 0.361548i | 0.983525 | + | 0.180774i | \(0.0578603\pi\) | ||||
−0.983525 | + | 0.180774i | \(0.942140\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −120.000 | − | 117.576i | −0.439560 | − | 0.430680i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.00000 | −0.0218182 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 170.000 | 0.613718 | 0.306859 | − | 0.951755i | \(-0.400722\pi\) | ||||
0.306859 | + | 0.951755i | \(0.400722\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 114.000 | 0.405694 | 0.202847 | − | 0.979210i | \(-0.434981\pi\) | ||||
0.202847 | + | 0.979210i | \(0.434981\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 338.030i | 1.19445i | 0.802073 | + | 0.597225i | \(0.203730\pi\) | ||||
−0.802073 | + | 0.597225i | \(0.796270\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − | 587.878i | − | 2.06273i | ||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 240.000 | − | 244.949i | 0.836237 | − | 0.853481i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −95.0000 | −0.328720 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −384.000 | −1.31959 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 151.868i | − | 0.518322i | −0.965834 | − | 0.259161i | \(-0.916554\pi\) | ||
0.965834 | − | 0.259161i | \(-0.0834460\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −120.000 | −0.406780 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 176.363i | − | 0.593816i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 146.969i | 0.491536i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 50.0000 | + | 48.9898i | 0.166113 | + | 0.162757i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −360.000 | −1.18812 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 120.000 | 0.393443 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 102.879i | − | 0.335109i | −0.985863 | − | 0.167555i | \(-0.946413\pi\) | ||
0.985863 | − | 0.167555i | \(-0.0535871\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 816.000 | 2.64078 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 244.949i | − | 0.787617i | −0.919192 | − | 0.393809i | \(-0.871157\pi\) | ||
0.919192 | − | 0.393809i | \(-0.128843\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 225.353i | − | 0.719978i | −0.932957 | − | 0.359989i | \(-0.882780\pi\) | ||
0.932957 | − | 0.359989i | \(-0.117220\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 360.000 | − | 367.423i | 1.14286 | − | 1.16642i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 90.0000 | 0.283912 | 0.141956 | − | 0.989873i | \(-0.454661\pi\) | ||||
0.141956 | + | 0.989873i | \(0.454661\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 36.0000 | 0.112853 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 734.847i | 2.28924i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 480.000 | 1.48607 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 4.89898i | − | 0.0150738i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 421.312i | 1.28842i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −96.0000 | + | 97.9796i | −0.291793 | + | 0.297810i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −38.0000 | −0.114804 | −0.0574018 | − | 0.998351i | \(-0.518282\pi\) | ||||
−0.0574018 | + | 0.998351i | \(0.518282\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −150.000 | −0.450450 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 342.929i | − | 1.02367i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −230.000 | −0.682493 | −0.341246 | − | 0.939974i | \(-0.610849\pi\) | ||||
−0.341246 | + | 0.939974i | \(0.610849\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 440.908i | − | 1.30061i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −235.000 | + | 249.848i | −0.685131 | + | 0.728420i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −720.000 | −2.08696 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −150.000 | −0.432277 | −0.216138 | − | 0.976363i | \(-0.569346\pi\) | ||||
−0.216138 | + | 0.976363i | \(0.569346\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 612.372i | − | 1.75465i | −0.479898 | − | 0.877324i | \(-0.659326\pi\) | ||
0.479898 | − | 0.877324i | \(-0.340674\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 144.000 | 0.410256 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 274.343i | − | 0.777175i | −0.921412 | − | 0.388588i | \(-0.872963\pi\) | ||
0.921412 | − | 0.388588i | \(-0.127037\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 205.757i | 0.579598i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 480.000 | + | 470.302i | 1.34454 | + | 1.31737i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −318.000 | −0.885794 | −0.442897 | − | 0.896573i | \(-0.646049\pi\) | ||||
−0.442897 | + | 0.896573i | \(0.646049\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −239.000 | −0.662050 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 416.413i | 1.14714i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −528.000 | −1.44658 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 215.555i | 0.587344i | 0.955906 | + | 0.293672i | \(0.0948773\pi\) | ||||
−0.955906 | + | 0.293672i | \(0.905123\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 734.847i | 1.99146i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 450.000 | + | 440.908i | 1.21294 | + | 1.18843i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −310.000 | −0.831099 | −0.415550 | − | 0.909571i | \(-0.636411\pi\) | ||||
−0.415550 | + | 0.909571i | \(0.636411\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 624.000 | 1.66400 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 29.3939i | 0.0779678i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 442.000 | 1.16623 | 0.583113 | − | 0.812391i | \(-0.301834\pi\) | ||||
0.583113 | + | 0.812391i | \(0.301834\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 244.949i | − | 0.642911i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 431.110i | − | 1.12561i | −0.826588 | − | 0.562807i | \(-0.809721\pi\) | ||
0.826588 | − | 0.562807i | \(-0.190279\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 144.000 | − | 146.969i | 0.374026 | − | 0.381739i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −150.000 | −0.387597 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −726.000 | −1.86632 | −0.933162 | − | 0.359456i | \(-0.882962\pi\) | ||||
−0.933162 | + | 0.359456i | \(0.882962\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 587.878i | − | 1.50352i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 360.000 | 0.916031 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 362.524i | 0.917783i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 191.060i | 0.481260i | 0.970617 | + | 0.240630i | \(0.0773540\pi\) | ||||
−0.970617 | + | 0.240630i | \(0.922646\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −600.000 | − | 587.878i | −1.50376 | − | 1.47338i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 474.000 | 1.18204 | 0.591022 | − | 0.806655i | \(-0.298724\pi\) | ||||
0.591022 | + | 0.806655i | \(0.298724\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 44.0908i | 0.108866i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −60.0000 | −0.147420 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 48.9898i | 0.119779i | 0.998205 | + | 0.0598897i | \(0.0190749\pi\) | ||||
−0.998205 | + | 0.0598897i | \(0.980925\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 1028.79i | − | 2.50313i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −120.000 | + | 122.474i | −0.290557 | + | 0.296548i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 312.000 | 0.751807 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 600.000 | 1.43885 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 269.444i | 0.643064i | 0.946899 | + | 0.321532i | \(0.104198\pi\) | ||||
−0.946899 | + | 0.321532i | \(0.895802\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 314.000 | 0.745843 | 0.372922 | − | 0.927863i | \(-0.378356\pi\) | ||||
0.372922 | + | 0.927863i | \(0.378356\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 293.939i | − | 0.694891i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 19.5959i | 0.0461080i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 120.000 | − | 122.474i | 0.281030 | − | 0.286825i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 144.000 | 0.335664 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −366.000 | −0.849188 | −0.424594 | − | 0.905384i | \(-0.639583\pi\) | ||||
−0.424594 | + | 0.905384i | \(0.639583\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 58.7878i | 0.135768i | 0.997693 | + | 0.0678842i | \(0.0216249\pi\) | ||||
−0.997693 | + | 0.0678842i | \(0.978375\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −144.000 | −0.331034 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 734.847i | 1.68157i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 146.969i | 0.334782i | 0.985891 | + | 0.167391i | \(0.0535343\pi\) | ||||
−0.985891 | + | 0.167391i | \(0.946466\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −15.0000 | − | 734.847i | −0.0340136 | − | 1.66632i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 90.0000 | 0.203160 | 0.101580 | − | 0.994827i | \(-0.467610\pi\) | ||||
0.101580 | + | 0.994827i | \(0.467610\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 720.000 | 1.61798 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 969.998i | 2.17002i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −606.000 | −1.34967 | −0.674833 | − | 0.737971i | \(-0.735784\pi\) | ||||
−0.674833 | + | 0.737971i | \(0.735784\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 293.939i | 0.651749i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 166.565i | − | 0.367694i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 120.000 | + | 117.576i | 0.263736 | + | 0.258408i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −230.000 | −0.503282 | −0.251641 | − | 0.967821i | \(-0.580970\pi\) | ||||
−0.251641 | + | 0.967821i | \(0.580970\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −576.000 | −1.25490 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 122.474i | − | 0.265671i | −0.991138 | − | 0.132836i | \(-0.957592\pi\) | ||
0.991138 | − | 0.132836i | \(-0.0424083\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −310.000 | −0.669546 | −0.334773 | − | 0.942299i | \(-0.608660\pi\) | ||||
−0.334773 | + | 0.942299i | \(0.608660\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 102.879i | − | 0.220297i | −0.993915 | − | 0.110148i | \(-0.964867\pi\) | ||
0.993915 | − | 0.110148i | \(-0.0351326\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −350.000 | − | 342.929i | −0.746269 | − | 0.731191i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 648.000 | 1.37580 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −60.0000 | −0.126850 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 24.4949i | − | 0.0515682i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1350.00 | −2.83019 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 391.918i | 0.818201i | 0.912489 | + | 0.409101i | \(0.134157\pi\) | ||||
−0.912489 | + | 0.409101i | \(0.865843\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 48.9898i | − | 0.101850i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −720.000 | + | 734.847i | −1.49068 | + | 1.52142i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 384.000 | 0.791753 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 130.000 | 0.266940 | 0.133470 | − | 0.991053i | \(-0.457388\pi\) | ||||
0.133470 | + | 0.991053i | \(0.457388\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 832.827i | − | 1.70312i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 234.000 | 0.476578 | 0.238289 | − | 0.971194i | \(-0.423413\pi\) | ||||
0.238289 | + | 0.971194i | \(0.423413\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 117.576i | − | 0.238490i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 440.908i | 0.890724i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 210.000 | + | 205.757i | 0.422535 | + | 0.413998i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 394.000 | 0.789579 | 0.394790 | − | 0.918772i | \(-0.370817\pi\) | ||||
0.394790 | + | 0.918772i | \(0.370817\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 816.000 | 1.62874 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 68.5857i | 0.136353i | 0.997673 | + | 0.0681767i | \(0.0217181\pi\) | ||||
−0.997673 | + | 0.0681767i | \(0.978282\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 360.000 | 0.712871 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 710.352i | − | 1.40109i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 759.342i | 1.49183i | 0.666041 | + | 0.745915i | \(0.267988\pi\) | ||||
−0.666041 | + | 0.745915i | \(0.732012\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −528.000 | + | 538.888i | −1.03327 | + | 1.05457i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 720.000 | 1.40351 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −816.000 | −1.58447 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 117.576i | − | 0.227419i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 936.000 | 1.80347 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 636.867i | − | 1.22239i | −0.791478 | − | 0.611197i | \(-0.790688\pi\) | ||
0.791478 | − | 0.611197i | \(-0.209312\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 504.595i | − | 0.964809i | −0.875949 | − | 0.482404i | \(-0.839764\pi\) | ||
0.875949 | − | 0.482404i | \(-0.160236\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 24.0000 | − | 24.4949i | 0.0457143 | − | 0.0466569i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 371.000 | 0.701323 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 367.423i | − | 0.691946i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −240.000 | −0.450281 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 734.847i | − | 1.37355i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 205.757i | − | 0.383160i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.00000 | − | 293.939i | −0.0111317 | − | 0.545341i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −406.000 | −0.750462 | −0.375231 | − | 0.926931i | \(-0.622437\pi\) | ||||
−0.375231 | + | 0.926931i | \(0.622437\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 120.000 | 0.220994 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 421.312i | − | 0.773050i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −790.000 | −1.44424 | −0.722121 | − | 0.691767i | \(-0.756832\pi\) | ||||
−0.722121 | + | 0.691767i | \(0.756832\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 367.423i | 0.669259i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 146.969i | 0.266732i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 370.000 | + | 362.524i | 0.669078 | + | 0.655560i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 240.000 | 0.432432 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −150.000 | −0.269300 | −0.134650 | − | 0.990893i | \(-0.542991\pi\) | ||||
−0.134650 | + | 0.990893i | \(0.542991\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 48.9898i | − | 0.0876383i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −576.000 | −1.02674 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 455.605i | − | 0.809245i | −0.914484 | − | 0.404623i | \(-0.867403\pi\) | ||
0.914484 | − | 0.404623i | \(-0.132597\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 440.908i | 0.780368i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 45.0000 | + | 44.0908i | 0.0793651 | + | 0.0777616i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 762.000 | 1.33919 | 0.669596 | − | 0.742726i | \(-0.266467\pi\) | ||||
0.669596 | + | 0.742726i | \(0.266467\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 842.000 | 1.47461 | 0.737303 | − | 0.675562i | \(-0.236099\pi\) | ||||
0.737303 | + | 0.675562i | \(0.236099\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1205.15i | 2.10323i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −30.0000 | −0.0521739 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 313.535i | 0.543388i | 0.962384 | + | 0.271694i | \(0.0875838\pi\) | ||||
−0.962384 | + | 0.271694i | \(0.912416\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1126.77i | 1.94605i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 312.000 | − | 318.434i | 0.537005 | − | 0.548079i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −540.000 | −0.926244 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −360.000 | −0.615385 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 279.242i | 0.475710i | 0.971301 | + | 0.237855i | \(0.0764443\pi\) | ||||
−0.971301 | + | 0.237855i | \(0.923556\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 734.847i | 1.24340i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 960.200i | − | 1.61922i | −0.586965 | − | 0.809612i | \(-0.699677\pi\) | ||
0.586965 | − | 0.809612i | \(-0.300323\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −480.000 | − | 470.302i | −0.806723 | − | 0.790424i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1680.00 | −2.81407 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −726.000 | −1.21202 | −0.606010 | − | 0.795457i | \(-0.707231\pi\) | ||||
−0.606010 | + | 0.795457i | \(0.707231\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1028.79i | 1.71179i | 0.517150 | + | 0.855895i | \(0.326993\pi\) | ||||
−0.517150 | + | 0.855895i | \(0.673007\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1050.00 | 1.74129 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 416.413i | − | 0.688286i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 666.261i | − | 1.09763i | −0.835944 | − | 0.548815i | \(-0.815079\pi\) | ||
0.835944 | − | 0.548815i | \(-0.184921\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −144.000 | + | 146.969i | −0.236453 | + | 0.241329i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 96.0000 | 0.157119 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1030.00 | −1.68026 | −0.840131 | − | 0.542384i | \(-0.817522\pi\) | ||||
−0.840131 | + | 0.542384i | \(0.817522\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 1175.76i | − | 1.91180i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 90.0000 | 0.145867 | 0.0729335 | − | 0.997337i | \(-0.476764\pi\) | ||||
0.0729335 | + | 0.997337i | \(0.476764\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 906.311i | 1.46415i | 0.681222 | + | 0.732077i | \(0.261449\pi\) | ||||
−0.681222 | + | 0.732077i | \(0.738551\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 881.816i | − | 1.41999i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 720.000 | − | 734.847i | 1.15570 | − | 1.17953i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −599.000 | −0.958400 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 720.000 | 1.14833 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 195.959i | 0.311541i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1034.00 | 1.63867 | 0.819334 | − | 0.573316i | \(-0.194343\pi\) | ||||
0.819334 | + | 0.573316i | \(0.194343\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1597.07i | 2.52301i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 244.949i | 0.385746i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 240.000 | − | 4.89898i | 0.376766 | − | 0.00769071i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −630.000 | −0.985915 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 282.000 | 0.439938 | 0.219969 | − | 0.975507i | \(-0.429404\pi\) | ||||
0.219969 | + | 0.975507i | \(0.429404\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 191.060i | 0.297139i | 0.988902 | + | 0.148569i | \(0.0474668\pi\) | ||||
−0.988902 | + | 0.148569i | \(0.952533\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 240.000 | 0.372093 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 205.757i | 0.318017i | 0.987277 | + | 0.159009i | \(0.0508298\pi\) | ||||
−0.987277 | + | 0.159009i | \(0.949170\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 146.969i | − | 0.226455i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1290.00 | 1.97550 | 0.987749 | − | 0.156052i | \(-0.0498767\pi\) | ||||
0.987749 | + | 0.156052i | \(0.0498767\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −360.000 | −0.549618 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 1616.66i | − | 2.46067i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 474.000 | 0.719272 | 0.359636 | − | 0.933093i | \(-0.382901\pi\) | ||||
0.359636 | + | 0.933093i | \(0.382901\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 1151.26i | − | 1.74169i | −0.491554 | − | 0.870847i | \(-0.663571\pi\) | ||
0.491554 | − | 0.870847i | \(-0.336429\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 470.302i | − | 0.709354i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 600.000 | + | 587.878i | 0.902256 | + | 0.884026i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 180.000 | 0.269865 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 576.000 | 0.860987 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 146.969i | 0.219030i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −350.000 | −0.520059 | −0.260030 | − | 0.965601i | \(-0.583732\pi\) | ||||
−0.260030 | + | 0.965601i | \(0.583732\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 29.3939i | 0.0435465i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 44.0908i | 0.0651268i | 0.999470 | + | 0.0325634i | \(0.0103671\pi\) | ||||
−0.999470 | + | 0.0325634i | \(0.989633\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 384.000 | − | 391.918i | 0.565538 | − | 0.577199i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1944.00 | −2.85463 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −630.000 | −0.922401 | −0.461201 | − | 0.887296i | \(-0.652581\pi\) | ||||
−0.461201 | + | 0.887296i | \(0.652581\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1028.79i | 1.50188i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −360.000 | −0.524017 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 440.908i | − | 0.639925i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 367.423i | 0.531727i | 0.964011 | + | 0.265864i | \(0.0856571\pi\) | ||||
−0.964011 | + | 0.265864i | \(0.914343\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 450.000 | + | 440.908i | 0.649351 | + | 0.636231i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −600.000 | −0.863309 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 960.000 | 1.37733 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 1028.79i | − | 1.47180i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 234.000 | 0.333809 | 0.166904 | − | 0.985973i | \(-0.446623\pi\) | ||||
0.166904 | + | 0.985973i | \(0.446623\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 244.949i | − | 0.348434i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 470.302i | 0.667095i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 360.000 | − | 367.423i | 0.509194 | − | 0.519694i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −326.000 | −0.459803 | −0.229901 | − | 0.973214i | \(-0.573840\pi\) | ||||
−0.229901 | + | 0.973214i | \(0.573840\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1110.00 | −1.56118 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −144.000 | −0.201399 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 558.484i | − | 0.778917i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 685.857i | 0.953904i | 0.878929 | + | 0.476952i | \(0.158258\pi\) | ||||
−0.878929 | + | 0.476952i | \(0.841742\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −816.000 | + | 832.827i | −1.13176 | + | 1.15510i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −480.000 | −0.663900 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.00000 | −0.00827586 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1087.57i | 1.49597i | 0.663713 | + | 0.747987i | \(0.268980\pi\) | ||||
−0.663713 | + | 0.747987i | \(0.731020\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1161.00 | 1.59259 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 195.959i | 0.268070i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 484.999i | 0.661663i | 0.943690 | + | 0.330831i | \(0.107329\pi\) | ||||
−0.943690 | + | 0.330831i | \(0.892671\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 24.0000 | + | 1175.76i | 0.0326531 | + | 1.59967i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 420.000 | 0.569878 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 74.0000 | 0.100135 | 0.0500677 | − | 0.998746i | \(-0.484056\pi\) | ||||
0.0500677 | + | 0.998746i | \(0.484056\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 587.878i | 0.793357i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −510.000 | −0.686406 | −0.343203 | − | 0.939261i | \(-0.611512\pi\) | ||||
−0.343203 | + | 0.939261i | \(0.611512\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 969.998i | − | 1.30201i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 955.301i | 1.27885i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −750.000 | − | 734.847i | −1.00134 | − | 0.981104i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 754.000 | 1.00399 | 0.501997 | − | 0.864869i | \(-0.332599\pi\) | ||||
0.501997 | + | 0.864869i | \(0.332599\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −840.000 | −1.11554 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 166.565i | 0.220616i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 730.000 | 0.964333 | 0.482166 | − | 0.876080i | \(-0.339850\pi\) | ||||
0.482166 | + | 0.876080i | \(0.339850\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 881.816i | − | 1.16181i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 244.949i | 0.321878i | 0.986964 | + | 0.160939i | \(0.0514522\pi\) | ||||
−0.986964 | + | 0.160939i | \(0.948548\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −430.000 | − | 421.312i | −0.563565 | − | 0.552179i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1440.00 | 1.88235 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 120.000 | 0.156454 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 979.796i | − | 1.27412i | −0.770815 | − | 0.637058i | \(-0.780151\pi\) | ||
0.770815 | − | 0.637058i | \(-0.219849\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1152.00 | −1.49416 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 935.705i | − | 1.21049i | −0.796041 | − | 0.605243i | \(-0.793076\pi\) | ||
0.796041 | − | 0.605243i | \(-0.206924\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 240.000 | − | 244.949i | 0.308880 | − | 0.315250i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1200.00 | −1.54044 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −252.000 | −0.322663 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 176.363i | − | 0.225240i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −648.000 | −0.825478 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 289.040i | 0.367268i | 0.982995 | + | 0.183634i | \(0.0587861\pi\) | ||||
−0.982995 | + | 0.183634i | \(0.941214\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 1616.66i | − | 2.04900i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 450.000 | + | 440.908i | 0.568900 | + | 0.557406i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −120.000 | −0.151324 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2160.00 | 2.71698 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 102.879i | − | 0.129082i | −0.997915 | − | 0.0645411i | \(-0.979442\pi\) | ||
0.997915 | − | 0.0645411i | \(-0.0205584\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −384.000 | −0.480601 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2204.54i | 2.75224i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 646.665i | − | 0.805312i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 720.000 | − | 734.847i | 0.894410 | − | 0.912853i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2280.00 | 2.82528 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −486.000 | −0.600742 | −0.300371 | − | 0.953823i | \(-0.597110\pi\) | ||||
−0.300371 | + | 0.953823i | \(0.597110\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 661.362i | − | 0.815490i | −0.913096 | − | 0.407745i | \(-0.866315\pi\) | ||
0.913096 | − | 0.407745i | \(-0.133685\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 480.000 | 0.590406 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 832.827i | 1.02187i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 244.949i | − | 0.299815i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −360.000 | + | 367.423i | −0.439560 | + | 0.448624i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 234.000 | 0.285018 | 0.142509 | − | 0.989793i | \(-0.454483\pi\) | ||||
0.142509 | + | 0.989793i | \(0.454483\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1130.00 | 1.37303 | 0.686513 | − | 0.727118i | \(-0.259141\pi\) | ||||
0.686513 | + | 0.727118i | \(0.259141\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 29.3939i | 0.0356289i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 90.0000 | 0.108827 | 0.0544135 | − | 0.998518i | \(-0.482671\pi\) | ||||
0.0544135 | + | 0.998518i | \(0.482671\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 759.342i | 0.915973i | 0.888959 | + | 0.457987i | \(0.151429\pi\) | ||||
−0.888959 | + | 0.457987i | \(0.848571\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 832.827i | − | 1.00220i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −960.000 | + | 19.5959i | −1.15246 | + | 0.0235245i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −816.000 | −0.977246 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1224.74i | 1.45977i | 0.683571 | + | 0.729884i | \(0.260426\pi\) | ||||
−0.683571 | + | 0.729884i | \(0.739574\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −805.000 | −0.957194 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 558.484i | − | 0.662495i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 710.352i | 0.840653i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −425.000 | − | 416.413i | −0.501771 | − | 0.491633i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1656.00 | 1.95053 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −300.000 | −0.352526 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 1386.41i | − | 1.62534i | −0.582727 | − | 0.812668i | \(-0.698014\pi\) | ||
0.582727 | − | 0.812668i | \(-0.301986\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1800.00 | −2.10526 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 989.594i | 1.15472i | 0.816490 | + | 0.577359i | \(0.195917\pi\) | ||||
−0.816490 | + | 0.577359i | \(0.804083\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 1151.26i | − | 1.34023i | −0.742256 | − | 0.670117i | \(-0.766244\pi\) | ||
0.742256 | − | 0.670117i | \(-0.233756\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1200.00 | − | 1175.76i | −1.39373 | − | 1.36557i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 330.000 | 0.382387 | 0.191194 | − | 0.981552i | \(-0.438764\pi\) | ||||
0.191194 | + | 0.981552i | \(0.438764\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −936.000 | −1.08208 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 465.403i | 0.536797i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −444.000 | −0.510932 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 342.929i | 0.393718i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1175.76i | 1.34680i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −624.000 | + | 636.867i | −0.713143 | + | 0.727848i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 410.000 | 0.467503 | 0.233751 | − | 0.972296i | \(-0.424900\pi\) | ||||
0.233751 | + | 0.972296i | \(0.424900\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −744.000 | −0.846416 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 881.816i | 1.00093i | 0.865758 | + | 0.500463i | \(0.166837\pi\) | ||||
−0.865758 | + | 0.500463i | \(0.833163\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 730.000 | 0.826727 | 0.413364 | − | 0.910566i | \(-0.364354\pi\) | ||||
0.413364 | + | 0.910566i | \(0.364354\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 587.878i | 0.664268i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 1067.98i | − | 1.20403i | −0.798484 | − | 0.602017i | \(-0.794364\pi\) | ||
0.798484 | − | 0.602017i | \(-0.205636\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 250.000 | + | 244.949i | 0.281215 | + | 0.275533i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −54.0000 | −0.0606061 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 480.000 | 0.537514 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 205.757i | 0.229896i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 720.000 | 0.802676 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1763.63i | 1.95742i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 240.000 | − | 244.949i | 0.265781 | − | 0.271261i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −120.000 | −0.132597 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 250.000 | 0.275634 | 0.137817 | − | 0.990458i | \(-0.455991\pi\) | ||||
0.137817 | + | 0.990458i | \(0.455991\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1102.27i | 1.21262i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −78.0000 | −0.0856202 | −0.0428101 | − | 0.999083i | \(-0.513631\pi\) | ||||
−0.0428101 | + | 0.999083i | \(0.513631\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 382.120i | 0.418533i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 587.878i | − | 0.642489i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −360.000 | + | 367.423i | −0.392585 | + | 0.400680i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1354.00 | 1.47334 | 0.736670 | − | 0.676252i | \(-0.236397\pi\) | ||||
0.736670 | + | 0.676252i | \(0.236397\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −504.000 | −0.547231 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 205.757i | − | 0.222922i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.0000 | 0.0108108 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 2498.48i | − | 2.69523i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 391.918i | − | 0.421871i | −0.977500 | − | 0.210936i | \(-0.932349\pi\) | ||
0.977500 | − | 0.210936i | \(-0.0676510\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1200.00 | − | 24.4949i | 1.28894 | − | 0.0263103i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1200.00 | −1.28617 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 576.000 | 0.616043 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 715.251i | − | 0.763342i | −0.924298 | − | 0.381671i | \(-0.875349\pi\) | ||
0.924298 | − | 0.381671i | \(-0.124651\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1104.00 | −1.17572 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 1298.23i | − | 1.37963i | −0.723987 | − | 0.689814i | \(-0.757692\pi\) | ||
0.723987 | − | 0.689814i | \(-0.242308\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1469.69i | 1.55853i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −720.000 | − | 705.453i | −0.761905 | − | 0.746511i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −390.000 | −0.411827 | −0.205913 | − | 0.978570i | \(-0.566017\pi\) | ||||
−0.205913 | + | 0.978570i | \(0.566017\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 528.000 | 0.556375 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 440.908i | − | 0.463626i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −270.000 | −0.283316 | −0.141658 | − | 0.989916i | \(-0.545243\pi\) | ||||
−0.141658 | + | 0.989916i | \(0.545243\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 1205.15i | − | 1.26194i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 176.363i | − | 0.184288i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1050.00 | + | 1028.79i | 1.09489 | + | 1.07277i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 961.000 | 1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2250.00 | 2.33645 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 1126.77i | − | 1.16763i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1150.00 | −1.18925 | −0.594623 | − | 0.804005i | \(-0.702698\pi\) | ||||
−0.594623 | + | 0.804005i | \(0.702698\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 2351.51i | − | 2.42674i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 906.311i | 0.933379i | 0.884421 | + | 0.466690i | \(0.154553\pi\) | ||||
−0.884421 | + | 0.466690i | \(0.845447\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −600.000 | + | 612.372i | −0.616650 | + | 0.629365i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −24.0000 | −0.0246154 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −30.0000 | −0.0307062 | −0.0153531 | − | 0.999882i | \(-0.504887\pi\) | ||||
−0.0153531 | + | 0.999882i | \(0.504887\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 881.816i | 0.900732i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1290.00 | 1.31498 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1244.34i | 1.26586i | 0.774209 | + | 0.632930i | \(0.218148\pi\) | ||||
−0.774209 | + | 0.632930i | \(0.781852\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 734.847i | − | 0.746037i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 480.000 | + | 470.302i | 0.486322 | + | 0.476496i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −300.000 | −0.303337 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1718.00 | −1.73360 | −0.866801 | − | 0.498654i | \(-0.833828\pi\) | ||||
−0.866801 | + | 0.498654i | \(0.833828\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 186.161i | 0.187474i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1680.00 | 1.68844 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1219.85i | 1.22352i | 0.791045 | + | 0.611758i | \(0.209537\pi\) | ||||
−0.791045 | + | 0.611758i | \(0.790463\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 293.939i | 0.294233i |
(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 | 28.3.b.a.13.1 | ✓ | 2 | |
3.2 | odd | 2 | 252.3.d.c.181.1 | 2 | |||
4.3 | odd | 2 | 112.3.c.b.97.2 | 2 | |||
5.2 | odd | 4 | 700.3.h.a.349.2 | 4 | |||
5.3 | odd | 4 | 700.3.h.a.349.3 | 4 | |||
5.4 | even | 2 | 700.3.d.a.601.2 | 2 | |||
7.2 | even | 3 | 196.3.h.b.129.2 | 4 | |||
7.3 | odd | 6 | 196.3.h.b.117.2 | 4 | |||
7.4 | even | 3 | 196.3.h.b.117.1 | 4 | |||
7.5 | odd | 6 | 196.3.h.b.129.1 | 4 | |||
7.6 | odd | 2 | inner | 28.3.b.a.13.2 | yes | 2 | |
8.3 | odd | 2 | 448.3.c.c.321.1 | 2 | |||
8.5 | even | 2 | 448.3.c.d.321.2 | 2 | |||
12.11 | even | 2 | 1008.3.f.c.433.1 | 2 | |||
21.2 | odd | 6 | 1764.3.z.i.325.1 | 4 | |||
21.5 | even | 6 | 1764.3.z.i.325.2 | 4 | |||
21.11 | odd | 6 | 1764.3.z.i.901.2 | 4 | |||
21.17 | even | 6 | 1764.3.z.i.901.1 | 4 | |||
21.20 | even | 2 | 252.3.d.c.181.2 | 2 | |||
28.3 | even | 6 | 784.3.s.d.705.1 | 4 | |||
28.11 | odd | 6 | 784.3.s.d.705.2 | 4 | |||
28.19 | even | 6 | 784.3.s.d.129.2 | 4 | |||
28.23 | odd | 6 | 784.3.s.d.129.1 | 4 | |||
28.27 | even | 2 | 112.3.c.b.97.1 | 2 | |||
35.13 | even | 4 | 700.3.h.a.349.1 | 4 | |||
35.27 | even | 4 | 700.3.h.a.349.4 | 4 | |||
35.34 | odd | 2 | 700.3.d.a.601.1 | 2 | |||
56.13 | odd | 2 | 448.3.c.d.321.1 | 2 | |||
56.27 | even | 2 | 448.3.c.c.321.2 | 2 | |||
84.83 | odd | 2 | 1008.3.f.c.433.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
28.3.b.a.13.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
28.3.b.a.13.2 | yes | 2 | 7.6 | odd | 2 | inner | |
112.3.c.b.97.1 | 2 | 28.27 | even | 2 | |||
112.3.c.b.97.2 | 2 | 4.3 | odd | 2 | |||
196.3.h.b.117.1 | 4 | 7.4 | even | 3 | |||
196.3.h.b.117.2 | 4 | 7.3 | odd | 6 | |||
196.3.h.b.129.1 | 4 | 7.5 | odd | 6 | |||
196.3.h.b.129.2 | 4 | 7.2 | even | 3 | |||
252.3.d.c.181.1 | 2 | 3.2 | odd | 2 | |||
252.3.d.c.181.2 | 2 | 21.20 | even | 2 | |||
448.3.c.c.321.1 | 2 | 8.3 | odd | 2 | |||
448.3.c.c.321.2 | 2 | 56.27 | even | 2 | |||
448.3.c.d.321.1 | 2 | 56.13 | odd | 2 | |||
448.3.c.d.321.2 | 2 | 8.5 | even | 2 | |||
700.3.d.a.601.1 | 2 | 35.34 | odd | 2 | |||
700.3.d.a.601.2 | 2 | 5.4 | even | 2 | |||
700.3.h.a.349.1 | 4 | 35.13 | even | 4 | |||
700.3.h.a.349.2 | 4 | 5.2 | odd | 4 | |||
700.3.h.a.349.3 | 4 | 5.3 | odd | 4 | |||
700.3.h.a.349.4 | 4 | 35.27 | even | 4 | |||
784.3.s.d.129.1 | 4 | 28.23 | odd | 6 | |||
784.3.s.d.129.2 | 4 | 28.19 | even | 6 | |||
784.3.s.d.705.1 | 4 | 28.3 | even | 6 | |||
784.3.s.d.705.2 | 4 | 28.11 | odd | 6 | |||
1008.3.f.c.433.1 | 2 | 12.11 | even | 2 | |||
1008.3.f.c.433.2 | 2 | 84.83 | odd | 2 | |||
1764.3.z.i.325.1 | 4 | 21.2 | odd | 6 | |||
1764.3.z.i.325.2 | 4 | 21.5 | even | 6 | |||
1764.3.z.i.901.1 | 4 | 21.17 | even | 6 | |||
1764.3.z.i.901.2 | 4 | 21.11 | odd | 6 |