Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [448,2,Mod(225,448)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(448, base_ring=CyclotomicField(2))
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("448.225");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 448 = 2^{6} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 448.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: | \(3.57729801055\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 225.2 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 448.225 |
Dual form | 448.2.b.c.225.3 |
$q$-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 \(\left(\mathbb{Z}/448\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 0.732051i | − 0.422650i | −0.977416 | − | 0.211325i | \(-0.932222\pi\) | ||||
0.977416 | − | 0.211325i | \(-0.0677778\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 0.732051i | − 0.327383i | −0.986512 | − | 0.163692i | \(-0.947660\pi\) | ||||
0.986512 | − | 0.163692i | \(-0.0523402\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.46410 | 0.821367 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 1.46410i | − 0.441443i | −0.975337 | − | 0.220722i | \(-0.929159\pi\) | ||||
0.975337 | − | 0.220722i | \(-0.0708412\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 3.26795i | − 0.906366i | −0.891417 | − | 0.453183i | \(-0.850288\pi\) | ||||
0.891417 | − | 0.453183i | \(-0.149712\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.535898 | −0.138368 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.00000 | 0.485071 | 0.242536 | − | 0.970143i | \(-0.422021\pi\) | ||||
0.242536 | + | 0.970143i | \(0.422021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 4.73205i | − 1.08561i | −0.839860 | − | 0.542803i | \(-0.817363\pi\) | ||||
0.839860 | − | 0.542803i | \(-0.182637\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.732051i | 0.159747i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.46410 | −0.722315 | −0.361158 | − | 0.932505i | \(-0.617618\pi\) | ||||
−0.361158 | + | 0.932505i | \(0.617618\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.46410 | 0.892820 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 4.00000i | − 0.769800i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 5.46410i | − 1.01466i | −0.861752 | − | 0.507329i | \(-0.830633\pi\) | ||||
0.861752 | − | 0.507329i | \(-0.169367\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.00000 | −0.718421 | −0.359211 | − | 0.933257i | \(-0.616954\pi\) | ||||
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.07180 | −0.186576 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.732051i | 0.123739i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.46410i | 0.898293i | 0.893458 | + | 0.449146i | \(0.148272\pi\) | ||||
−0.893458 | + | 0.449146i | \(0.851728\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.39230 | −0.383075 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.00000 | −0.312348 | −0.156174 | − | 0.987730i | \(-0.549916\pi\) | ||||
−0.156174 | + | 0.987730i | \(0.549916\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 1.46410i | − 0.223273i | −0.993749 | − | 0.111637i | \(-0.964391\pi\) | ||||
0.993749 | − | 0.111637i | \(-0.0356093\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 1.80385i | − 0.268902i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.9282 | 1.59404 | 0.797021 | − | 0.603951i | \(-0.206408\pi\) | ||||
0.797021 | + | 0.603951i | \(0.206408\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 1.46410i | − 0.205015i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.0000i | 1.64833i | 0.566352 | + | 0.824163i | \(0.308354\pi\) | ||||
−0.566352 | + | 0.824163i | \(0.691646\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.07180 | −0.144521 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.46410 | −0.458831 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.66025i | 0.997280i | 0.866809 | + | 0.498640i | \(0.166167\pi\) | ||||
−0.866809 | + | 0.498640i | \(0.833833\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 13.1244i | − 1.68040i | −0.542275 | − | 0.840201i | \(-0.682437\pi\) | ||||
0.542275 | − | 0.840201i | \(-0.317563\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.46410 | −0.310448 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.39230 | −0.296729 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.00000i | 0.977356i | 0.872464 | + | 0.488678i | \(0.162521\pi\) | ||||
−0.872464 | + | 0.488678i | \(0.837479\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.53590i | 0.305286i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.9282 | 1.29694 | 0.648470 | − | 0.761241i | \(-0.275409\pi\) | ||||
0.648470 | + | 0.761241i | \(0.275409\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.928203 | −0.108638 | −0.0543190 | − | 0.998524i | \(-0.517299\pi\) | ||||
−0.0543190 | + | 0.998524i | \(0.517299\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 3.26795i | − 0.377350i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.46410i | 0.166850i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.92820 | −0.329449 | −0.164724 | − | 0.986340i | \(-0.552673\pi\) | ||||
−0.164724 | + | 0.986340i | \(0.552673\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.46410 | 0.496011 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.6603i | 1.27988i | 0.768425 | + | 0.639940i | \(0.221041\pi\) | ||||
−0.768425 | + | 0.639940i | \(0.778959\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 1.46410i | − 0.158804i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.00000 | −0.428845 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −15.8564 | −1.68078 | −0.840388 | − | 0.541985i | \(-0.817673\pi\) | ||||
−0.840388 | + | 0.541985i | \(0.817673\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.26795i | 0.342574i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.92820i | 0.303641i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.46410 | −0.355409 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.92820 | −0.500383 | −0.250192 | − | 0.968196i | \(-0.580494\pi\) | ||||
−0.250192 | + | 0.968196i | \(0.580494\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 3.60770i | − 0.362587i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.6603i | 1.55825i | 0.626866 | + | 0.779127i | \(0.284337\pi\) | ||||
−0.626866 | + | 0.779127i | \(0.715663\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.8564 | 1.75944 | 0.879722 | − | 0.475488i | \(-0.157729\pi\) | ||||
0.879722 | + | 0.475488i | \(0.157729\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.535898 | 0.0522983 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 18.9282i | 1.82986i | 0.403614 | + | 0.914929i | \(0.367754\pi\) | ||||
−0.403614 | + | 0.914929i | \(0.632246\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.39230i | 0.803837i | 0.915675 | + | 0.401919i | \(0.131656\pi\) | ||||
−0.915675 | + | 0.401919i | \(0.868344\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.00000 | 0.379663 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.4641 | −1.26660 | −0.633298 | − | 0.773908i | \(-0.718299\pi\) | ||||
−0.633298 | + | 0.773908i | \(0.718299\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.53590i | 0.236474i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 8.05256i | − 0.744459i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.00000 | −0.183340 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.85641 | 0.805128 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.46410i | 0.132014i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 6.92820i | − 0.619677i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.53590 | 0.402496 | 0.201248 | − | 0.979540i | \(-0.435500\pi\) | ||||
0.201248 | + | 0.979540i | \(0.435500\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.07180 | −0.0943664 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 7.26795i | − 0.635004i | −0.948258 | − | 0.317502i | \(-0.897156\pi\) | ||||
0.948258 | − | 0.317502i | \(-0.102844\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.73205i | 0.410321i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.92820 | −0.252020 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.85641 | −0.671218 | −0.335609 | − | 0.942001i | \(-0.608942\pi\) | ||||
−0.335609 | + | 0.942001i | \(0.608942\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 12.7321i | − 1.07992i | −0.841691 | − | 0.539959i | \(-0.818440\pi\) | ||||
0.841691 | − | 0.539959i | \(-0.181560\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 8.00000i | − 0.673722i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.78461 | −0.400109 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.00000 | −0.332182 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 0.732051i | − 0.0603785i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 14.9282i | 1.22297i | 0.791258 | + | 0.611483i | \(0.209427\pi\) | ||||
−0.791258 | + | 0.611483i | \(0.790573\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.3923 | −1.49674 | −0.748372 | − | 0.663279i | \(-0.769164\pi\) | ||||
−0.748372 | + | 0.663279i | \(0.769164\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.92820 | 0.398422 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.92820i | 0.235199i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.80385i | 0.143963i | 0.997406 | + | 0.0719814i | \(0.0229322\pi\) | ||||
−0.997406 | + | 0.0719814i | \(0.977068\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.78461 | 0.696665 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.46410 | 0.273009 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 6.53590i | − 0.511931i | −0.966686 | − | 0.255966i | \(-0.917607\pi\) | ||||
0.966686 | − | 0.255966i | \(-0.0823934\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.784610i | 0.0610818i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.9282 | 1.46471 | 0.732354 | − | 0.680924i | \(-0.238422\pi\) | ||||
0.732354 | + | 0.680924i | \(0.238422\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.32051 | 0.178501 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 11.6603i | − 0.891682i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 14.1962i | − 1.07931i | −0.841885 | − | 0.539657i | \(-0.818554\pi\) | ||||
0.841885 | − | 0.539657i | \(-0.181446\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.46410 | −0.337454 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.60770 | 0.421500 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.9282i | 0.816812i | 0.912800 | + | 0.408406i | \(0.133915\pi\) | ||||
−0.912800 | + | 0.408406i | \(0.866085\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 7.26795i | − 0.540222i | −0.962829 | − | 0.270111i | \(-0.912940\pi\) | ||||
0.962829 | − | 0.270111i | \(-0.0870605\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.60770 | −0.710221 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.00000 | 0.294086 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 2.92820i | − 0.214131i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.00000i | 0.290957i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.0000 | −1.15772 | −0.578860 | − | 0.815427i | \(-0.696502\pi\) | ||||
−0.578860 | + | 0.815427i | \(0.696502\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.4641 | 0.969167 | 0.484584 | − | 0.874745i | \(-0.338971\pi\) | ||||
0.484584 | + | 0.874745i | \(0.338971\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.75129i | 0.125412i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 1.85641i | − 0.132263i | −0.997811 | − | 0.0661317i | \(-0.978934\pi\) | ||||
0.997811 | − | 0.0661317i | \(-0.0210658\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.00000 | 0.283552 | 0.141776 | − | 0.989899i | \(-0.454719\pi\) | ||||
0.141776 | + | 0.989899i | \(0.454719\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.85641 | 0.413079 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.46410i | 0.383505i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.46410i | 0.102257i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −8.53590 | −0.593286 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.92820 | −0.479234 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 24.7846i | − 1.70624i | −0.521712 | − | 0.853121i | \(-0.674707\pi\) | ||||
0.521712 | − | 0.853121i | \(-0.325293\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 8.00000i | − 0.548151i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.07180 | −0.0730959 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.00000 | 0.271538 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.679492i | 0.0459158i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 6.53590i | − 0.439652i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.92820 | −0.463947 | −0.231973 | − | 0.972722i | \(-0.574518\pi\) | ||||
−0.231973 | + | 0.972722i | \(0.574518\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 11.0000 | 0.733333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 14.1962i | 0.942232i | 0.882071 | + | 0.471116i | \(0.156149\pi\) | ||||
−0.882071 | + | 0.471116i | \(0.843851\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 20.7321i | − 1.37001i | −0.728537 | − | 0.685006i | \(-0.759799\pi\) | ||||
0.728537 | − | 0.685006i | \(-0.240201\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.07180 | 0.0705191 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.00000 | 0.393073 | 0.196537 | − | 0.980497i | \(-0.437031\pi\) | ||||
0.196537 | + | 0.980497i | \(0.437031\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 8.00000i | − 0.521862i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.14359i | 0.139241i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.4641 | 1.25903 | 0.629514 | − | 0.776989i | \(-0.283254\pi\) | ||||
0.629514 | + | 0.776989i | \(0.283254\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.7846 | 1.46769 | 0.733843 | − | 0.679319i | \(-0.237725\pi\) | ||||
0.733843 | + | 0.679319i | \(0.237725\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 15.2679i | − 0.979439i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 0.732051i | − 0.0467690i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −15.4641 | −0.983957 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.53590 | 0.540941 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 26.1962i | − 1.65349i | −0.562579 | − | 0.826743i | \(-0.690191\pi\) | ||||
0.562579 | − | 0.826743i | \(-0.309809\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.07180i | 0.318861i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.07180 | −0.0671185 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.00000 | −0.374270 | −0.187135 | − | 0.982334i | \(-0.559920\pi\) | ||||
−0.187135 | + | 0.982334i | \(0.559920\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 5.46410i | − 0.339523i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 13.4641i | − 0.833407i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.92820 | 0.180561 | 0.0902804 | − | 0.995916i | \(-0.471224\pi\) | ||||
0.0902804 | + | 0.995916i | \(0.471224\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.78461 | 0.539634 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 11.6077i | 0.710379i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 18.5885i | 1.13336i | 0.823939 | + | 0.566679i | \(0.191772\pi\) | ||||
−0.823939 | + | 0.566679i | \(0.808228\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.07180 | −0.0651070 | −0.0325535 | − | 0.999470i | \(-0.510364\pi\) | ||||
−0.0325535 | + | 0.999470i | \(0.510364\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.39230 | 0.144789 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 6.53590i | − 0.394130i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 4.00000i | − 0.240337i | −0.992754 | − | 0.120168i | \(-0.961657\pi\) | ||||
0.992754 | − | 0.120168i | \(-0.0383434\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9.85641 | −0.590088 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.00000 | 0.119310 | 0.0596550 | − | 0.998219i | \(-0.481000\pi\) | ||||
0.0596550 | + | 0.998219i | \(0.481000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 14.5885i | − 0.867194i | −0.901107 | − | 0.433597i | \(-0.857244\pi\) | ||||
0.901107 | − | 0.433597i | \(-0.142756\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.53590i | 0.150214i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.00000 | 0.118056 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.60770i | 0.211487i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.80385i | 0.105382i | 0.998611 | + | 0.0526910i | \(0.0167798\pi\) | ||||
−0.998611 | + | 0.0526910i | \(0.983220\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.60770 | 0.326493 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.85641 | −0.339823 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 11.3205i | 0.654682i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.46410i | 0.0843894i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 11.4641 | 0.658595 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9.60770 | −0.550135 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.5885i | 1.28919i | 0.764524 | + | 0.644596i | \(0.222974\pi\) | ||||
−0.764524 | + | 0.644596i | \(0.777026\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 13.0718i | − 0.743629i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −21.8564 | −1.23936 | −0.619682 | − | 0.784853i | \(-0.712738\pi\) | ||||
−0.619682 | + | 0.784853i | \(0.712738\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.85641 | −0.444070 | −0.222035 | − | 0.975039i | \(-0.571270\pi\) | ||||
−0.222035 | + | 0.975039i | \(0.571270\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.80385i | 0.101635i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.7846i | 0.718055i | 0.933327 | + | 0.359028i | \(0.116892\pi\) | ||||
−0.933327 | + | 0.359028i | \(0.883108\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.00000 | −0.447914 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 13.8564 | 0.773389 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 9.46410i | − 0.526597i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 14.5885i | − 0.809222i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.14359 | 0.339741 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −10.9282 | −0.602491 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.39230i | 0.241423i | 0.992688 | + | 0.120711i | \(0.0385176\pi\) | ||||
−0.992688 | + | 0.120711i | \(0.961482\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 13.4641i | 0.737828i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.85641 | 0.319970 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.39230 | −0.239264 | −0.119632 | − | 0.992818i | \(-0.538171\pi\) | ||||
−0.119632 | + | 0.992818i | \(0.538171\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9.85641i | 0.535327i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.85641i | 0.317142i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.85641 | 0.0999456 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 0.679492i | − 0.0364770i | −0.999834 | − | 0.0182385i | \(-0.994194\pi\) | ||||
0.999834 | − | 0.0182385i | \(-0.00580582\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 24.0526i | 1.28750i | 0.765234 | + | 0.643752i | \(0.222623\pi\) | ||||
−0.765234 | + | 0.643752i | \(0.777377\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −13.0718 | −0.697721 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.9282 | −0.688099 | −0.344049 | − | 0.938952i | \(-0.611799\pi\) | ||||
−0.344049 | + | 0.938952i | \(0.611799\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 8.00000i | − 0.424596i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.46410i | 0.0774885i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 20.5359 | 1.08384 | 0.541922 | − | 0.840429i | \(-0.317697\pi\) | ||||
0.541922 | + | 0.840429i | \(0.317697\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.39230 | −0.178542 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 6.48334i | − 0.340287i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.679492i | 0.0355662i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 20.7846 | 1.08495 | 0.542474 | − | 0.840073i | \(-0.317488\pi\) | ||||
0.542474 | + | 0.840073i | \(0.317488\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.92820 | −0.256552 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 12.0000i | − 0.623009i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 17.0718i | − 0.883944i | −0.897029 | − | 0.441972i | \(-0.854279\pi\) | ||||
0.897029 | − | 0.441972i | \(-0.145721\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.07180 | −0.261906 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −17.8564 | −0.919652 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 34.2487i | 1.75924i | 0.475679 | + | 0.879619i | \(0.342202\pi\) | ||||
−0.475679 | + | 0.879619i | \(0.657798\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 3.32051i | − 0.170115i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8.78461 | −0.448873 | −0.224436 | − | 0.974489i | \(-0.572054\pi\) | ||||
−0.224436 | + | 0.974489i | \(0.572054\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.07180 | 0.0546238 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 3.60770i | − 0.183389i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 11.3205i | − 0.573973i | −0.957935 | − | 0.286986i | \(-0.907347\pi\) | ||||
0.957935 | − | 0.286986i | \(-0.0926534\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.92820 | −0.350374 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.32051 | −0.268384 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.14359i | 0.107856i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 29.1244i | 1.46171i | 0.682533 | + | 0.730855i | \(0.260878\pi\) | ||||
−0.682533 | + | 0.730855i | \(0.739122\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.46410 | 0.173422 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.53590 | 0.326387 | 0.163194 | − | 0.986594i | \(-0.447820\pi\) | ||||
0.163194 | + | 0.986594i | \(0.447820\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 13.0718i | 0.651153i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 3.26795i | − 0.162386i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.00000 | 0.396545 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.9282 | −0.837046 | −0.418523 | − | 0.908206i | \(-0.637452\pi\) | ||||
−0.418523 | + | 0.908206i | \(0.637452\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.75129i | 0.283690i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 7.66025i | − 0.376936i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.53590 | 0.419011 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9.32051 | −0.456427 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 34.1962i | 1.67059i | 0.549801 | + | 0.835296i | \(0.314704\pi\) | ||||
−0.549801 | + | 0.835296i | \(0.685296\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.85641i | 0.0904757i | 0.998976 | + | 0.0452379i | \(0.0144046\pi\) | ||||
−0.998976 | + | 0.0452379i | \(0.985595\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 26.9282 | 1.30929 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 8.92820 | 0.433081 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13.1244i | 0.635132i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.50258i | 0.169106i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 28.5359 | 1.37453 | 0.687263 | − | 0.726409i | \(-0.258812\pi\) | ||||
0.687263 | + | 0.726409i | \(0.258812\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.8564 | −0.569783 | −0.284891 | − | 0.958560i | \(-0.591957\pi\) | ||||
−0.284891 | + | 0.958560i | \(0.591957\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.92820i | 0.140397i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 16.3923i | 0.784150i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17.0718 | −0.814792 | −0.407396 | − | 0.913252i | \(-0.633563\pi\) | ||||
−0.407396 | + | 0.913252i | \(0.633563\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.46410 | 0.117338 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 24.0000i | 1.14027i | 0.821549 | + | 0.570137i | \(0.193110\pi\) | ||||
−0.821549 | + | 0.570137i | \(0.806890\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11.6077i | 0.550258i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.9282 | 0.516886 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.00000 | −0.0943858 | −0.0471929 | − | 0.998886i | \(-0.515028\pi\) | ||||
−0.0471929 | + | 0.998886i | \(0.515028\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.92820i | 0.137884i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 13.4641i | 0.632599i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.39230 | 0.112153 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −19.3205 | −0.903775 | −0.451888 | − | 0.892075i | \(-0.649249\pi\) | ||||
−0.451888 | + | 0.892075i | \(0.649249\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 8.00000i | − 0.373408i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 13.8038i | − 0.642909i | −0.946925 | − | 0.321455i | \(-0.895828\pi\) | ||||
0.946925 | − | 0.321455i | \(-0.104172\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.0000 | −0.743583 | −0.371792 | − | 0.928316i | \(-0.621256\pi\) | ||||
−0.371792 | + | 0.928316i | \(0.621256\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.14359 | 0.0994068 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 25.1244i | 1.16262i | 0.813683 | + | 0.581308i | \(0.197459\pi\) | ||||
−0.813683 | + | 0.581308i | \(0.802541\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 8.00000i | − 0.369406i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.32051 | 0.0608458 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.14359 | −0.0985625 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 21.1244i | − 0.969252i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 29.5692i | 1.35388i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −17.8564 | −0.815880 | −0.407940 | − | 0.913009i | \(-0.633753\pi\) | ||||
−0.407940 | + | 0.913009i | \(0.633753\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 17.8564 | 0.814182 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 2.53590i | − 0.115387i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.60770i | 0.163817i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 42.3923 | 1.92098 | 0.960489 | − | 0.278317i | \(-0.0897765\pi\) | ||||
0.960489 | + | 0.278317i | \(0.0897765\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.78461 | −0.216368 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 8.78461i | − 0.396444i | −0.980157 | − | 0.198222i | \(-0.936483\pi\) | ||||
0.980157 | − | 0.198222i | \(-0.0635167\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 10.9282i | − 0.492182i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.64102 | −0.118705 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −10.9282 | −0.490197 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 26.9282i | − 1.20547i | −0.797941 | − | 0.602736i | \(-0.794077\pi\) | ||||
0.797941 | − | 0.602736i | \(-0.205923\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 13.8564i | − 0.619059i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −17.0718 | −0.761194 | −0.380597 | − | 0.924741i | \(-0.624281\pi\) | ||||
−0.380597 | + | 0.924741i | \(0.624281\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.4641 | 0.510146 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 1.69873i | − 0.0754432i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 21.1244i | 0.936321i | 0.883644 | + | 0.468160i | \(0.155083\pi\) | ||||
−0.883644 | + | 0.468160i | \(0.844917\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.928203 | 0.0410613 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −18.9282 | −0.835701 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 13.0718i | − 0.576012i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 16.0000i | − 0.703679i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10.3923 | −0.456172 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 26.7846 | 1.17346 | 0.586728 | − | 0.809784i | \(-0.300416\pi\) | ||||
0.586728 | + | 0.809784i | \(0.300416\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 34.5885i | 1.51245i | 0.654313 | + | 0.756224i | \(0.272958\pi\) | ||||
−0.654313 | + | 0.756224i | \(0.727042\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.26795i | 0.142625i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.00000 | −0.348485 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.0000 | −0.478261 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 18.8756i | 0.819133i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.53590i | 0.283101i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13.8564 | 0.599065 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8.00000 | 0.345225 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 1.46410i | − 0.0630633i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 4.00000i | − 0.171973i | −0.996296 | − | 0.0859867i | \(-0.972596\pi\) | ||||
0.996296 | − | 0.0859867i | \(-0.0274043\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5.32051 | −0.228325 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.14359 | 0.263163 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.24871i | 0.0961480i | 0.998844 | + | 0.0480740i | \(0.0153083\pi\) | ||||
−0.998844 | + | 0.0480740i | \(0.984692\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 32.3397i | − 1.38023i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −25.8564 | −1.10152 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.92820 | 0.124520 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 2.92820i | − 0.124295i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 31.7128i | − 1.34372i | −0.740680 | − | 0.671858i | \(-0.765497\pi\) | ||||
0.740680 | − | 0.671858i | \(-0.234503\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.78461 | −0.202367 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.14359 | −0.0905026 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 4.05256i | − 0.170795i | −0.996347 | − | 0.0853975i | \(-0.972784\pi\) | ||||
0.996347 | − | 0.0853975i | \(-0.0272160\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.85641i | 0.414662i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.46410 | −0.187475 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.46410 | 0.0613783 | 0.0306892 | − | 0.999529i | \(-0.490230\pi\) | ||||
0.0306892 | + | 0.999529i | \(0.490230\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 37.1769i | − 1.55581i | −0.628385 | − | 0.777903i | \(-0.716284\pi\) | ||||
0.628385 | − | 0.777903i | \(-0.283716\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 11.7128i | 0.489310i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −15.4641 | −0.644898 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −44.9282 | −1.87039 | −0.935193 | − | 0.354139i | \(-0.884774\pi\) | ||||
−0.935193 | + | 0.354139i | \(0.884774\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 9.85641i | − 0.409618i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 11.6603i | − 0.483749i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 17.5692 | 0.727643 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.89488 | −0.243723 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 36.7321i | − 1.51609i | −0.652200 | − | 0.758047i | \(-0.726154\pi\) | ||||
0.652200 | − | 0.758047i | \(-0.273846\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18.9282i | 0.779923i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.35898 | −0.0559011 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 39.8564 | 1.63671 | 0.818353 | − | 0.574716i | \(-0.194887\pi\) | ||||
0.818353 | + | 0.574716i | \(0.194887\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.46410i | 0.0600223i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 2.92820i | − 0.119843i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 27.7128 | 1.13231 | 0.566157 | − | 0.824297i | \(-0.308429\pi\) | ||||
0.566157 | + | 0.824297i | \(0.308429\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.0000 | 0.897399 | 0.448699 | − | 0.893683i | \(-0.351887\pi\) | ||||
0.448699 | + | 0.893683i | \(0.351887\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 19.7128i | 0.802768i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 6.48334i | − 0.263585i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −27.7128 | −1.12483 | −0.562414 | − | 0.826856i | \(-0.690127\pi\) | ||||
−0.562414 | + | 0.826856i | \(0.690127\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.00000 | 0.162088 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 35.7128i | − 1.44479i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.67949i | 0.189003i | 0.995525 | + | 0.0945014i | \(0.0301257\pi\) | ||||
−0.995525 | + | 0.0945014i | \(0.969874\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.07180 | 0.0432190 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.60770 | −0.145240 | −0.0726202 | − | 0.997360i | \(-0.523136\pi\) | ||||
−0.0726202 | + | 0.997360i | \(0.523136\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 13.8038i | − 0.554823i | −0.960751 | − | 0.277412i | \(-0.910523\pi\) | ||||
0.960751 | − | 0.277412i | \(-0.0894766\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 13.8564i | 0.556038i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 15.8564 | 0.635274 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.2487 | 0.689948 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.07180i | 0.202548i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 10.9282i | 0.435736i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −33.5692 | −1.33637 | −0.668185 | − | 0.743995i | \(-0.732928\pi\) | ||||
−0.668185 | + | 0.743995i | \(0.732928\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −18.1436 | −0.721143 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 3.32051i | − 0.131770i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 3.26795i | − 0.129481i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 26.9282 | 1.06526 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 26.2487 | 1.03676 | 0.518381 | − | 0.855150i | \(-0.326535\pi\) | ||||
0.518381 | + | 0.855150i | \(0.326535\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 31.6603i | 1.24856i | 0.781201 | + | 0.624279i | \(0.214607\pi\) | ||||
−0.781201 | + | 0.624279i | \(0.785393\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.784610i | 0.0308940i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −25.8564 | −1.01652 | −0.508260 | − | 0.861204i | \(-0.669711\pi\) | ||||
−0.508260 | + | 0.861204i | \(0.669711\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.2154 | 0.440243 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 2.92820i | − 0.114765i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 45.4641i | − 1.77915i | −0.456791 | − | 0.889574i | \(-0.651001\pi\) | ||||
0.456791 | − | 0.889574i | \(-0.348999\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.32051 | −0.207889 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.28719 | −0.0892317 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 31.3205i | − 1.22007i | −0.792373 | − | 0.610037i | \(-0.791155\pi\) | ||||
0.792373 | − | 0.610037i | \(-0.208845\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 22.9808i | − 0.893848i | −0.894572 | − | 0.446924i | \(-0.852519\pi\) | ||||
0.894572 | − | 0.446924i | \(-0.147481\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.78461 | −0.185819 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.46410 | 0.134332 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18.9282i | 0.732903i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.07180i | 0.196087i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −19.2154 | −0.741802 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 31.8564 | 1.22797 | 0.613987 | − | 0.789316i | \(-0.289565\pi\) | ||||
0.613987 | + | 0.789316i | \(0.289565\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 17.8564i | − 0.687293i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 44.4449i | 1.70815i | 0.520146 | + | 0.854077i | \(0.325878\pi\) | ||||
−0.520146 | + | 0.854077i | \(0.674122\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.92820 | 0.189127 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10.3923 | 0.398234 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 38.6410i | − 1.47856i | −0.673400 | − | 0.739279i | \(-0.735167\pi\) | ||||
0.673400 | − | 0.739279i | \(-0.264833\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.75129i | 0.219745i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −15.1769 | −0.579035 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 39.2154 | 1.49399 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 13.1244i | − 0.499274i | −0.968339 | − | 0.249637i | \(-0.919689\pi\) | ||||
0.968339 | − | 0.249637i | \(-0.0803113\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.60770i | 0.137045i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −9.32051 | −0.353547 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.00000 | −0.151511 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 4.39230i | − 0.166132i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 40.3923i | − 1.52560i | −0.646637 | − | 0.762798i | \(-0.723825\pi\) | ||||
0.646637 | − | 0.762798i | \(-0.276175\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 25.8564 | 0.975193 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.85641 | −0.220565 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 15.6603i | − 0.588964i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 28.1051i | − 1.05551i | −0.849397 | − | 0.527755i | \(-0.823034\pi\) | ||||
0.849397 | − | 0.527755i | \(-0.176966\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.21539 | −0.270598 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 13.8564 | 0.518927 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.50258i | 0.130989i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 14.2487i | − 0.532128i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −34.9282 | −1.30260 | −0.651301 | − | 0.758819i | \(-0.725777\pi\) | ||||
−0.651301 | + | 0.758819i | \(0.725777\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17.8564 | −0.665007 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 16.6795i | − 0.620317i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 24.3923i | − 0.905907i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.92820 | 0.108601 | 0.0543005 | − | 0.998525i | \(-0.482707\pi\) | ||||
0.0543005 | + | 0.998525i | \(0.482707\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.21539 | 0.0820515 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 2.92820i | − 0.108304i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.66025i | 0.135195i | 0.997713 | + | 0.0675973i | \(0.0215333\pi\) | ||||
−0.997713 | + | 0.0675973i | \(0.978467\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.535898 | −0.0197669 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11.7128 | 0.431447 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 31.3205i | 1.15214i | 0.817399 | + | 0.576072i | \(0.195415\pi\) | ||||
−0.817399 | + | 0.576072i | \(0.804585\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 11.3205i | 0.415869i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.2487 | 0.596107 | 0.298054 | − | 0.954549i | \(-0.403663\pi\) | ||||
0.298054 | + | 0.954549i | \(0.403663\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.9282 | 0.400378 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 28.7321i | 1.05125i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 18.9282i | − 0.691621i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.2487 | 0.884848 | 0.442424 | − | 0.896806i | \(-0.354119\pi\) | ||||
0.442424 | + | 0.896806i | \(0.354119\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −19.1769 | −0.698846 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 13.4641i | 0.490009i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 38.2487i | 1.39017i | 0.718926 | + | 0.695087i | \(0.244634\pi\) | ||||
−0.718926 | + | 0.695087i | \(0.755366\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.71281 | 0.134767 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 33.7128 | 1.22209 | 0.611044 | − | 0.791596i | \(-0.290750\pi\) | ||||
0.611044 | + | 0.791596i | \(0.290750\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 8.39230i | − 0.303822i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 3.60770i | − 0.130436i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 25.0333 | 0.903901 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30.7846 | 1.11012 | 0.555061 | − | 0.831810i | \(-0.312695\pi\) | ||||
0.555061 | + | 0.831810i | \(0.312695\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.39230i | 0.158185i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 45.1244i | 1.62301i | 0.584345 | + | 0.811505i | \(0.301351\pi\) | ||||
−0.584345 | + | 0.811505i | \(0.698649\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −17.8564 | −0.641421 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.00000 | −0.143499 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.46410i | 0.339087i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 16.0000i | − 0.572525i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −21.8564 | −0.781084 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.32051 | 0.0471310 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 10.5885i | − 0.377438i | −0.982031 | − | 0.188719i | \(-0.939567\pi\) | ||||
0.982031 | − | 0.188719i | \(-0.0604335\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 2.14359i | − 0.0763140i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13.4641 | 0.478728 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −42.8897 | −1.52306 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 6.43078i | − 0.228076i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 38.9808i | − 1.38077i | −0.723442 | − | 0.690385i | \(-0.757441\pi\) | ||||
0.723442 | − | 0.690385i | \(-0.242559\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21.8564 | 0.773224 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −39.0718 | −1.38053 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.35898i | 0.0479575i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 2.53590i | − 0.0893787i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 13.6077 | 0.479014 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −11.3205 | −0.398008 | −0.199004 | − | 0.979999i | \(-0.563771\pi\) | ||||
−0.199004 | + | 0.979999i | \(0.563771\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 2.87564i | − 0.100978i | −0.998725 | − | 0.0504888i | \(-0.983922\pi\) | ||||
0.998725 | − | 0.0504888i | \(-0.0160779\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.784610i | 0.0275175i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.78461 | −0.167598 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.92820 | −0.242387 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 8.05256i | 0.281379i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.92820i | 0.241796i | 0.992665 | + | 0.120898i | \(0.0385774\pi\) | ||||
−0.992665 | + | 0.120898i | \(0.961423\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10.9282 | −0.380933 | −0.190467 | − | 0.981694i | \(-0.561000\pi\) | ||||
−0.190467 | + | 0.981694i | \(0.561000\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.78461 | −0.166579 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13.8564i | 0.481834i | 0.970546 | + | 0.240917i | \(0.0774482\pi\) | ||||
−0.970546 | + | 0.240917i | \(0.922552\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 10.9808i | − 0.381378i | −0.981651 | − | 0.190689i | \(-0.938928\pi\) | ||||
0.981651 | − | 0.190689i | \(-0.0610721\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.92820 | −0.101578 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.00000 | 0.0692959 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 13.8564i | − 0.479521i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 16.0000i | 0.553041i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −15.7128 | −0.542467 | −0.271233 | − | 0.962514i | \(-0.587431\pi\) | ||||
−0.271233 | + | 0.962514i | \(0.587431\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.856406 | −0.0295313 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 1.46410i | − 0.0504263i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 1.69873i | − 0.0584381i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.85641 | −0.304310 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −10.6795 | −0.366519 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 18.9282i | − 0.648850i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 46.9808i | 1.60859i | 0.594230 | + | 0.804295i | \(0.297457\pi\) | ||||
−0.594230 | + | 0.804295i | \(0.702543\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.53590 | −0.291922 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10.7846 | 0.368395 | 0.184198 | − | 0.982889i | \(-0.441031\pi\) | ||||
0.184198 | + | 0.982889i | \(0.441031\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 28.4449i | 0.970526i | 0.874368 | + | 0.485263i | \(0.161276\pi\) | ||||
−0.874368 | + | 0.485263i | \(0.838724\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 1.46410i | − 0.0498964i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −24.0000 | −0.816970 | −0.408485 | − | 0.912765i | \(-0.633943\pi\) | ||||
−0.408485 | + | 0.912765i | \(0.633943\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10.3923 | −0.353349 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9.51666i | 0.323203i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.28719i | 0.145433i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 26.1436 | 0.885842 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −12.1436 | −0.410998 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.92820i | 0.234216i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 0.392305i | − 0.0132472i | −0.999978 | − | 0.00662360i | \(-0.997892\pi\) | ||||
0.999978 | − | 0.00662360i | \(-0.00210837\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.32051 | 0.0445396 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9.21539 | −0.310474 | −0.155237 | − | 0.987877i | \(-0.549614\pi\) | ||||
−0.155237 | + | 0.987877i | \(0.549614\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.9282i | 0.636985i | 0.947925 | + | 0.318492i | \(0.103177\pi\) | ||||
−0.947925 | + | 0.318492i | \(0.896823\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 4.10512i | − 0.137992i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −22.6410 | −0.760211 | −0.380105 | − | 0.924943i | \(-0.624112\pi\) | ||||
−0.380105 | + | 0.924943i | \(0.624112\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.53590 | −0.152129 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 6.53590i | − 0.218961i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 51.7128i | − 1.73050i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.00000 | 0.267411 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.28719 | 0.276701 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 21.8564i | 0.728952i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24.0000i | 0.799556i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.07180 | 0.0356672 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.32051 | −0.176860 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11.7128i | 0.388918i | 0.980911 | + | 0.194459i | \(0.0622951\pi\) | ||||
−0.980911 | + | 0.194459i | \(0.937705\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 38.5885i | 1.27990i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11.4641 | 0.379823 | 0.189911 | − | 0.981801i | \(-0.439180\pi\) | ||||
0.189911 | + | 0.981801i | \(0.439180\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 17.0718 | 0.564994 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 7.03332i | 0.232514i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.26795i | 0.240009i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 48.7846 | 1.60926 | 0.804628 | − | 0.593779i | \(-0.202365\pi\) | ||||
0.804628 | + | 0.593779i | \(0.202365\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 16.5359 | 0.544876 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 35.7128i | − 1.17550i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 24.3923i | 0.802014i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 44.0000 | 1.44515 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −17.7128 | −0.581139 | −0.290569 | − | 0.956854i | \(-0.593845\pi\) | ||||
−0.290569 | + | 0.956854i | \(0.593845\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 4.73205i | − 0.155087i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 16.0000i | 0.523816i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.14359 | −0.0701030 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −60.6410 | −1.98106 | −0.990528 | − | 0.137312i | \(-0.956154\pi\) | ||||
−0.990528 | + | 0.137312i | \(0.956154\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.75129i | 0.187686i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.98076i | 0.227566i | 0.993506 | + | 0.113783i | \(0.0362969\pi\) | ||||
−0.993506 | + | 0.113783i | \(0.963703\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.92820 | 0.225613 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.92820 | 0.0952545 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 3.60770i | − 0.117234i | −0.998281 | − | 0.0586172i | \(-0.981331\pi\) | ||||
0.998281 | − | 0.0586172i | \(-0.0186691\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.03332i | 0.0984658i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.35898 | 0.303486 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 7.85641 | 0.254494 | 0.127247 | − | 0.991871i | \(-0.459386\pi\) | ||||
0.127247 | + | 0.991871i | \(0.459386\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 11.7128i | 0.379018i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.85641i | 0.189311i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.85641 | 0.253697 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 46.6410i | 1.50299i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 9.85641i | − 0.317289i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −47.1769 | −1.51711 | −0.758554 | − | 0.651611i | \(-0.774094\pi\) | ||||
−0.758554 | + | 0.651611i | \(0.774094\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.92820 | −0.222566 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 10.4833i | − 0.336426i | −0.985751 | − | 0.168213i | \(-0.946200\pi\) | ||||
0.985751 | − | 0.168213i | \(-0.0537997\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.7321i | 0.408171i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −10.6795 | −0.342017 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −55.8564 | −1.78700 | −0.893502 | − | 0.449058i | \(-0.851759\pi\) | ||||
−0.893502 | + | 0.449058i | \(0.851759\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 23.2154i | 0.741967i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 20.6795i | 0.660245i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7.71281 | −0.246001 | −0.123000 | − | 0.992407i | \(-0.539252\pi\) | ||||
−0.123000 | + | 0.992407i | \(0.539252\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.35898 | −0.0433008 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8.00000i | 0.254643i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.07180i | 0.161274i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.7846 | 0.533181 | 0.266590 | − | 0.963810i | \(-0.414103\pi\) | ||||
0.266590 | + | 0.963810i | \(0.414103\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.21539 | 0.102037 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 2.92820i | − 0.0928303i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 8.73205i | − 0.276547i | −0.990394 | − | 0.138273i | \(-0.955845\pi\) | ||||
0.990394 | − | 0.138273i | \(-0.0441553\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 21.8564 | 0.691506 |
(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 | 448.2.b.c.225.2 | ✓ | 4 | |
3.2 | odd | 2 | 4032.2.c.k.2017.3 | 4 | |||
4.3 | odd | 2 | 448.2.b.d.225.3 | yes | 4 | ||
7.6 | odd | 2 | 3136.2.b.g.1569.3 | 4 | |||
8.3 | odd | 2 | 448.2.b.d.225.2 | yes | 4 | ||
8.5 | even | 2 | inner | 448.2.b.c.225.3 | yes | 4 | |
12.11 | even | 2 | 4032.2.c.n.2017.3 | 4 | |||
16.3 | odd | 4 | 1792.2.a.s.1.1 | 2 | |||
16.5 | even | 4 | 1792.2.a.q.1.1 | 2 | |||
16.11 | odd | 4 | 1792.2.a.i.1.2 | 2 | |||
16.13 | even | 4 | 1792.2.a.k.1.2 | 2 | |||
24.5 | odd | 2 | 4032.2.c.k.2017.2 | 4 | |||
24.11 | even | 2 | 4032.2.c.n.2017.2 | 4 | |||
28.27 | even | 2 | 3136.2.b.h.1569.2 | 4 | |||
56.13 | odd | 2 | 3136.2.b.g.1569.2 | 4 | |||
56.27 | even | 2 | 3136.2.b.h.1569.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
448.2.b.c.225.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
448.2.b.c.225.3 | yes | 4 | 8.5 | even | 2 | inner | |
448.2.b.d.225.2 | yes | 4 | 8.3 | odd | 2 | ||
448.2.b.d.225.3 | yes | 4 | 4.3 | odd | 2 | ||
1792.2.a.i.1.2 | 2 | 16.11 | odd | 4 | |||
1792.2.a.k.1.2 | 2 | 16.13 | even | 4 | |||
1792.2.a.q.1.1 | 2 | 16.5 | even | 4 | |||
1792.2.a.s.1.1 | 2 | 16.3 | odd | 4 | |||
3136.2.b.g.1569.2 | 4 | 56.13 | odd | 2 | |||
3136.2.b.g.1569.3 | 4 | 7.6 | odd | 2 | |||
3136.2.b.h.1569.2 | 4 | 28.27 | even | 2 | |||
3136.2.b.h.1569.3 | 4 | 56.27 | even | 2 | |||
4032.2.c.k.2017.2 | 4 | 24.5 | odd | 2 | |||
4032.2.c.k.2017.3 | 4 | 3.2 | odd | 2 | |||
4032.2.c.n.2017.2 | 4 | 24.11 | even | 2 | |||
4032.2.c.n.2017.3 | 4 | 12.11 | even | 2 |