Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3200,2,Mod(449,3200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3200, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3200.449");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3200 = 2^{7} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3200.f (of order \(2\), degree \(1\), not 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: | \(25.5521286468\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.40960000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 7x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{10}\cdot 5^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 449.8 | ||
Root | \(-1.14412 - 1.14412i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3200.449 |
Dual form | 3200.2.f.r.449.5 |
$q$-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 \(\left(\mathbb{Z}/3200\mathbb{Z}\right)^\times\).
\(n\) | \(901\) | \(1151\) | \(2177\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 2.23607 | 1.29099 | 0.645497 | − | 0.763763i | \(-0.276650\pi\) | ||||
0.645497 | + | 0.763763i | \(0.276650\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.82843i | 1.06904i | 0.845154 | + | 0.534522i | \(0.179509\pi\) | ||||
−0.845154 | + | 0.534522i | \(0.820491\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.00000 | 0.666667 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.23607i | 0.674200i | 0.941469 | + | 0.337100i | \(0.109446\pi\) | ||||
−0.941469 | + | 0.337100i | \(0.890554\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.32456 | 1.75412 | 0.877058 | − | 0.480384i | \(-0.159503\pi\) | ||||
0.877058 | + | 0.480384i | \(0.159503\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 5.00000i | − 1.21268i | −0.795206 | − | 0.606339i | \(-0.792637\pi\) | ||||
0.795206 | − | 0.606339i | \(-0.207363\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.23607i | 0.512989i | 0.966546 | + | 0.256495i | \(0.0825676\pi\) | ||||
−0.966546 | + | 0.256495i | \(0.917432\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.32456i | 1.38013i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.65685i | 1.17954i | 0.807573 | + | 0.589768i | \(0.200781\pi\) | ||||
−0.807573 | + | 0.589768i | \(0.799219\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.23607 | −0.430331 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.32456i | 1.17444i | 0.809427 | + | 0.587220i | \(0.199778\pi\) | ||||
−0.809427 | + | 0.587220i | \(0.800222\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.00000i | 0.870388i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.32456 | −1.03975 | −0.519875 | − | 0.854242i | \(-0.674022\pi\) | ||||
−0.519875 | + | 0.854242i | \(0.674022\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 14.1421 | 2.26455 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.00000 | 0.468521 | 0.234261 | − | 0.972174i | \(-0.424733\pi\) | ||||
0.234261 | + | 0.972174i | \(0.424733\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.94427 | −1.36399 | −0.681994 | − | 0.731357i | \(-0.738887\pi\) | ||||
−0.681994 | + | 0.731357i | \(0.738887\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.82843i | 0.412568i | 0.978492 | + | 0.206284i | \(0.0661372\pi\) | ||||
−0.978492 | + | 0.206284i | \(0.933863\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 11.1803i | − 1.56556i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.6491 | 1.73749 | 0.868744 | − | 0.495261i | \(-0.164927\pi\) | ||||
0.868744 | + | 0.495261i | \(0.164927\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.00000i | 0.662266i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 8.94427i | − 1.16445i | −0.813029 | − | 0.582223i | \(-0.802183\pi\) | ||||
0.813029 | − | 0.582223i | \(-0.197817\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.32456i | 0.809776i | 0.914366 | + | 0.404888i | \(0.132690\pi\) | ||||
−0.914366 | + | 0.404888i | \(0.867310\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.65685i | 0.712697i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.1803 | 1.36590 | 0.682948 | − | 0.730467i | \(-0.260698\pi\) | ||||
0.682948 | + | 0.730467i | \(0.260698\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 12.6491i | 1.52277i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.1421 | −1.67836 | −0.839181 | − | 0.543852i | \(-0.816965\pi\) | ||||
−0.839181 | + | 0.543852i | \(0.816965\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 15.0000i | − 1.75562i | −0.479012 | − | 0.877809i | \(-0.659005\pi\) | ||||
0.479012 | − | 0.877809i | \(-0.340995\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.32456 | −0.720750 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.1421 | 1.59111 | 0.795557 | − | 0.605878i | \(-0.207178\pi\) | ||||
0.795557 | + | 0.605878i | \(0.207178\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.0000 | −1.22222 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.70820 | 0.736321 | 0.368161 | − | 0.929762i | \(-0.379988\pi\) | ||||
0.368161 | + | 0.929762i | \(0.379988\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 14.1421i | 1.51620i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.00000 | −0.106000 | −0.0529999 | − | 0.998595i | \(-0.516878\pi\) | ||||
−0.0529999 | + | 0.998595i | \(0.516878\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 17.8885i | 1.87523i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.0000i | 1.01535i | 0.861550 | + | 0.507673i | \(0.169494\pi\) | ||||
−0.861550 | + | 0.507673i | \(0.830506\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.47214i | 0.449467i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 6.32456i | − 0.629317i | −0.949205 | − | 0.314658i | \(-0.898110\pi\) | ||||
0.949205 | − | 0.314658i | \(-0.101890\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.48528i | 0.836080i | 0.908429 | + | 0.418040i | \(0.137283\pi\) | ||||
−0.908429 | + | 0.418040i | \(0.862717\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −15.6525 | −1.51318 | −0.756591 | − | 0.653888i | \(-0.773137\pi\) | ||||
−0.756591 | + | 0.653888i | \(0.773137\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 6.32456i | − 0.605783i | −0.953025 | − | 0.302891i | \(-0.902048\pi\) | ||||
0.953025 | − | 0.302891i | \(-0.0979519\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −14.1421 | −1.34231 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15.0000i | 1.41108i | 0.708669 | + | 0.705541i | \(0.249296\pi\) | ||||
−0.708669 | + | 0.705541i | \(0.750704\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 12.6491 | 1.16941 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 14.1421 | 1.29641 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.00000 | 0.545455 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.70820 | 0.604858 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.9706i | 1.50589i | 0.658081 | + | 0.752947i | \(0.271368\pi\) | ||||
−0.658081 | + | 0.752947i | \(0.728632\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −20.0000 | −1.76090 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 8.94427i | − 0.781465i | −0.920504 | − | 0.390732i | \(-0.872222\pi\) | ||||
0.920504 | − | 0.390732i | \(-0.127778\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.32456 | −0.548408 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.00000i | 0.427179i | 0.976924 | + | 0.213589i | \(0.0685155\pi\) | ||||
−0.976924 | + | 0.213589i | \(0.931485\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.6525i | 1.32763i | 0.747899 | + | 0.663813i | \(0.231063\pi\) | ||||
−0.747899 | + | 0.663813i | \(0.768937\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.32456i | 0.532624i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 14.1421i | 1.18262i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.23607 | −0.184428 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 18.9737i | − 1.55438i | −0.629264 | − | 0.777192i | \(-0.716644\pi\) | ||||
0.629264 | − | 0.777192i | \(-0.283356\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.1421 | 1.15087 | 0.575435 | − | 0.817847i | \(-0.304833\pi\) | ||||
0.575435 | + | 0.817847i | \(0.304833\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 10.0000i | − 0.808452i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 28.2843 | 2.24309 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −16.0000 | −1.26098 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.70820 | 0.525427 | 0.262714 | − | 0.964874i | \(-0.415383\pi\) | ||||
0.262714 | + | 0.964874i | \(0.415383\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 2.82843i | − 0.218870i | −0.993994 | − | 0.109435i | \(-0.965096\pi\) | ||||
0.993994 | − | 0.109435i | \(-0.0349042\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 27.0000 | 2.07692 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.47214i | 0.341993i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −12.6491 | −0.961694 | −0.480847 | − | 0.876804i | \(-0.659671\pi\) | ||||
−0.480847 | + | 0.876804i | \(0.659671\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 20.0000i | − 1.50329i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.23607i | 0.167132i | 0.996502 | + | 0.0835658i | \(0.0266309\pi\) | ||||
−0.996502 | + | 0.0835658i | \(0.973369\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 12.6491i | − 0.940201i | −0.882613 | − | 0.470100i | \(-0.844218\pi\) | ||||
0.882613 | − | 0.470100i | \(-0.155782\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 14.1421i | 1.04542i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.1803 | 0.817587 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 6.32456i | − 0.460044i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.00000i | 0.359908i | 0.983675 | + | 0.179954i | \(0.0575949\pi\) | ||||
−0.983675 | + | 0.179954i | \(0.942405\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 25.0000 | 1.76336 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −17.8885 | −1.25553 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 11.3137i | 0.786357i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.00000 | −0.345857 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 6.70820i | − 0.461812i | −0.972976 | − | 0.230906i | \(-0.925831\pi\) | ||||
0.972976 | − | 0.230906i | \(-0.0741690\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −31.6228 | −2.16676 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 33.5410i | − 2.26649i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 31.6228i | − 2.12718i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 22.6274i | 1.51524i | 0.652694 | + | 0.757622i | \(0.273639\pi\) | ||||
−0.652694 | + | 0.757622i | \(0.726361\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.94427 | 0.593652 | 0.296826 | − | 0.954932i | \(-0.404072\pi\) | ||||
0.296826 | + | 0.954932i | \(0.404072\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 12.6491i | − 0.835877i | −0.908475 | − | 0.417938i | \(-0.862753\pi\) | ||||
0.908475 | − | 0.417938i | \(-0.137247\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −14.1421 | −0.930484 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 10.0000i | − 0.655122i | −0.944830 | − | 0.327561i | \(-0.893773\pi\) | ||||
0.944830 | − | 0.327561i | \(-0.106227\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 31.6228 | 2.05412 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.1421 | 0.914779 | 0.457389 | − | 0.889267i | \(-0.348785\pi\) | ||||
0.457389 | + | 0.889267i | \(0.348785\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.0000 | 0.837404 | 0.418702 | − | 0.908124i | \(-0.362485\pi\) | ||||
0.418702 | + | 0.908124i | \(0.362485\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −17.8885 | −1.14755 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 14.1421i | 0.899843i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 15.0000 | 0.950586 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 11.1803i | − 0.705697i | −0.935681 | − | 0.352848i | \(-0.885213\pi\) | ||||
0.935681 | − | 0.352848i | \(-0.114787\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.6491 | −0.795243 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 10.0000i | − 0.623783i | −0.950118 | − | 0.311891i | \(-0.899037\pi\) | ||||
0.950118 | − | 0.311891i | \(-0.100963\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 17.8885i | − 1.11154i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 12.6491i | 0.782960i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 22.6274i | − 1.39527i | −0.716455 | − | 0.697633i | \(-0.754237\pi\) | ||||
0.716455 | − | 0.697633i | \(-0.245763\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.23607 | −0.136845 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 40.0000i | 2.42091i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.9737 | −1.14002 | −0.570009 | − | 0.821639i | \(-0.693060\pi\) | ||||
−0.570009 | + | 0.821639i | \(0.693060\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.00000 | −0.119310 | −0.0596550 | − | 0.998219i | \(-0.519000\pi\) | ||||
−0.0596550 | + | 0.998219i | \(0.519000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.1803 | 0.664602 | 0.332301 | − | 0.943173i | \(-0.392175\pi\) | ||||
0.332301 | + | 0.943173i | \(0.392175\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.48528i | 0.500870i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.00000 | −0.470588 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 22.3607i | 1.31081i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.32456 | −0.369484 | −0.184742 | − | 0.982787i | \(-0.559145\pi\) | ||||
−0.184742 | + | 0.982787i | \(0.559145\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 5.00000i | − 0.290129i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 35.7771i | 2.06904i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 25.2982i | − 1.45817i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 14.1421i | − 0.812444i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −20.1246 | −1.14857 | −0.574286 | − | 0.818655i | \(-0.694720\pi\) | ||||
−0.574286 | + | 0.818655i | \(0.694720\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 18.9737i | 1.07937i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −14.1421 | −0.801927 | −0.400963 | − | 0.916094i | \(-0.631325\pi\) | ||||
−0.400963 | + | 0.916094i | \(0.631325\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 30.0000i | − 1.69570i | −0.530236 | − | 0.847850i | \(-0.677897\pi\) | ||||
0.530236 | − | 0.847850i | \(-0.322103\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −12.6491 | −0.710445 | −0.355222 | − | 0.934782i | \(-0.615595\pi\) | ||||
−0.355222 | + | 0.934782i | \(0.615595\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −14.1421 | −0.791808 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −35.0000 | −1.95351 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 11.1803 | 0.622091 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 14.1421i | − 0.782062i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.00000 | −0.441054 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 33.5410i | − 1.84358i | −0.387688 | − | 0.921791i | \(-0.626726\pi\) | ||||
0.387688 | − | 0.921791i | \(-0.373274\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −12.6491 | −0.693167 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 15.0000i | − 0.817102i | −0.912735 | − | 0.408551i | \(-0.866034\pi\) | ||||
0.912735 | − | 0.408551i | \(-0.133966\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 33.5410i | 1.82170i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.9706i | 0.916324i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 20.1246 | 1.08035 | 0.540173 | − | 0.841554i | \(-0.318359\pi\) | ||||
0.540173 | + | 0.841554i | \(0.318359\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 18.9737i | − 1.01564i | −0.861464 | − | 0.507819i | \(-0.830452\pi\) | ||||
0.861464 | − | 0.507819i | \(-0.169548\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −14.1421 | −0.754851 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.0000i | 0.532246i | 0.963939 | + | 0.266123i | \(0.0857428\pi\) | ||||
−0.963939 | + | 0.266123i | \(0.914257\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 31.6228 | 1.67365 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 14.1421 | 0.746393 | 0.373197 | − | 0.927752i | \(-0.378262\pi\) | ||||
0.373197 | + | 0.927752i | \(0.378262\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.0000 | 0.736842 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 13.4164 | 0.704179 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 16.9706i | − 0.885856i | −0.896557 | − | 0.442928i | \(-0.853940\pi\) | ||||
0.896557 | − | 0.442928i | \(-0.146060\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.00000 | 0.312348 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 35.7771i | 1.85745i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.6491 | 0.654946 | 0.327473 | − | 0.944861i | \(-0.393803\pi\) | ||||
0.327473 | + | 0.944861i | \(0.393803\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 40.0000i | 2.06010i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 6.70820i | − 0.344577i | −0.985047 | − | 0.172289i | \(-0.944884\pi\) | ||||
0.985047 | − | 0.172289i | \(-0.0551162\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 37.9473i | 1.94410i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 19.7990i | − 1.01168i | −0.862627 | − | 0.505841i | \(-0.831182\pi\) | ||||
0.862627 | − | 0.505841i | \(-0.168818\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −17.8885 | −0.909326 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 25.2982i | − 1.28267i | −0.767261 | − | 0.641335i | \(-0.778381\pi\) | ||||
0.767261 | − | 0.641335i | \(-0.221619\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 28.2843 | 1.43040 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 20.0000i | − 1.00887i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −25.2982 | −1.26968 | −0.634841 | − | 0.772643i | \(-0.718934\pi\) | ||||
−0.634841 | + | 0.772643i | \(0.718934\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −14.1421 | −0.707992 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.0000 | 0.649189 | 0.324595 | − | 0.945853i | \(-0.394772\pi\) | ||||
0.324595 | + | 0.945853i | \(0.394772\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 14.1421i | − 0.701000i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.0000 | −0.543915 | −0.271957 | − | 0.962309i | \(-0.587671\pi\) | ||||
−0.271957 | + | 0.962309i | \(0.587671\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.1803i | 0.551485i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 25.2982 | 1.24484 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 35.0000i | 1.71396i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 33.5410i | − 1.63859i | −0.573375 | − | 0.819293i | \(-0.694366\pi\) | ||||
0.573375 | − | 0.819293i | \(-0.305634\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 12.6491i | − 0.616480i | −0.951309 | − | 0.308240i | \(-0.900260\pi\) | ||||
0.951309 | − | 0.308240i | \(-0.0997400\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.65685i | 0.275046i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −17.8885 | −0.865687 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 31.6228i | 1.52676i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.1421 | 0.681203 | 0.340601 | − | 0.940208i | \(-0.389369\pi\) | ||||
0.340601 | + | 0.940208i | \(0.389369\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.00000i | 0.240285i | 0.992757 | + | 0.120142i | \(0.0383351\pi\) | ||||
−0.992757 | + | 0.120142i | \(0.961665\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −12.6491 | −0.605089 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.1421 | −0.674967 | −0.337484 | − | 0.941331i | \(-0.609576\pi\) | ||||
−0.337484 | + | 0.941331i | \(0.609576\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.00000 | −0.0952381 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 29.0689 | 1.38110 | 0.690552 | − | 0.723283i | \(-0.257368\pi\) | ||||
0.690552 | + | 0.723283i | \(0.257368\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 42.4264i | − 2.00670i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −21.0000 | −0.991051 | −0.495526 | − | 0.868593i | \(-0.665025\pi\) | ||||
−0.495526 | + | 0.868593i | \(0.665025\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.70820i | 0.315877i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 31.6228 | 1.48577 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.00000i | 0.233890i | 0.993138 | + | 0.116945i | \(0.0373101\pi\) | ||||
−0.993138 | + | 0.116945i | \(0.962690\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 11.1803i | 0.521854i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 37.9473i | 1.76738i | 0.468069 | + | 0.883692i | \(0.344950\pi\) | ||||
−0.468069 | + | 0.883692i | \(0.655050\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 5.65685i | − 0.262896i | −0.991323 | − | 0.131448i | \(-0.958037\pi\) | ||||
0.991323 | − | 0.131448i | \(-0.0419627\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.94427 | 0.413892 | 0.206946 | − | 0.978352i | \(-0.433648\pi\) | ||||
0.206946 | + | 0.978352i | \(0.433648\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 31.6228i | 1.46020i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 20.0000i | − 0.919601i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 25.2982 | 1.15833 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −28.2843 | −1.29234 | −0.646171 | − | 0.763193i | \(-0.723631\pi\) | ||||
−0.646171 | + | 0.763193i | \(0.723631\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −40.0000 | −1.82384 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −35.7771 | −1.62791 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 39.5980i | 1.79436i | 0.441669 | + | 0.897178i | \(0.354386\pi\) | ||||
−0.441669 | + | 0.897178i | \(0.645614\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 15.0000 | 0.678323 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 26.8328i | − 1.21095i | −0.795865 | − | 0.605474i | \(-0.792984\pi\) | ||||
0.795865 | − | 0.605474i | \(-0.207016\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 31.6228 | 1.42422 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 40.0000i | − 1.79425i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 26.8328i | − 1.20120i | −0.799549 | − | 0.600601i | \(-0.794928\pi\) | ||||
0.799549 | − | 0.600601i | \(-0.205072\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 6.32456i | − 0.282560i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 33.9411i | − 1.51336i | −0.653785 | − | 0.756680i | \(-0.726820\pi\) | ||||
0.653785 | − | 0.756680i | \(-0.273180\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 60.3738 | 2.68130 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 42.4264 | 1.87683 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − 5.00000i | − 0.220755i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.32456 | −0.278154 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −28.2843 | −1.24154 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.0000 | −0.569540 | −0.284770 | − | 0.958596i | \(-0.591917\pi\) | ||||
−0.284770 | + | 0.958596i | \(0.591917\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −20.1246 | −0.879988 | −0.439994 | − | 0.898001i | \(-0.645019\pi\) | ||||
−0.439994 | + | 0.898001i | \(0.645019\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.00000 | −0.391304 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 17.8885i | − 0.776297i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 18.9737 | 0.821841 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.00000i | 0.215766i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 2.23607i | − 0.0963143i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.6491i | 0.543828i | 0.962322 | + | 0.271914i | \(0.0876566\pi\) | ||||
−0.962322 | + | 0.271914i | \(0.912343\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 28.2843i | − 1.21379i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20.1246 | −0.860466 | −0.430233 | − | 0.902718i | \(-0.641569\pi\) | ||||
−0.430233 | + | 0.902718i | \(0.641569\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 12.6491i | 0.539851i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −14.1421 | −0.602475 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 40.0000i | 1.70097i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −44.2719 | −1.87586 | −0.937930 | − | 0.346825i | \(-0.887260\pi\) | ||||
−0.937930 | + | 0.346825i | \(0.887260\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −56.5685 | −2.39259 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 25.0000 | 1.05550 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −44.7214 | −1.88478 | −0.942390 | − | 0.334515i | \(-0.891427\pi\) | ||||
−0.942390 | + | 0.334515i | \(0.891427\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 31.1127i | − 1.30661i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 21.0000 | 0.880366 | 0.440183 | − | 0.897908i | \(-0.354914\pi\) | ||||
0.440183 | + | 0.897908i | \(0.354914\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 26.8328i | − 1.12292i | −0.827504 | − | 0.561459i | \(-0.810240\pi\) | ||||
0.827504 | − | 0.561459i | \(-0.189760\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 25.0000i | 1.04076i | 0.853934 | + | 0.520382i | \(0.174210\pi\) | ||||
−0.853934 | + | 0.520382i | \(0.825790\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 11.1803i | 0.464639i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 18.9737i | 0.787160i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 28.2843i | 1.17141i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −11.1803 | −0.461462 | −0.230731 | − | 0.973018i | \(-0.574112\pi\) | ||||
−0.230731 | + | 0.973018i | \(0.574112\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15.0000i | 0.615976i | 0.951390 | + | 0.307988i | \(0.0996557\pi\) | ||||
−0.951390 | + | 0.307988i | \(0.900344\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −14.1421 | −0.577832 | −0.288916 | − | 0.957354i | \(-0.593295\pi\) | ||||
−0.288916 | + | 0.957354i | \(0.593295\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.0000 | 0.693444 | 0.346722 | − | 0.937968i | \(-0.387295\pi\) | ||||
0.346722 | + | 0.937968i | \(0.387295\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 22.3607 | 0.910597 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.9706i | 0.688814i | 0.938820 | + | 0.344407i | \(0.111920\pi\) | ||||
−0.938820 | + | 0.344407i | \(0.888080\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −40.0000 | −1.62088 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 17.8885i | 0.723693i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 25.2982 | 1.02179 | 0.510893 | − | 0.859644i | \(-0.329315\pi\) | ||||
0.510893 | + | 0.859644i | \(0.329315\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 30.0000i | − 1.20775i | −0.797077 | − | 0.603877i | \(-0.793622\pi\) | ||||
0.797077 | − | 0.603877i | \(-0.206378\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 26.8328i | 1.07850i | 0.842145 | + | 0.539251i | \(0.181293\pi\) | ||||
−0.842145 | + | 0.539251i | \(0.818707\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 12.6491i | − 0.507591i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 2.82843i | − 0.113319i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −11.1803 | −0.446500 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 31.6228i | 1.26088i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28.2843 | 1.12598 | 0.562990 | − | 0.826464i | \(-0.309651\pi\) | ||||
0.562990 | + | 0.826464i | \(0.309651\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 15.0000i | − 0.596196i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.32456 | −0.250588 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −28.2843 | −1.11891 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 22.0000 | 0.868948 | 0.434474 | − | 0.900684i | \(-0.356934\pi\) | ||||
0.434474 | + | 0.900684i | \(0.356934\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 26.8328 | 1.05818 | 0.529091 | − | 0.848565i | \(-0.322533\pi\) | ||||
0.529091 | + | 0.848565i | \(0.322533\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 45.2548i | − 1.77915i | −0.456788 | − | 0.889576i | \(-0.651000\pi\) | ||||
0.456788 | − | 0.889576i | \(-0.349000\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 20.0000 | 0.785069 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.32456 | 0.247499 | 0.123749 | − | 0.992313i | \(-0.460508\pi\) | ||||
0.123749 | + | 0.992313i | \(0.460508\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 30.0000i | − 1.17041i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.70820i | 0.261315i | 0.991428 | + | 0.130657i | \(0.0417087\pi\) | ||||
−0.991428 | + | 0.130657i | \(0.958291\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 44.2719i | 1.72198i | 0.508625 | + | 0.860988i | \(0.330154\pi\) | ||||
−0.508625 | + | 0.860988i | \(0.669846\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 70.7107i | − 2.74618i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −35.7771 | −1.38529 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 50.5964i | 1.95617i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −14.1421 | −0.545951 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 10.0000i | − 0.385472i | −0.981251 | − | 0.192736i | \(-0.938264\pi\) | ||||
0.981251 | − | 0.192736i | \(-0.0617360\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −37.9473 | −1.45843 | −0.729217 | − | 0.684282i | \(-0.760116\pi\) | ||||
−0.729217 | + | 0.684282i | \(0.760116\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −28.2843 | −1.08545 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 20.0000 | 0.766402 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.23607 | −0.0855608 | −0.0427804 | − | 0.999085i | \(-0.513622\pi\) | ||||
−0.0427804 | + | 0.999085i | \(0.513622\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 28.2843i | − 1.07911i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 80.0000 | 3.04776 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 33.5410i | 1.27596i | 0.770053 | + | 0.637980i | \(0.220230\pi\) | ||||
−0.770053 | + | 0.637980i | \(0.779770\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −12.6491 | −0.480500 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 15.0000i | − 0.568166i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 22.3607i | − 0.845759i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 31.6228i | − 1.19438i | −0.802101 | − | 0.597188i | \(-0.796285\pi\) | ||||
0.802101 | − | 0.597188i | \(-0.203715\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 14.1421i | − 0.533381i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 17.8885 | 0.672768 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 12.6491i | − 0.475047i | −0.971382 | − | 0.237524i | \(-0.923664\pi\) | ||||
0.971382 | − | 0.237524i | \(-0.0763357\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 28.2843 | 1.06074 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 31.6228 | 1.18097 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 14.1421 | 0.527413 | 0.263706 | − | 0.964603i | \(-0.415055\pi\) | ||||
0.263706 | + | 0.964603i | \(0.415055\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −24.0000 | −0.893807 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 29.0689 | 1.08108 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 25.4558i | − 0.944105i | −0.881570 | − | 0.472052i | \(-0.843513\pi\) | ||||
0.881570 | − | 0.472052i | \(-0.156487\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −7.00000 | −0.259259 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 44.7214i | 1.65408i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.32456 | 0.233603 | 0.116801 | − | 0.993155i | \(-0.462736\pi\) | ||||
0.116801 | + | 0.993155i | \(0.462736\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 25.0000i | 0.920887i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 8.94427i | − 0.329020i | −0.986375 | − | 0.164510i | \(-0.947396\pi\) | ||||
0.986375 | − | 0.164510i | \(-0.0526043\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 31.6228i | 1.16169i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 5.65685i | − 0.207530i | −0.994602 | − | 0.103765i | \(-0.966911\pi\) | ||||
0.994602 | − | 0.103765i | \(-0.0330890\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 13.4164 | 0.490881 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 44.2719i | − 1.61766i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 42.4264 | 1.54816 | 0.774081 | − | 0.633087i | \(-0.218212\pi\) | ||||
0.774081 | + | 0.633087i | \(0.218212\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 25.0000i | − 0.911051i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12.6491 | 0.459740 | 0.229870 | − | 0.973221i | \(-0.426170\pi\) | ||||
0.229870 | + | 0.973221i | \(0.426170\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −28.2843 | −1.02665 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.00000 | 0.108750 | 0.0543750 | − | 0.998521i | \(-0.482683\pi\) | ||||
0.0543750 | + | 0.998521i | \(0.482683\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 17.8885 | 0.647609 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 56.5685i | − 2.04257i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −21.0000 | −0.757279 | −0.378640 | − | 0.925544i | \(-0.623608\pi\) | ||||
−0.378640 | + | 0.925544i | \(0.623608\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 22.3607i | − 0.805300i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −31.6228 | −1.13739 | −0.568696 | − | 0.822548i | \(-0.692552\pi\) | ||||
−0.568696 | + | 0.822548i | \(0.692552\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 40.0000i | − 1.43499i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.70820i | 0.240346i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 31.6228i | − 1.13155i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 14.1421i | − 0.505399i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26.8328 | 0.956487 | 0.478243 | − | 0.878227i | \(-0.341274\pi\) | ||||
0.478243 | + | 0.878227i | \(0.341274\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 50.5964i | − 1.80128i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −42.4264 | −1.50851 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 40.0000i | 1.42044i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 25.2982 | 0.896109 | 0.448054 | − | 0.894006i | \(-0.352117\pi\) | ||||
0.448054 | + | 0.894006i | \(0.352117\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 14.1421 | 0.500313 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.00000 | −0.0706665 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 33.5410 | 1.18364 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −34.0000 | −1.19538 | −0.597688 | − | 0.801729i | \(-0.703914\pi\) | ||||
−0.597688 | + | 0.801729i | \(0.703914\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.94427i | 0.314076i | 0.987593 | + | 0.157038i | \(0.0501945\pi\) | ||||
−0.987593 | + | 0.157038i | \(0.949806\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 20.0000i | − 0.699711i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 35.7771i | 1.25015i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 37.9473i | − 1.32437i | −0.749340 | − | 0.662186i | \(-0.769629\pi\) | ||||
0.749340 | − | 0.662186i | \(-0.230371\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.65685i | 0.197186i | 0.995128 | + | 0.0985928i | \(0.0314341\pi\) | ||||
−0.995128 | + | 0.0985928i | \(0.968566\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −11.1803 | −0.388779 | −0.194389 | − | 0.980924i | \(-0.562272\pi\) | ||||
−0.194389 | + | 0.980924i | \(0.562272\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.32456i | 0.219661i | 0.993950 | + | 0.109830i | \(0.0350308\pi\) | ||||
−0.993950 | + | 0.109830i | \(0.964969\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −42.4264 | −1.47176 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.00000i | 0.173240i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −56.5685 | −1.95296 | −0.976481 | − | 0.215601i | \(-0.930829\pi\) | ||||
−0.976481 | + | 0.215601i | \(0.930829\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.0000 | −0.379310 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −4.47214 | −0.154029 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 16.9706i | 0.583115i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 25.0000 | 0.857998 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 35.7771i | − 1.22642i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12.6491 | −0.433097 | −0.216549 | − | 0.976272i | \(-0.569480\pi\) | ||||
−0.216549 | + | 0.976272i | \(0.569480\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 45.0000i | 1.53717i | 0.639747 | + | 0.768585i | \(0.279039\pi\) | ||||
−0.639747 | + | 0.768585i | \(0.720961\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 2.23607i | − 0.0762937i | −0.999272 | − | 0.0381468i | \(-0.987855\pi\) | ||||
0.999272 | − | 0.0381468i | \(-0.0121455\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 18.9737i | 0.646621i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 8.48528i | − 0.288842i | −0.989516 | − | 0.144421i | \(-0.953868\pi\) | ||||
0.989516 | − | 0.144421i | \(-0.0461320\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −17.8885 | −0.607527 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 31.6228i | 1.07273i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 70.7107 | 2.39594 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 20.0000i | 0.676897i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 12.6491 | 0.427130 | 0.213565 | − | 0.976929i | \(-0.431492\pi\) | ||||
0.213565 | + | 0.976929i | \(0.431492\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −14.1421 | −0.477002 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 42.0000 | 1.41502 | 0.707508 | − | 0.706705i | \(-0.249819\pi\) | ||||
0.707508 | + | 0.706705i | \(0.249819\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15.6525 | −0.526748 | −0.263374 | − | 0.964694i | \(-0.584835\pi\) | ||||
−0.263374 | + | 0.964694i | \(0.584835\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 11.3137i | − 0.379877i | −0.981796 | − | 0.189939i | \(-0.939171\pi\) | ||||
0.981796 | − | 0.189939i | \(-0.0608289\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −48.0000 | −1.60987 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 24.5967i | − 0.824022i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.32456 | −0.211643 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 80.0000i | 2.67112i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 63.2456i | − 2.10701i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 56.5685i | − 1.88248i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.94427 | 0.296990 | 0.148495 | − | 0.988913i | \(-0.452557\pi\) | ||||
0.148495 | + | 0.988913i | \(0.452557\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 12.6491i | − 0.419545i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −28.2843 | −0.937100 | −0.468550 | − | 0.883437i | \(-0.655223\pi\) | ||||
−0.468550 | + | 0.883437i | \(0.655223\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15.0000i | 0.496428i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 25.2982 | 0.835421 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −28.2843 | −0.933012 | −0.466506 | − | 0.884518i | \(-0.654487\pi\) | ||||
−0.466506 | + | 0.884518i | \(0.654487\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −45.0000 | −1.48280 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −89.4427 | −2.94404 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 16.9706i | 0.557386i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −6.00000 | −0.196854 | −0.0984268 | − | 0.995144i | \(-0.531381\pi\) | ||||
−0.0984268 | + | 0.995144i | \(0.531381\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 2.23607i | − 0.0732842i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −31.6228 | −1.03528 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 25.0000i | − 0.816714i | −0.912822 | − | 0.408357i | \(-0.866102\pi\) | ||||
0.912822 | − | 0.408357i | \(-0.133898\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 67.0820i | − 2.18914i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 31.6228i | 1.03087i | 0.856928 | + | 0.515437i | \(0.172370\pi\) | ||||
−0.856928 | + | 0.515437i | \(0.827630\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16.9706i | 0.552638i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −26.8328 | −0.871949 | −0.435975 | − | 0.899959i | \(-0.643596\pi\) | ||||
−0.435975 | + | 0.899959i | \(0.643596\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 94.8683i | − 3.07956i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −28.2843 | −0.917180 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 45.0000i | − 1.45769i | −0.684677 | − | 0.728846i | \(-0.740057\pi\) | ||||
0.684677 | − | 0.728846i | \(-0.259943\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −31.6228 | −1.02222 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −14.1421 | −0.456673 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −31.3050 | −1.00879 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.9706i | 0.545737i | 0.962051 | + | 0.272868i | \(0.0879723\pi\) | ||||
−0.962051 | + | 0.272868i | \(0.912028\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 25.0000 | 0.803116 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.23607i | 0.0717588i | 0.999356 | + | 0.0358794i | \(0.0114232\pi\) | ||||
−0.999356 | + | 0.0358794i | \(0.988577\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −44.2719 | −1.41929 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 45.0000i | − 1.43968i | −0.694141 | − | 0.719839i | \(-0.744216\pi\) | ||||
0.694141 | − | 0.719839i | \(-0.255784\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 2.23607i | − 0.0714650i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 12.6491i | − 0.403855i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 19.7990i | 0.631490i | 0.948844 | + | 0.315745i | \(0.102254\pi\) | ||||
−0.948844 | + | 0.315745i | \(0.897746\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −17.8885 | −0.569399 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 50.5964i | − 1.60887i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 42.4264 | 1.34772 | 0.673860 | − | 0.738859i | \(-0.264635\pi\) | ||||
0.673860 | + | 0.738859i | \(0.264635\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 75.0000i | − 2.38005i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 25.2982 | 0.801203 | 0.400601 | − | 0.916252i | \(-0.368801\pi\) | ||||
0.400601 | + | 0.916252i | \(0.368801\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 14.1421 | 0.447437 |
(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 | 3200.2.f.r.449.8 | 8 | ||
4.3 | odd | 2 | inner | 3200.2.f.r.449.1 | 8 | ||
5.2 | odd | 4 | 3200.2.d.r.1601.1 | yes | 4 | ||
5.3 | odd | 4 | 3200.2.d.m.1601.4 | yes | 4 | ||
5.4 | even | 2 | inner | 3200.2.f.r.449.2 | 8 | ||
8.3 | odd | 2 | inner | 3200.2.f.r.449.6 | 8 | ||
8.5 | even | 2 | inner | 3200.2.f.r.449.3 | 8 | ||
20.3 | even | 4 | 3200.2.d.m.1601.1 | ✓ | 4 | ||
20.7 | even | 4 | 3200.2.d.r.1601.4 | yes | 4 | ||
20.19 | odd | 2 | inner | 3200.2.f.r.449.7 | 8 | ||
40.3 | even | 4 | 3200.2.d.m.1601.3 | yes | 4 | ||
40.13 | odd | 4 | 3200.2.d.m.1601.2 | yes | 4 | ||
40.19 | odd | 2 | inner | 3200.2.f.r.449.4 | 8 | ||
40.27 | even | 4 | 3200.2.d.r.1601.2 | yes | 4 | ||
40.29 | even | 2 | inner | 3200.2.f.r.449.5 | 8 | ||
40.37 | odd | 4 | 3200.2.d.r.1601.3 | yes | 4 | ||
80.3 | even | 4 | 6400.2.a.cp.1.4 | 4 | |||
80.13 | odd | 4 | 6400.2.a.cp.1.1 | 4 | |||
80.27 | even | 4 | 6400.2.a.cs.1.3 | 4 | |||
80.37 | odd | 4 | 6400.2.a.cs.1.2 | 4 | |||
80.43 | even | 4 | 6400.2.a.cp.1.2 | 4 | |||
80.53 | odd | 4 | 6400.2.a.cp.1.3 | 4 | |||
80.67 | even | 4 | 6400.2.a.cs.1.1 | 4 | |||
80.77 | odd | 4 | 6400.2.a.cs.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3200.2.d.m.1601.1 | ✓ | 4 | 20.3 | even | 4 | ||
3200.2.d.m.1601.2 | yes | 4 | 40.13 | odd | 4 | ||
3200.2.d.m.1601.3 | yes | 4 | 40.3 | even | 4 | ||
3200.2.d.m.1601.4 | yes | 4 | 5.3 | odd | 4 | ||
3200.2.d.r.1601.1 | yes | 4 | 5.2 | odd | 4 | ||
3200.2.d.r.1601.2 | yes | 4 | 40.27 | even | 4 | ||
3200.2.d.r.1601.3 | yes | 4 | 40.37 | odd | 4 | ||
3200.2.d.r.1601.4 | yes | 4 | 20.7 | even | 4 | ||
3200.2.f.r.449.1 | 8 | 4.3 | odd | 2 | inner | ||
3200.2.f.r.449.2 | 8 | 5.4 | even | 2 | inner | ||
3200.2.f.r.449.3 | 8 | 8.5 | even | 2 | inner | ||
3200.2.f.r.449.4 | 8 | 40.19 | odd | 2 | inner | ||
3200.2.f.r.449.5 | 8 | 40.29 | even | 2 | inner | ||
3200.2.f.r.449.6 | 8 | 8.3 | odd | 2 | inner | ||
3200.2.f.r.449.7 | 8 | 20.19 | odd | 2 | inner | ||
3200.2.f.r.449.8 | 8 | 1.1 | even | 1 | trivial | ||
6400.2.a.cp.1.1 | 4 | 80.13 | odd | 4 | |||
6400.2.a.cp.1.2 | 4 | 80.43 | even | 4 | |||
6400.2.a.cp.1.3 | 4 | 80.53 | odd | 4 | |||
6400.2.a.cp.1.4 | 4 | 80.3 | even | 4 | |||
6400.2.a.cs.1.1 | 4 | 80.67 | even | 4 | |||
6400.2.a.cs.1.2 | 4 | 80.37 | odd | 4 | |||
6400.2.a.cs.1.3 | 4 | 80.27 | even | 4 | |||
6400.2.a.cs.1.4 | 4 | 80.77 | odd | 4 |