Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1600,2,Mod(543,1600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1600, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1600.543");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1600.o (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.7760643234\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 607.4 | ||
Root | \(0.965926 - 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1600.607 |
Dual form | 1600.2.o.g.543.4 |
$q$-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 \(\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1151\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.41421 | − | 1.41421i | 0.816497 | − | 0.816497i | −0.169102 | − | 0.985599i | \(-0.554087\pi\) |
0.985599 | + | 0.169102i | \(0.0540867\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.44949 | − | 2.44949i | 0.925820 | − | 0.925820i | −0.0716124 | − | 0.997433i | \(-0.522814\pi\) |
0.997433 | + | 0.0716124i | \(0.0228145\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.46410 | −1.04447 | −0.522233 | − | 0.852803i | \(-0.674901\pi\) | ||||
−0.522233 | + | 0.852803i | \(0.674901\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.82843 | − | 2.82843i | −0.784465 | − | 0.784465i | 0.196116 | − | 0.980581i | \(-0.437167\pi\) |
−0.980581 | + | 0.196116i | \(0.937167\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.89898 | − | 4.89898i | −1.18818 | − | 1.18818i | −0.977571 | − | 0.210606i | \(-0.932456\pi\) |
−0.210606 | − | 0.977571i | \(-0.567544\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.46410i | 0.794719i | 0.917663 | + | 0.397360i | \(0.130073\pi\) | ||||
−0.917663 | + | 0.397360i | \(0.869927\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 6.92820i | − | 1.51186i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.44949 | − | 2.44949i | −0.510754 | − | 0.510754i | 0.404004 | − | 0.914757i | \(-0.367618\pi\) |
−0.914757 | + | 0.404004i | \(0.867618\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.82843 | + | 2.82843i | 0.544331 | + | 0.544331i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.92820 | −1.28654 | −0.643268 | − | 0.765641i | \(-0.722422\pi\) | ||||
−0.643268 | + | 0.765641i | \(0.722422\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 8.00000i | − | 1.43684i | −0.695608 | − | 0.718421i | \(-0.744865\pi\) | ||
0.695608 | − | 0.718421i | \(-0.255135\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.89898 | + | 4.89898i | −0.852803 | + | 0.852803i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.65685 | − | 5.65685i | 0.929981 | − | 0.929981i | −0.0677230 | − | 0.997704i | \(-0.521573\pi\) |
0.997704 | + | 0.0677230i | \(0.0215734\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −8.00000 | −1.28103 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.00000 | 0.937043 | 0.468521 | − | 0.883452i | \(-0.344787\pi\) | ||||
0.468521 | + | 0.883452i | \(0.344787\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.41421 | + | 1.41421i | −0.215666 | + | 0.215666i | −0.806669 | − | 0.591003i | \(-0.798732\pi\) |
0.591003 | + | 0.806669i | \(0.298732\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.44949 | − | 2.44949i | 0.357295 | − | 0.357295i | −0.505520 | − | 0.862815i | \(-0.668699\pi\) |
0.862815 | + | 0.505520i | \(0.168699\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 5.00000i | − | 0.714286i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −13.8564 | −1.94029 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.48528 | + | 8.48528i | 1.16554 | + | 1.16554i | 0.983243 | + | 0.182300i | \(0.0583542\pi\) |
0.182300 | + | 0.983243i | \(0.441646\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.89898 | + | 4.89898i | 0.648886 | + | 0.648886i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.3923i | 1.35296i | 0.736460 | + | 0.676481i | \(0.236496\pi\) | ||||
−0.736460 | + | 0.676481i | \(0.763504\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 13.8564i | − | 1.77413i | −0.461644 | − | 0.887066i | \(-0.652740\pi\) | ||
0.461644 | − | 0.887066i | \(-0.347260\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.44949 | − | 2.44949i | −0.308607 | − | 0.308607i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.41421 | + | 1.41421i | 0.172774 | + | 0.172774i | 0.788197 | − | 0.615423i | \(-0.211015\pi\) |
−0.615423 | + | 0.788197i | \(0.711015\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.92820 | −0.834058 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.89898 | − | 4.89898i | 0.573382 | − | 0.573382i | −0.359690 | − | 0.933072i | \(-0.617117\pi\) |
0.933072 | + | 0.359690i | \(0.117117\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −8.48528 | + | 8.48528i | −0.966988 | + | 0.966988i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.00000 | 0.900070 | 0.450035 | − | 0.893011i | \(-0.351411\pi\) | ||||
0.450035 | + | 0.893011i | \(0.351411\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 11.0000 | 1.22222 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.24264 | + | 4.24264i | −0.465690 | + | 0.465690i | −0.900515 | − | 0.434825i | \(-0.856810\pi\) |
0.434825 | + | 0.900515i | \(0.356810\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −9.79796 | + | 9.79796i | −1.05045 | + | 1.05045i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 6.00000i | − | 0.635999i | −0.948091 | − | 0.317999i | \(-0.896989\pi\) | ||
0.948091 | − | 0.317999i | \(-0.103011\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −13.8564 | −1.45255 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −11.3137 | − | 11.3137i | −1.17318 | − | 1.17318i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.89898 | + | 4.89898i | 0.497416 | + | 0.497416i | 0.910633 | − | 0.413217i | \(-0.135595\pi\) |
−0.413217 | + | 0.910633i | \(0.635595\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.46410i | 0.348155i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 6.92820i | − | 0.689382i | −0.938716 | − | 0.344691i | \(-0.887984\pi\) | ||
0.938716 | − | 0.344691i | \(-0.112016\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.2474 | + | 12.2474i | 1.20678 | + | 1.20678i | 0.972065 | + | 0.234712i | \(0.0754147\pi\) |
0.234712 | + | 0.972065i | \(0.424585\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.7279 | − | 12.7279i | −1.23045 | − | 1.23045i | −0.963789 | − | 0.266666i | \(-0.914078\pi\) |
−0.266666 | − | 0.963789i | \(-0.585922\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 16.0000i | − | 1.51865i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.79796 | − | 9.79796i | 0.921714 | − | 0.921714i | −0.0754362 | − | 0.997151i | \(-0.524035\pi\) |
0.997151 | + | 0.0754362i | \(0.0240349\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.82843 | + | 2.82843i | −0.261488 | + | 0.261488i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −24.0000 | −2.20008 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.48528 | − | 8.48528i | 0.765092 | − | 0.765092i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.34847 | + | 7.34847i | −0.652071 | + | 0.652071i | −0.953491 | − | 0.301420i | \(-0.902539\pi\) |
0.301420 | + | 0.953491i | \(0.402539\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.00000i | 0.352180i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.46410 | 0.302660 | 0.151330 | − | 0.988483i | \(-0.451644\pi\) | ||||
0.151330 | + | 0.988483i | \(0.451644\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.48528 | + | 8.48528i | 0.735767 | + | 0.735767i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 3.46410i | − | 0.293821i | −0.989150 | − | 0.146911i | \(-0.953067\pi\) | ||
0.989150 | − | 0.146911i | \(-0.0469330\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 6.92820i | − | 0.583460i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.79796 | + | 9.79796i | 0.819346 | + | 0.819346i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −7.07107 | − | 7.07107i | −0.583212 | − | 0.583212i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −13.8564 | −1.13516 | −0.567581 | − | 0.823318i | \(-0.692120\pi\) | ||||
−0.567581 | + | 0.823318i | \(0.692120\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.00000i | 0.651031i | 0.945537 | + | 0.325515i | \(0.105538\pi\) | ||||
−0.945537 | + | 0.325515i | \(0.894462\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.89898 | + | 4.89898i | −0.396059 | + | 0.396059i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.65685 | + | 5.65685i | −0.451466 | + | 0.451466i | −0.895841 | − | 0.444375i | \(-0.853426\pi\) |
0.444375 | + | 0.895841i | \(0.353426\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 24.0000 | 1.90332 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −12.0000 | −0.945732 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.41421 | + | 1.41421i | −0.110770 | + | 0.110770i | −0.760319 | − | 0.649550i | \(-0.774958\pi\) |
0.649550 | + | 0.760319i | \(0.274958\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.34847 | − | 7.34847i | 0.568642 | − | 0.568642i | −0.363106 | − | 0.931748i | \(-0.618284\pi\) |
0.931748 | + | 0.363106i | \(0.118284\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.00000i | 0.230769i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.46410 | 0.264906 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 14.6969 | + | 14.6969i | 1.10469 | + | 1.10469i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.3923i | 0.776757i | 0.921500 | + | 0.388379i | \(0.126965\pi\) | ||||
−0.921500 | + | 0.388379i | \(0.873035\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.92820i | 0.514969i | 0.966282 | + | 0.257485i | \(0.0828937\pi\) | ||||
−0.966282 | + | 0.257485i | \(0.917106\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −19.5959 | − | 19.5959i | −1.44857 | − | 1.44857i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 16.9706 | + | 16.9706i | 1.24101 | + | 1.24101i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 13.8564 | 1.00791 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.89898 | − | 4.89898i | 0.352636 | − | 0.352636i | −0.508453 | − | 0.861090i | \(-0.669783\pi\) |
0.861090 | + | 0.508453i | \(0.169783\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.48528 | − | 8.48528i | 0.604551 | − | 0.604551i | −0.336966 | − | 0.941517i | \(-0.609401\pi\) |
0.941517 | + | 0.336966i | \(0.109401\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.0000 | −1.13421 | −0.567105 | − | 0.823646i | \(-0.691937\pi\) | ||||
−0.567105 | + | 0.823646i | \(0.691937\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.00000 | 0.282138 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −16.9706 | + | 16.9706i | −1.19110 | + | 1.19110i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.44949 | + | 2.44949i | −0.170251 | + | 0.170251i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 12.0000i | − | 0.830057i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.46410 | 0.238479 | 0.119239 | − | 0.992866i | \(-0.461954\pi\) | ||||
0.119239 | + | 0.992866i | \(0.461954\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −19.5959 | − | 19.5959i | −1.33026 | − | 1.33026i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 13.8564i | − | 0.936329i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 27.7128i | 1.86417i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.34847 | − | 7.34847i | −0.492090 | − | 0.492090i | 0.416874 | − | 0.908964i | \(-0.363126\pi\) |
−0.908964 | + | 0.416874i | \(0.863126\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.7279 | + | 12.7279i | 0.844782 | + | 0.844782i | 0.989476 | − | 0.144695i | \(-0.0462199\pi\) |
−0.144695 | + | 0.989476i | \(0.546220\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 20.7846 | 1.37349 | 0.686743 | − | 0.726900i | \(-0.259040\pi\) | ||||
0.686743 | + | 0.726900i | \(0.259040\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 24.0000i | 1.57908i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −14.6969 | + | 14.6969i | −0.962828 | + | 0.962828i | −0.999333 | − | 0.0365050i | \(-0.988378\pi\) |
0.0365050 | + | 0.999333i | \(0.488378\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 11.3137 | − | 11.3137i | 0.734904 | − | 0.734904i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 24.0000 | 1.55243 | 0.776215 | − | 0.630468i | \(-0.217137\pi\) | ||||
0.776215 | + | 0.630468i | \(0.217137\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.0000 | 0.644157 | 0.322078 | − | 0.946713i | \(-0.395619\pi\) | ||||
0.322078 | + | 0.946713i | \(0.395619\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 7.07107 | − | 7.07107i | 0.453609 | − | 0.453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.79796 | − | 9.79796i | 0.623429 | − | 0.623429i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.0000i | 0.760469i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.2487 | 1.53057 | 0.765283 | − | 0.643695i | \(-0.222599\pi\) | ||||
0.765283 | + | 0.643695i | \(0.222599\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.48528 | + | 8.48528i | 0.533465 | + | 0.533465i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.79796 | − | 9.79796i | −0.611180 | − | 0.611180i | 0.332074 | − | 0.943253i | \(-0.392252\pi\) |
−0.943253 | + | 0.332074i | \(0.892252\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 27.7128i | − | 1.72199i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.92820i | 0.428845i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.34847 | + | 7.34847i | 0.453126 | + | 0.453126i | 0.896391 | − | 0.443265i | \(-0.146180\pi\) |
−0.443265 | + | 0.896391i | \(0.646180\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.48528 | − | 8.48528i | −0.519291 | − | 0.519291i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.8564 | −0.844840 | −0.422420 | − | 0.906400i | \(-0.638819\pi\) | ||||
−0.422420 | + | 0.906400i | \(0.638819\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 8.00000i | − | 0.485965i | −0.970031 | − | 0.242983i | \(-0.921874\pi\) | ||
0.970031 | − | 0.242983i | \(-0.0781258\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −19.5959 | + | 19.5959i | −1.18600 | + | 1.18600i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.65685 | − | 5.65685i | 0.339887 | − | 0.339887i | −0.516437 | − | 0.856325i | \(-0.672742\pi\) |
0.856325 | + | 0.516437i | \(0.172742\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −8.00000 | −0.478947 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −30.0000 | −1.78965 | −0.894825 | − | 0.446417i | \(-0.852700\pi\) | ||||
−0.894825 | + | 0.446417i | \(0.852700\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.89949 | − | 9.89949i | 0.588464 | − | 0.588464i | −0.348751 | − | 0.937215i | \(-0.613394\pi\) |
0.937215 | + | 0.348751i | \(0.113394\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 14.6969 | − | 14.6969i | 0.867533 | − | 0.867533i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 31.0000i | 1.82353i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 13.8564 | 0.812277 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −16.9706 | − | 16.9706i | −0.991431 | − | 0.991431i | 0.00853273 | − | 0.999964i | \(-0.497284\pi\) |
−0.999964 | + | 0.00853273i | \(0.997284\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −9.79796 | − | 9.79796i | −0.568535 | − | 0.568535i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 13.8564i | 0.801337i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.92820i | 0.399335i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −9.79796 | − | 9.79796i | −0.562878 | − | 0.562878i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.89949 | − | 9.89949i | −0.564994 | − | 0.564994i | 0.365728 | − | 0.930722i | \(-0.380820\pi\) |
−0.930722 | + | 0.365728i | \(0.880820\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 34.6410 | 1.97066 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 24.0000i | 1.36092i | 0.732787 | + | 0.680458i | \(0.238219\pi\) | ||||
−0.732787 | + | 0.680458i | \(0.761781\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.79796 | − | 9.79796i | 0.553813 | − | 0.553813i | −0.373726 | − | 0.927539i | \(-0.621920\pi\) |
0.927539 | + | 0.373726i | \(0.121920\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.48528 | − | 8.48528i | 0.476581 | − | 0.476581i | −0.427456 | − | 0.904036i | \(-0.640590\pi\) |
0.904036 | + | 0.427456i | \(0.140590\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 24.0000 | 1.34374 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −36.0000 | −2.00932 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 16.9706 | − | 16.9706i | 0.944267 | − | 0.944267i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 12.0000i | − | 0.661581i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.3205 | 0.952021 | 0.476011 | − | 0.879440i | \(-0.342082\pi\) | ||||
0.476011 | + | 0.879440i | \(0.342082\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5.65685 | − | 5.65685i | −0.309994 | − | 0.309994i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.79796 | − | 9.79796i | −0.533729 | − | 0.533729i | 0.387951 | − | 0.921680i | \(-0.373183\pi\) |
−0.921680 | + | 0.387951i | \(0.873183\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 27.7128i | − | 1.50515i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 27.7128i | 1.50073i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.89898 | + | 4.89898i | 0.264520 | + | 0.264520i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 21.2132 | + | 21.2132i | 1.13878 | + | 1.13878i | 0.988668 | + | 0.150116i | \(0.0479647\pi\) |
0.150116 | + | 0.988668i | \(0.452035\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.92820 | 0.370858 | 0.185429 | − | 0.982658i | \(-0.440632\pi\) | ||||
0.185429 | + | 0.982658i | \(0.440632\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 16.0000i | − | 0.854017i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 19.5959 | − | 19.5959i | 1.04299 | − | 1.04299i | 0.0439518 | − | 0.999034i | \(-0.486005\pi\) |
0.999034 | − | 0.0439518i | \(-0.0139948\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −33.9411 | + | 33.9411i | −1.79635 | + | 1.79635i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −24.0000 | −1.26667 | −0.633336 | − | 0.773877i | \(-0.718315\pi\) | ||||
−0.633336 | + | 0.773877i | \(0.718315\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.00000 | 0.368421 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.41421 | − | 1.41421i | 0.0742270 | − | 0.0742270i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.1464 | − | 17.1464i | 0.895036 | − | 0.895036i | −0.0999556 | − | 0.994992i | \(-0.531870\pi\) |
0.994992 | + | 0.0999556i | \(0.0318701\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 6.00000i | − | 0.312348i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 41.5692 | 2.15817 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −22.6274 | − | 22.6274i | −1.17160 | − | 1.17160i | −0.981827 | − | 0.189776i | \(-0.939224\pi\) |
−0.189776 | − | 0.981827i | \(-0.560776\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 19.5959 | + | 19.5959i | 1.00924 | + | 1.00924i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 24.2487i | − | 1.24557i | −0.782392 | − | 0.622786i | \(-0.786001\pi\) | ||
0.782392 | − | 0.622786i | \(-0.213999\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 20.7846i | 1.06483i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.44949 | + | 2.44949i | 0.125163 | + | 0.125163i | 0.766914 | − | 0.641750i | \(-0.221792\pi\) |
−0.641750 | + | 0.766914i | \(0.721792\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.41421 | + | 1.41421i | 0.0718885 | + | 0.0718885i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −13.8564 | −0.702548 | −0.351274 | − | 0.936273i | \(-0.614251\pi\) | ||||
−0.351274 | + | 0.936273i | \(0.614251\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.0000i | 1.21373i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.89898 | − | 4.89898i | 0.247121 | − | 0.247121i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.82843 | − | 2.82843i | 0.141955 | − | 0.141955i | −0.632558 | − | 0.774513i | \(-0.717995\pi\) |
0.774513 | + | 0.632558i | \(0.217995\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 24.0000 | 1.20150 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 18.0000 | 0.898877 | 0.449439 | − | 0.893311i | \(-0.351624\pi\) | ||||
0.449439 | + | 0.893311i | \(0.351624\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −22.6274 | + | 22.6274i | −1.12715 | + | 1.12715i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −19.5959 | + | 19.5959i | −0.971334 | + | 0.971334i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 22.0000i | 1.08783i | 0.839140 | + | 0.543915i | \(0.183059\pi\) | ||||
−0.839140 | + | 0.543915i | \(0.816941\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 25.4558 | + | 25.4558i | 1.25260 | + | 1.25260i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.89898 | − | 4.89898i | −0.239904 | − | 0.239904i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 38.1051i | 1.86156i | 0.365584 | + | 0.930778i | \(0.380869\pi\) | ||||
−0.365584 | + | 0.930778i | \(0.619131\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.8564i | 0.675320i | 0.941268 | + | 0.337660i | \(0.109635\pi\) | ||||
−0.941268 | + | 0.337660i | \(0.890365\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.44949 | − | 2.44949i | −0.119098 | − | 0.119098i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −33.9411 | − | 33.9411i | −1.64253 | − | 1.64253i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 27.7128 | 1.33799 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 24.0000i | 1.15604i | 0.816023 | + | 0.578020i | \(0.196174\pi\) | ||||
−0.816023 | + | 0.578020i | \(0.803826\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.6969 | + | 14.6969i | −0.706290 | + | 0.706290i | −0.965753 | − | 0.259463i | \(-0.916454\pi\) |
0.259463 | + | 0.965753i | \(0.416454\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.48528 | − | 8.48528i | 0.405906 | − | 0.405906i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.00000 | 0.381819 | 0.190910 | − | 0.981608i | \(-0.438856\pi\) | ||||
0.190910 | + | 0.981608i | \(0.438856\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.00000 | −0.238095 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.7279 | − | 12.7279i | 0.604722 | − | 0.604722i | −0.336840 | − | 0.941562i | \(-0.609358\pi\) |
0.941562 | + | 0.336840i | \(0.109358\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −19.5959 | + | 19.5959i | −0.926855 | + | 0.926855i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 6.00000i | − | 0.283158i | −0.989927 | − | 0.141579i | \(-0.954782\pi\) | ||
0.989927 | − | 0.141579i | \(-0.0452178\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −20.7846 | −0.978709 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11.3137 | + | 11.3137i | 0.531564 | + | 0.531564i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 29.3939 | + | 29.3939i | 1.37499 | + | 1.37499i | 0.852879 | + | 0.522108i | \(0.174854\pi\) |
0.522108 | + | 0.852879i | \(0.325146\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 27.7128i | − | 1.29352i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 20.7846i | 0.968036i | 0.875058 | + | 0.484018i | \(0.160823\pi\) | ||||
−0.875058 | + | 0.484018i | \(0.839177\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.2474 | + | 12.2474i | 0.569187 | + | 0.569187i | 0.931901 | − | 0.362713i | \(-0.118150\pi\) |
−0.362713 | + | 0.931901i | \(0.618150\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.24264 | + | 4.24264i | 0.196326 | + | 0.196326i | 0.798423 | − | 0.602097i | \(-0.205668\pi\) |
−0.602097 | + | 0.798423i | \(0.705668\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.92820 | 0.319915 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 16.0000i | 0.737241i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.89898 | − | 4.89898i | 0.225255 | − | 0.225255i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.48528 | − | 8.48528i | 0.388514 | − | 0.388514i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −32.0000 | −1.45907 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −16.9706 | + | 16.9706i | −0.772187 | + | 0.772187i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.2474 | + | 12.2474i | −0.554985 | + | 0.554985i | −0.927875 | − | 0.372890i | \(-0.878367\pi\) |
0.372890 | + | 0.927875i | \(0.378367\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.00000i | 0.180886i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.3923 | 0.468998 | 0.234499 | − | 0.972116i | \(-0.424655\pi\) | ||||
0.234499 | + | 0.972116i | \(0.424655\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 33.9411 | + | 33.9411i | 1.52863 | + | 1.52863i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 10.3923i | − | 0.465223i | −0.972570 | − | 0.232612i | \(-0.925273\pi\) | ||
0.972570 | − | 0.232612i | \(-0.0747271\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 20.7846i | − | 0.928588i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.2474 | + | 12.2474i | 0.546087 | + | 0.546087i | 0.925307 | − | 0.379220i | \(-0.123808\pi\) |
−0.379220 | + | 0.925307i | \(0.623808\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.24264 | + | 4.24264i | 0.188422 | + | 0.188422i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.92820 | −0.307087 | −0.153544 | − | 0.988142i | \(-0.549069\pi\) | ||||
−0.153544 | + | 0.988142i | \(0.549069\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 24.0000i | − | 1.06170i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −9.79796 | + | 9.79796i | −0.432590 | + | 0.432590i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.48528 | + | 8.48528i | −0.373182 | + | 0.373182i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.00000 | −0.262865 | −0.131432 | − | 0.991325i | \(-0.541958\pi\) | ||||
−0.131432 | + | 0.991325i | \(0.541958\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −24.0416 | + | 24.0416i | −1.05127 | + | 1.05127i | −0.0526543 | + | 0.998613i | \(0.516768\pi\) |
−0.998613 | + | 0.0526543i | \(0.983232\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −39.1918 | + | 39.1918i | −1.70722 | + | 1.70722i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 11.0000i | − | 0.478261i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.3923 | 0.450988 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −16.9706 | − | 16.9706i | −0.735077 | − | 0.735077i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 14.6969 | + | 14.6969i | 0.634220 | + | 0.634220i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 17.3205i | 0.746047i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 34.6410i | − | 1.48933i | −0.667436 | − | 0.744667i | \(-0.732608\pi\) | ||
0.667436 | − | 0.744667i | \(-0.267392\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9.79796 | + | 9.79796i | 0.420471 | + | 0.420471i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.07107 | + | 7.07107i | 0.302337 | + | 0.302337i | 0.841928 | − | 0.539591i | \(-0.181421\pi\) |
−0.539591 | + | 0.841928i | \(0.681421\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −13.8564 | −0.591377 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 24.0000i | − | 1.02243i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 19.5959 | − | 19.5959i | 0.833303 | − | 0.833303i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.00000 | 0.338364 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 48.0000 | 2.02656 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.24264 | + | 4.24264i | −0.178806 | + | 0.178806i | −0.790835 | − | 0.612029i | \(-0.790353\pi\) |
0.612029 | + | 0.790835i | \(0.290353\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 26.9444 | − | 26.9444i | 1.13156 | − | 1.13156i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 6.00000i | − | 0.251533i | −0.992060 | − | 0.125767i | \(-0.959861\pi\) | ||
0.992060 | − | 0.125767i | \(-0.0401390\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.46410 | 0.144968 | 0.0724841 | − | 0.997370i | \(-0.476907\pi\) | ||||
0.0724841 | + | 0.997370i | \(0.476907\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.79796 | + | 9.79796i | 0.407894 | + | 0.407894i | 0.881004 | − | 0.473109i | \(-0.156868\pi\) |
−0.473109 | + | 0.881004i | \(0.656868\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 13.8564i | − | 0.575853i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 20.7846i | 0.862291i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −29.3939 | − | 29.3939i | −1.21737 | − | 1.21737i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.24264 | − | 4.24264i | −0.175113 | − | 0.175113i | 0.614109 | − | 0.789221i | \(-0.289516\pi\) |
−0.789221 | + | 0.614109i | \(0.789516\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 27.7128 | 1.14189 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 24.0000i | − | 0.987228i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 19.5959 | − | 19.5959i | 0.804708 | − | 0.804708i | −0.179119 | − | 0.983827i | \(-0.557325\pi\) |
0.983827 | + | 0.179119i | \(0.0573249\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −22.6274 | + | 22.6274i | −0.926079 | + | 0.926079i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −48.0000 | −1.96123 | −0.980613 | − | 0.195952i | \(-0.937220\pi\) | ||||
−0.980613 | + | 0.195952i | \(0.937220\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.00000 | −0.0815817 | −0.0407909 | − | 0.999168i | \(-0.512988\pi\) | ||||
−0.0407909 | + | 0.999168i | \(0.512988\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.41421 | − | 1.41421i | 0.0575912 | − | 0.0575912i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.44949 | − | 2.44949i | 0.0994217 | − | 0.0994217i | −0.655646 | − | 0.755068i | \(-0.727604\pi\) |
0.755068 | + | 0.655646i | \(0.227604\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 48.0000i | 1.94506i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −13.8564 | −0.560570 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.1421 | − | 14.1421i | −0.571195 | − | 0.571195i | 0.361267 | − | 0.932462i | \(-0.382344\pi\) |
−0.932462 | + | 0.361267i | \(0.882344\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.89898 | − | 4.89898i | −0.197225 | − | 0.197225i | 0.601584 | − | 0.798810i | \(-0.294536\pi\) |
−0.798810 | + | 0.601584i | \(0.794536\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17.3205i | 0.696170i | 0.937463 | + | 0.348085i | \(0.113168\pi\) | ||||
−0.937463 | + | 0.348085i | \(0.886832\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 13.8564i | − | 0.556038i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −14.6969 | − | 14.6969i | −0.588820 | − | 0.588820i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −16.9706 | − | 16.9706i | −0.677739 | − | 0.677739i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −55.4256 | −2.20996 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 8.00000i | − | 0.318475i | −0.987240 | − | 0.159237i | \(-0.949096\pi\) | ||
0.987240 | − | 0.159237i | \(-0.0509036\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.89898 | − | 4.89898i | 0.194717 | − | 0.194717i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −14.1421 | + | 14.1421i | −0.560332 | + | 0.560332i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −42.0000 | −1.65890 | −0.829450 | − | 0.558581i | \(-0.811346\pi\) | ||||
−0.829450 | + | 0.558581i | \(0.811346\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 32.5269 | − | 32.5269i | 1.28274 | − | 1.28274i | 0.343632 | − | 0.939105i | \(-0.388343\pi\) |
0.939105 | − | 0.343632i | \(-0.111657\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.34847 | − | 7.34847i | 0.288898 | − | 0.288898i | −0.547746 | − | 0.836644i | \(-0.684514\pi\) |
0.836644 | + | 0.547746i | \(0.184514\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 36.0000i | − | 1.41312i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −55.4256 | −2.17230 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8.48528 | − | 8.48528i | −0.332055 | − | 0.332055i | 0.521312 | − | 0.853366i | \(-0.325443\pi\) |
−0.853366 | + | 0.521312i | \(0.825443\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.89898 | − | 4.89898i | −0.191127 | − | 0.191127i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.3923i | 0.404827i | 0.979300 | + | 0.202413i | \(0.0648785\pi\) | ||||
−0.979300 | + | 0.202413i | \(0.935122\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 27.7128i | − | 1.07790i | −0.842337 | − | 0.538952i | \(-0.818821\pi\) | ||
0.842337 | − | 0.538952i | \(-0.181179\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 39.1918 | + | 39.1918i | 1.52208 | + | 1.52208i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 16.9706 | + | 16.9706i | 0.657103 | + | 0.657103i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −20.7846 | −0.803579 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 48.0000i | 1.85302i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24.4949 | + | 24.4949i | −0.944209 | + | 0.944209i | −0.998524 | − | 0.0543149i | \(-0.982703\pi\) |
0.0543149 | + | 0.998524i | \(0.482703\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.48528 | − | 8.48528i | 0.326116 | − | 0.326116i | −0.524992 | − | 0.851107i | \(-0.675932\pi\) |
0.851107 | + | 0.524992i | \(0.175932\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 24.0000 | 0.921035 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 36.0000 | 1.37952 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 21.2132 | − | 21.2132i | 0.811701 | − | 0.811701i | −0.173188 | − | 0.984889i | \(-0.555407\pi\) |
0.984889 | + | 0.173188i | \(0.0554069\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 29.3939 | − | 29.3939i | 1.12145 | − | 1.12145i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 48.0000i | − | 1.82865i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −31.1769 | −1.18603 | −0.593013 | − | 0.805193i | \(-0.702062\pi\) | ||||
−0.593013 | + | 0.805193i | \(0.702062\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8.48528 | + | 8.48528i | 0.322329 | + | 0.322329i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −29.3939 | − | 29.3939i | −1.11337 | − | 1.11337i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 41.5692i | 1.57229i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 27.7128i | − | 1.04670i | −0.852118 | − | 0.523349i | \(-0.824682\pi\) | ||
0.852118 | − | 0.523349i | \(-0.175318\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 19.5959 | + | 19.5959i | 0.739074 | + | 0.739074i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −16.9706 | − | 16.9706i | −0.638244 | − | 0.638244i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 34.6410 | 1.30097 | 0.650485 | − | 0.759519i | \(-0.274566\pi\) | ||||
0.650485 | + | 0.759519i | \(0.274566\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 8.00000i | − | 0.300023i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −19.5959 | + | 19.5959i | −0.733873 | + | 0.733873i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 33.9411 | − | 33.9411i | 1.26755 | − | 1.26755i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −24.0000 | −0.895049 | −0.447524 | − | 0.894272i | \(-0.647694\pi\) | ||||
−0.447524 | + | 0.894272i | \(0.647694\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 60.0000 | 2.23452 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 14.1421 | − | 14.1421i | 0.525952 | − | 0.525952i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.34847 | + | 7.34847i | −0.272540 | + | 0.272540i | −0.830122 | − | 0.557582i | \(-0.811729\pi\) |
0.557582 | + | 0.830122i | \(0.311729\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0000i | 0.481481i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 13.8564 | 0.512498 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −22.6274 | − | 22.6274i | −0.835763 | − | 0.835763i | 0.152535 | − | 0.988298i | \(-0.451256\pi\) |
−0.988298 | + | 0.152535i | \(0.951256\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.89898 | − | 4.89898i | −0.180456 | − | 0.180456i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10.3923i | 0.382287i | 0.981562 | + | 0.191144i | \(0.0612196\pi\) | ||||
−0.981562 | + | 0.191144i | \(0.938780\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 27.7128i | − | 1.01806i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −26.9444 | − | 26.9444i | −0.988494 | − | 0.988494i | 0.0114409 | − | 0.999935i | \(-0.496358\pi\) |
−0.999935 | + | 0.0114409i | \(0.996358\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.24264 | + | 4.24264i | 0.155230 | + | 0.155230i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −62.3538 | −2.27836 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 32.0000i | − | 1.16770i | −0.811863 | − | 0.583848i | \(-0.801546\pi\) | ||
0.811863 | − | 0.583848i | \(-0.198454\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 34.2929 | − | 34.2929i | 1.24970 | − | 1.24970i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.3137 | − | 11.3137i | 0.411204 | − | 0.411204i | −0.470954 | − | 0.882158i | \(-0.656090\pi\) |
0.882158 | + | 0.470954i | \(0.156090\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 24.0000 | 0.871145 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.00000 | 0.217500 | 0.108750 | − | 0.994069i | \(-0.465315\pi\) | ||||
0.108750 | + | 0.994069i | \(0.465315\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 29.3939 | − | 29.3939i | 1.06135 | − | 1.06135i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 14.0000i | − | 0.504853i | −0.967616 | − | 0.252426i | \(-0.918771\pi\) | ||
0.967616 | − | 0.252426i | \(-0.0812286\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −27.7128 | −0.998053 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −8.48528 | − | 8.48528i | −0.305194 | − | 0.305194i | 0.537848 | − | 0.843042i | \(-0.319238\pi\) |
−0.843042 | + | 0.537848i | \(0.819238\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −39.1918 | − | 39.1918i | −1.40600 | − | 1.40600i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 20.7846i | 0.744686i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −19.5959 | − | 19.5959i | −0.700301 | − | 0.700301i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.5563 | + | 15.5563i | 0.554524 | + | 0.554524i | 0.927743 | − | 0.373219i | \(-0.121746\pi\) |
−0.373219 | + | 0.927743i | \(0.621746\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 20.7846 | 0.739952 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 48.0000i | − | 1.70668i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −39.1918 | + | 39.1918i | −1.39174 | + | 1.39174i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −8.48528 | + | 8.48528i | −0.300564 | + | 0.300564i | −0.841235 | − | 0.540670i | \(-0.818171\pi\) |
0.540670 | + | 0.841235i | \(0.318171\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −24.0000 | −0.849059 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.00000 | −0.212000 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −16.9706 | + | 16.9706i | −0.598878 | + | 0.598878i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −19.5959 | + | 19.5959i | −0.689809 | + | 0.689809i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 6.00000i | − | 0.210949i | −0.994422 | − | 0.105474i | \(-0.966364\pi\) | ||
0.994422 | − | 0.105474i | \(-0.0336361\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −31.1769 | −1.09477 | −0.547385 | − | 0.836881i | \(-0.684377\pi\) | ||||
−0.547385 | + | 0.836881i | \(0.684377\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −11.3137 | − | 11.3137i | −0.396789 | − | 0.396789i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.89898 | − | 4.89898i | −0.171394 | − | 0.171394i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 13.8564i | 0.484182i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.2474 | − | 12.2474i | −0.426919 | − | 0.426919i | 0.460658 | − | 0.887578i | \(-0.347613\pi\) |
−0.887578 | + | 0.460658i | \(0.847613\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.24264 | + | 4.24264i | 0.147531 | + | 0.147531i | 0.777014 | − | 0.629483i | \(-0.216733\pi\) |
−0.629483 | + | 0.777014i | \(0.716733\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13.8564 | −0.481253 | −0.240626 | − | 0.970618i | \(-0.577353\pi\) | ||||
−0.240626 | + | 0.970618i | \(0.577353\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 16.0000i | − | 0.555034i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −24.4949 | + | 24.4949i | −0.848698 | + | 0.848698i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 22.6274 | − | 22.6274i | 0.782118 | − | 0.782118i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −24.0000 | −0.828572 | −0.414286 | − | 0.910147i | \(-0.635969\pi\) | ||||
−0.414286 | + | 0.910147i | \(0.635969\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 19.0000 | 0.655172 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −42.4264 | + | 42.4264i | −1.46124 | + | 1.46124i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.44949 | − | 2.44949i | 0.0841655 | − | 0.0841655i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 28.0000i | − | 0.960958i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −27.7128 | −0.949983 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 19.7990 | + | 19.7990i | 0.677905 | + | 0.677905i | 0.959526 | − | 0.281621i | \(-0.0908721\pi\) |
−0.281621 | + | 0.959526i | \(0.590872\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 45.0333i | − | 1.53652i | −0.640140 | − | 0.768259i | \(-0.721124\pi\) | ||
0.640140 | − | 0.768259i | \(-0.278876\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 41.5692i | − | 1.41668i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −31.8434 | − | 31.8434i | −1.08396 | − | 1.08396i | −0.996136 | − | 0.0878249i | \(-0.972008\pi\) |
−0.0878249 | − | 0.996136i | \(-0.527992\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 43.8406 | + | 43.8406i | 1.48891 | + | 1.48891i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −27.7128 | −0.940093 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 8.00000i | − | 0.271070i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.89898 | − | 4.89898i | 0.165805 | − | 0.165805i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −28.2843 | + | 28.2843i | −0.955092 | + | 0.955092i | −0.999034 | − | 0.0439421i | \(-0.986008\pi\) |
0.0439421 | + | 0.999034i | \(0.486008\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −48.0000 | −1.61900 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18.0000 | 0.606435 | 0.303218 | − | 0.952921i | \(-0.401939\pi\) | ||||
0.303218 | + | 0.952921i | \(0.401939\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.3848 | − | 18.3848i | 0.618697 | − | 0.618697i | −0.326500 | − | 0.945197i | \(-0.605869\pi\) |
0.945197 | + | 0.326500i | \(0.105869\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 31.8434 | − | 31.8434i | 1.06920 | − | 1.06920i | 0.0717747 | − | 0.997421i | \(-0.477134\pi\) |
0.997421 | − | 0.0717747i | \(-0.0228663\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 36.0000i | 1.20740i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −38.1051 | −1.27657 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.48528 | + | 8.48528i | 0.283949 | + | 0.283949i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 19.5959 | + | 19.5959i | 0.654289 | + | 0.654289i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 55.4256i | 1.84855i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 83.1384i | − | 2.76974i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9.79796 | + | 9.79796i | 0.326056 | + | 0.326056i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.3848 | + | 18.3848i | 0.610456 | + | 0.610456i | 0.943065 | − | 0.332609i | \(-0.107929\pi\) |
−0.332609 | + | 0.943065i | \(0.607929\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.92820 | −0.229794 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.0000i | 0.795155i | 0.917568 | + | 0.397578i | \(0.130149\pi\) | ||||
−0.917568 | + | 0.397578i | \(0.869851\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.6969 | − | 14.6969i | 0.486398 | − | 0.486398i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.48528 | − | 8.48528i | 0.280209 | − | 0.280209i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 32.0000 | 1.05558 | 0.527791 | − | 0.849374i | \(-0.323020\pi\) | ||||
0.527791 | + | 0.849374i | \(0.323020\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −28.0000 | −0.922631 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 12.2474 | − | 12.2474i | 0.402259 | − | 0.402259i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 42.0000i | 1.37798i | 0.724773 | + | 0.688988i | \(0.241945\pi\) | ||||
−0.724773 | + | 0.688988i | \(0.758055\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 17.3205 | 0.567657 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 33.9411 | + | 33.9411i | 1.11118 | + | 1.11118i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.89898 | + | 4.89898i | 0.160043 | + | 0.160043i | 0.782586 | − | 0.622543i | \(-0.213900\pi\) |
−0.622543 | + | 0.782586i | \(0.713900\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 27.7128i | − | 0.904373i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 6.92820i | − | 0.225853i | −0.993603 | − | 0.112926i | \(-0.963978\pi\) | ||
0.993603 | − | 0.112926i | \(-0.0360225\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −14.6969 | − | 14.6969i | −0.478598 | − | 0.478598i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −21.2132 | − | 21.2132i | −0.689336 | − | 0.689336i | 0.272749 | − | 0.962085i | \(-0.412067\pi\) |
−0.962085 | + | 0.272749i | \(0.912067\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −27.7128 | −0.899596 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 24.0000i | − | 0.778253i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −19.5959 | + | 19.5959i | −0.634774 | + | 0.634774i | −0.949262 | − | 0.314488i | \(-0.898167\pi\) |
0.314488 | + | 0.949262i | \(0.398167\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 33.9411 | − | 33.9411i | 1.09716 | − | 1.09716i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −33.0000 | −1.06452 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12.7279 | + | 12.7279i | −0.410152 | + | 0.410152i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17.1464 | + | 17.1464i | −0.551392 | + | 0.551392i | −0.926842 | − | 0.375450i | \(-0.877488\pi\) |
0.375450 | + | 0.926842i | \(0.377488\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 48.0000i | − | 1.54198i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 17.3205 | 0.555842 | 0.277921 | − | 0.960604i | \(-0.410355\pi\) | ||||
0.277921 | + | 0.960604i | \(0.410355\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.48528 | − | 8.48528i | −0.272026 | − | 0.272026i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 24.4949 | + | 24.4949i | 0.783661 | + | 0.783661i | 0.980447 | − | 0.196785i | \(-0.0630502\pi\) |
−0.196785 | + | 0.980447i | \(0.563050\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 20.7846i | 0.664279i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 17.1464 | + | 17.1464i | 0.546886 | + | 0.546886i | 0.925539 | − | 0.378653i | \(-0.123613\pi\) |
−0.378653 | + | 0.925539i | \(0.623613\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −16.9706 | − | 16.9706i | −0.540179 | − | 0.540179i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.92820 | 0.220304 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 16.0000i | − | 0.508257i | −0.967170 | − | 0.254128i | \(-0.918211\pi\) | ||
0.967170 | − | 0.254128i | \(-0.0817886\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 24.4949 | − | 24.4949i | 0.777322 | − | 0.777322i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 36.7696 | − | 36.7696i | 1.16450 | − | 1.16450i | 0.181025 | − | 0.983479i | \(-0.442059\pi\) |
0.983479 | − | 0.181025i | \(-0.0579415\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 32.0000 | 1.01244 |
(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 | 1600.2.o.g.607.4 | yes | 8 | |
4.3 | odd | 2 | 1600.2.o.j.607.1 | yes | 8 | ||
5.2 | odd | 4 | 1600.2.o.j.543.2 | yes | 8 | ||
5.3 | odd | 4 | 1600.2.o.j.543.3 | yes | 8 | ||
5.4 | even | 2 | inner | 1600.2.o.g.607.1 | yes | 8 | |
8.3 | odd | 2 | 1600.2.o.j.607.3 | yes | 8 | ||
8.5 | even | 2 | inner | 1600.2.o.g.607.2 | yes | 8 | |
20.3 | even | 4 | inner | 1600.2.o.g.543.2 | yes | 8 | |
20.7 | even | 4 | inner | 1600.2.o.g.543.3 | yes | 8 | |
20.19 | odd | 2 | 1600.2.o.j.607.4 | yes | 8 | ||
40.3 | even | 4 | inner | 1600.2.o.g.543.4 | yes | 8 | |
40.13 | odd | 4 | 1600.2.o.j.543.1 | yes | 8 | ||
40.19 | odd | 2 | 1600.2.o.j.607.2 | yes | 8 | ||
40.27 | even | 4 | inner | 1600.2.o.g.543.1 | ✓ | 8 | |
40.29 | even | 2 | inner | 1600.2.o.g.607.3 | yes | 8 | |
40.37 | odd | 4 | 1600.2.o.j.543.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1600.2.o.g.543.1 | ✓ | 8 | 40.27 | even | 4 | inner | |
1600.2.o.g.543.2 | yes | 8 | 20.3 | even | 4 | inner | |
1600.2.o.g.543.3 | yes | 8 | 20.7 | even | 4 | inner | |
1600.2.o.g.543.4 | yes | 8 | 40.3 | even | 4 | inner | |
1600.2.o.g.607.1 | yes | 8 | 5.4 | even | 2 | inner | |
1600.2.o.g.607.2 | yes | 8 | 8.5 | even | 2 | inner | |
1600.2.o.g.607.3 | yes | 8 | 40.29 | even | 2 | inner | |
1600.2.o.g.607.4 | yes | 8 | 1.1 | even | 1 | trivial | |
1600.2.o.j.543.1 | yes | 8 | 40.13 | odd | 4 | ||
1600.2.o.j.543.2 | yes | 8 | 5.2 | odd | 4 | ||
1600.2.o.j.543.3 | yes | 8 | 5.3 | odd | 4 | ||
1600.2.o.j.543.4 | yes | 8 | 40.37 | odd | 4 | ||
1600.2.o.j.607.1 | yes | 8 | 4.3 | odd | 2 | ||
1600.2.o.j.607.2 | yes | 8 | 40.19 | odd | 2 | ||
1600.2.o.j.607.3 | yes | 8 | 8.3 | odd | 2 | ||
1600.2.o.j.607.4 | yes | 8 | 20.19 | odd | 2 |