Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [432,2,Mod(109,432)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(432, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("432.109");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 432 = 2^{4} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 432.k (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: | \(3.44953736732\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 325.1 | ||
Root | \(-0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 432.325 |
Dual form | 432.2.k.a.109.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).
\(n\) | \(271\) | \(325\) | \(353\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.41421i | − | 1.00000i | ||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.00000 | −1.00000 | ||||||||
\(5\) | 0.707107 | + | 0.707107i | 0.316228 | + | 0.316228i | 0.847316 | − | 0.531089i | \(-0.178217\pi\) |
−0.531089 | + | 0.847316i | \(0.678217\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.00000i | 1.13389i | 0.823754 | + | 0.566947i | \(0.191875\pi\) | ||||
−0.823754 | + | 0.566947i | \(0.808125\pi\) | |||||||
\(8\) | 2.82843i | 1.00000i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.00000 | − | 1.00000i | 0.316228 | − | 0.316228i | ||||
\(11\) | 0.707107 | + | 0.707107i | 0.213201 | + | 0.213201i | 0.805626 | − | 0.592425i | \(-0.201829\pi\) |
−0.592425 | + | 0.805626i | \(0.701829\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.00000 | + | 5.00000i | −1.38675 | + | 1.38675i | −0.554700 | + | 0.832050i | \(0.687167\pi\) |
−0.832050 | + | 0.554700i | \(0.812833\pi\) | |||||||
\(14\) | 4.24264 | 1.13389 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 1.00000 | ||||||||
\(17\) | 4.24264 | 1.02899 | 0.514496 | − | 0.857493i | \(-0.327979\pi\) | ||||
0.514496 | + | 0.857493i | \(0.327979\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.00000 | + | 2.00000i | −0.458831 | + | 0.458831i | −0.898272 | − | 0.439440i | \(-0.855177\pi\) |
0.439440 | + | 0.898272i | \(0.355177\pi\) | |||||||
\(20\) | −1.41421 | − | 1.41421i | −0.316228 | − | 0.316228i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | − | 1.00000i | 0.213201 | − | 0.213201i | ||||
\(23\) | 5.65685i | 1.17954i | 0.807573 | + | 0.589768i | \(0.200781\pi\) | ||||
−0.807573 | + | 0.589768i | \(0.799219\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 4.00000i | − | 0.800000i | ||||||
\(26\) | 7.07107 | + | 7.07107i | 1.38675 | + | 1.38675i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − | 6.00000i | − | 1.13389i | ||||||
\(29\) | 5.65685 | − | 5.65685i | 1.05045 | − | 1.05045i | 0.0517937 | − | 0.998658i | \(-0.483506\pi\) |
0.998658 | − | 0.0517937i | \(-0.0164938\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.00000 | −0.179605 | −0.0898027 | − | 0.995960i | \(-0.528624\pi\) | ||||
−0.0898027 | + | 0.995960i | \(0.528624\pi\) | |||||||
\(32\) | − | 5.65685i | − | 1.00000i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 6.00000i | − | 1.02899i | ||||||
\(35\) | −2.12132 | + | 2.12132i | −0.358569 | + | 0.358569i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.00000 | + | 4.00000i | 0.657596 | + | 0.657596i | 0.954811 | − | 0.297215i | \(-0.0960577\pi\) |
−0.297215 | + | 0.954811i | \(0.596058\pi\) | |||||||
\(38\) | 2.82843 | + | 2.82843i | 0.458831 | + | 0.458831i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.00000 | + | 2.00000i | −0.316228 | + | 0.316228i | ||||
\(41\) | − | 2.82843i | − | 0.441726i | −0.975305 | − | 0.220863i | \(-0.929113\pi\) | ||
0.975305 | − | 0.220863i | \(-0.0708874\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.00000 | + | 1.00000i | 0.152499 | + | 0.152499i | 0.779233 | − | 0.626734i | \(-0.215609\pi\) |
−0.626734 | + | 0.779233i | \(0.715609\pi\) | |||||||
\(44\) | −1.41421 | − | 1.41421i | −0.213201 | − | 0.213201i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 8.00000 | 1.17954 | ||||||||
\(47\) | −4.24264 | −0.618853 | −0.309426 | − | 0.950923i | \(-0.600137\pi\) | ||||
−0.309426 | + | 0.950923i | \(0.600137\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.00000 | −0.285714 | ||||||||
\(50\) | −5.65685 | −0.800000 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 10.0000 | − | 10.0000i | 1.38675 | − | 1.38675i | ||||
\(53\) | −7.77817 | − | 7.77817i | −1.06841 | − | 1.06841i | −0.997481 | − | 0.0709334i | \(-0.977402\pi\) |
−0.0709334 | − | 0.997481i | \(-0.522598\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.00000i | 0.134840i | ||||||||
\(56\) | −8.48528 | −1.13389 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −8.00000 | − | 8.00000i | −1.05045 | − | 1.05045i | ||||
\(59\) | 7.07107 | + | 7.07107i | 0.920575 | + | 0.920575i | 0.997070 | − | 0.0764953i | \(-0.0243730\pi\) |
−0.0764953 | + | 0.997070i | \(0.524373\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.00000 | + | 2.00000i | −0.256074 | + | 0.256074i | −0.823455 | − | 0.567381i | \(-0.807957\pi\) |
0.567381 | + | 0.823455i | \(0.307957\pi\) | |||||||
\(62\) | 1.41421i | 0.179605i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | −7.07107 | −0.877058 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.00000 | + | 5.00000i | −0.610847 | + | 0.610847i | −0.943167 | − | 0.332320i | \(-0.892169\pi\) |
0.332320 | + | 0.943167i | \(0.392169\pi\) | |||||||
\(68\) | −8.48528 | −1.02899 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3.00000 | + | 3.00000i | 0.358569 | + | 0.358569i | ||||
\(71\) | 1.41421i | 0.167836i | 0.996473 | + | 0.0839181i | \(0.0267434\pi\) | ||||
−0.996473 | + | 0.0839181i | \(0.973257\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.00000i | 0.351123i | 0.984468 | + | 0.175562i | \(0.0561742\pi\) | ||||
−0.984468 | + | 0.175562i | \(0.943826\pi\) | |||||||
\(74\) | 5.65685 | − | 5.65685i | 0.657596 | − | 0.657596i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.00000 | − | 4.00000i | 0.458831 | − | 0.458831i | ||||
\(77\) | −2.12132 | + | 2.12132i | −0.241747 | + | 0.241747i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.0000 | 1.57512 | 0.787562 | − | 0.616236i | \(-0.211343\pi\) | ||||
0.787562 | + | 0.616236i | \(0.211343\pi\) | |||||||
\(80\) | 2.82843 | + | 2.82843i | 0.316228 | + | 0.316228i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.00000 | −0.441726 | ||||||||
\(83\) | −4.94975 | + | 4.94975i | −0.543305 | + | 0.543305i | −0.924496 | − | 0.381191i | \(-0.875514\pi\) |
0.381191 | + | 0.924496i | \(0.375514\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.00000 | + | 3.00000i | 0.325396 | + | 0.325396i | ||||
\(86\) | 1.41421 | − | 1.41421i | 0.152499 | − | 0.152499i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.00000 | + | 2.00000i | −0.213201 | + | 0.213201i | ||||
\(89\) | − | 15.5563i | − | 1.64897i | −0.565884 | − | 0.824485i | \(-0.691465\pi\) | ||
0.565884 | − | 0.824485i | \(-0.308535\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −15.0000 | − | 15.0000i | −1.57243 | − | 1.57243i | ||||
\(92\) | − | 11.3137i | − | 1.17954i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.00000i | 0.618853i | ||||||||
\(95\) | −2.82843 | −0.290191 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.00000 | 0.507673 | 0.253837 | − | 0.967247i | \(-0.418307\pi\) | ||||
0.253837 | + | 0.967247i | \(0.418307\pi\) | |||||||
\(98\) | 2.82843i | 0.285714i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 8.00000i | 0.800000i | ||||||||
\(101\) | 4.94975 | + | 4.94975i | 0.492518 | + | 0.492518i | 0.909099 | − | 0.416581i | \(-0.136772\pi\) |
−0.416581 | + | 0.909099i | \(0.636772\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.00000i | 0.591198i | 0.955312 | + | 0.295599i | \(0.0955191\pi\) | ||||
−0.955312 | + | 0.295599i | \(0.904481\pi\) | |||||||
\(104\) | −14.1421 | − | 14.1421i | −1.38675 | − | 1.38675i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −11.0000 | + | 11.0000i | −1.06841 | + | 1.06841i | ||||
\(107\) | −12.0208 | − | 12.0208i | −1.16210 | − | 1.16210i | −0.984016 | − | 0.178080i | \(-0.943011\pi\) |
−0.178080 | − | 0.984016i | \(-0.556989\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.00000 | + | 8.00000i | −0.766261 | + | 0.766261i | −0.977446 | − | 0.211185i | \(-0.932268\pi\) |
0.211185 | + | 0.977446i | \(0.432268\pi\) | |||||||
\(110\) | 1.41421 | 0.134840 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 12.0000i | 1.13389i | ||||||||
\(113\) | 16.9706 | 1.59646 | 0.798228 | − | 0.602355i | \(-0.205771\pi\) | ||||
0.798228 | + | 0.602355i | \(0.205771\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.00000 | + | 4.00000i | −0.373002 | + | 0.373002i | ||||
\(116\) | −11.3137 | + | 11.3137i | −1.05045 | + | 1.05045i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 10.0000 | − | 10.0000i | 0.920575 | − | 0.920575i | ||||
\(119\) | 12.7279i | 1.16677i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 10.0000i | − | 0.909091i | ||||||
\(122\) | 2.82843 | + | 2.82843i | 0.256074 | + | 0.256074i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.00000 | 0.179605 | ||||||||
\(125\) | 6.36396 | − | 6.36396i | 0.569210 | − | 0.569210i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.0000 | 1.50851 | 0.754253 | − | 0.656584i | \(-0.227999\pi\) | ||||
0.754253 | + | 0.656584i | \(0.227999\pi\) | |||||||
\(128\) | 11.3137i | 1.00000i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 10.0000i | 0.877058i | ||||||||
\(131\) | −13.4350 | + | 13.4350i | −1.17382 | + | 1.17382i | −0.192534 | + | 0.981290i | \(0.561670\pi\) |
−0.981290 | + | 0.192534i | \(0.938330\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.00000 | − | 6.00000i | −0.520266 | − | 0.520266i | ||||
\(134\) | 7.07107 | + | 7.07107i | 0.610847 | + | 0.610847i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 12.0000i | 1.02899i | ||||||||
\(137\) | 1.41421i | 0.120824i | 0.998174 | + | 0.0604122i | \(0.0192415\pi\) | ||||
−0.998174 | + | 0.0604122i | \(0.980758\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.0000 | − | 14.0000i | −1.18746 | − | 1.18746i | −0.977766 | − | 0.209698i | \(-0.932752\pi\) |
−0.209698 | − | 0.977766i | \(-0.567248\pi\) | |||||||
\(140\) | 4.24264 | − | 4.24264i | 0.358569 | − | 0.358569i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.00000 | 0.167836 | ||||||||
\(143\) | −7.07107 | −0.591312 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.00000 | 0.664364 | ||||||||
\(146\) | 4.24264 | 0.351123 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −8.00000 | − | 8.00000i | −0.657596 | − | 0.657596i | ||||
\(149\) | −3.53553 | − | 3.53553i | −0.289642 | − | 0.289642i | 0.547297 | − | 0.836939i | \(-0.315657\pi\) |
−0.836939 | + | 0.547297i | \(0.815657\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.0000i | 1.22068i | 0.792139 | + | 0.610341i | \(0.208968\pi\) | ||||
−0.792139 | + | 0.610341i | \(0.791032\pi\) | |||||||
\(152\) | −5.65685 | − | 5.65685i | −0.458831 | − | 0.458831i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.00000 | + | 3.00000i | 0.241747 | + | 0.241747i | ||||
\(155\) | −0.707107 | − | 0.707107i | −0.0567962 | − | 0.0567962i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.00000 | + | 2.00000i | −0.159617 | + | 0.159617i | −0.782397 | − | 0.622780i | \(-0.786003\pi\) |
0.622780 | + | 0.782397i | \(0.286003\pi\) | |||||||
\(158\) | − | 19.7990i | − | 1.57512i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 4.00000 | − | 4.00000i | 0.316228 | − | 0.316228i | ||||
\(161\) | −16.9706 | −1.33747 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.00000 | − | 7.00000i | 0.548282 | − | 0.548282i | −0.377661 | − | 0.925944i | \(-0.623272\pi\) |
0.925944 | + | 0.377661i | \(0.123272\pi\) | |||||||
\(164\) | 5.65685i | 0.441726i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 7.00000 | + | 7.00000i | 0.543305 | + | 0.543305i | ||||
\(167\) | − | 15.5563i | − | 1.20379i | −0.798577 | − | 0.601893i | \(-0.794413\pi\) | ||
0.798577 | − | 0.601893i | \(-0.205587\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 37.0000i | − | 2.84615i | ||||||
\(170\) | 4.24264 | − | 4.24264i | 0.325396 | − | 0.325396i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.00000 | − | 2.00000i | −0.152499 | − | 0.152499i | ||||
\(173\) | 7.77817 | − | 7.77817i | 0.591364 | − | 0.591364i | −0.346636 | − | 0.938000i | \(-0.612676\pi\) |
0.938000 | + | 0.346636i | \(0.112676\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 12.0000 | 0.907115 | ||||||||
\(176\) | 2.82843 | + | 2.82843i | 0.213201 | + | 0.213201i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −22.0000 | −1.64897 | ||||||||
\(179\) | 12.0208 | − | 12.0208i | 0.898478 | − | 0.898478i | −0.0968236 | − | 0.995302i | \(-0.530868\pi\) |
0.995302 | + | 0.0968236i | \(0.0308683\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.00000 | + | 4.00000i | 0.297318 | + | 0.297318i | 0.839962 | − | 0.542645i | \(-0.182577\pi\) |
−0.542645 | + | 0.839962i | \(0.682577\pi\) | |||||||
\(182\) | −21.2132 | + | 21.2132i | −1.57243 | + | 1.57243i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −16.0000 | −1.17954 | ||||||||
\(185\) | 5.65685i | 0.415900i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.00000 | + | 3.00000i | 0.219382 | + | 0.219382i | ||||
\(188\) | 8.48528 | 0.618853 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.00000i | 0.290191i | ||||||||
\(191\) | 21.2132 | 1.53493 | 0.767467 | − | 0.641089i | \(-0.221517\pi\) | ||||
0.767467 | + | 0.641089i | \(0.221517\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.0000 | 1.22369 | 0.611843 | − | 0.790979i | \(-0.290428\pi\) | ||||
0.611843 | + | 0.790979i | \(0.290428\pi\) | |||||||
\(194\) | − | 7.07107i | − | 0.507673i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.00000 | 0.285714 | ||||||||
\(197\) | 9.19239 | + | 9.19239i | 0.654931 | + | 0.654931i | 0.954176 | − | 0.299246i | \(-0.0967350\pi\) |
−0.299246 | + | 0.954176i | \(0.596735\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 21.0000i | − | 1.48865i | −0.667817 | − | 0.744325i | \(-0.732771\pi\) | ||
0.667817 | − | 0.744325i | \(-0.267229\pi\) | |||||||
\(200\) | 11.3137 | 0.800000 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 7.00000 | − | 7.00000i | 0.492518 | − | 0.492518i | ||||
\(203\) | 16.9706 | + | 16.9706i | 1.19110 | + | 1.19110i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.00000 | − | 2.00000i | 0.139686 | − | 0.139686i | ||||
\(206\) | 8.48528 | 0.591198 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −20.0000 | + | 20.0000i | −1.38675 | + | 1.38675i | ||||
\(209\) | −2.82843 | −0.195646 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.0000 | − | 10.0000i | 0.688428 | − | 0.688428i | −0.273456 | − | 0.961884i | \(-0.588167\pi\) |
0.961884 | + | 0.273456i | \(0.0881668\pi\) | |||||||
\(212\) | 15.5563 | + | 15.5563i | 1.06841 | + | 1.06841i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −17.0000 | + | 17.0000i | −1.16210 | + | 1.16210i | ||||
\(215\) | 1.41421i | 0.0964486i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 3.00000i | − | 0.203653i | ||||||
\(218\) | 11.3137 | + | 11.3137i | 0.766261 | + | 0.766261i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − | 2.00000i | − | 0.134840i | ||||||
\(221\) | −21.2132 | + | 21.2132i | −1.42695 | + | 1.42695i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.00000 | 0.133930 | 0.0669650 | − | 0.997755i | \(-0.478668\pi\) | ||||
0.0669650 | + | 0.997755i | \(0.478668\pi\) | |||||||
\(224\) | 16.9706 | 1.13389 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − | 24.0000i | − | 1.59646i | ||||||
\(227\) | 9.89949 | − | 9.89949i | 0.657053 | − | 0.657053i | −0.297629 | − | 0.954682i | \(-0.596196\pi\) |
0.954682 | + | 0.297629i | \(0.0961959\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.00000 | + | 7.00000i | 0.462573 | + | 0.462573i | 0.899498 | − | 0.436925i | \(-0.143932\pi\) |
−0.436925 | + | 0.899498i | \(0.643932\pi\) | |||||||
\(230\) | 5.65685 | + | 5.65685i | 0.373002 | + | 0.373002i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 16.0000 | + | 16.0000i | 1.05045 | + | 1.05045i | ||||
\(233\) | 1.41421i | 0.0926482i | 0.998926 | + | 0.0463241i | \(0.0147507\pi\) | ||||
−0.998926 | + | 0.0463241i | \(0.985249\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.00000 | − | 3.00000i | −0.195698 | − | 0.195698i | ||||
\(236\) | −14.1421 | − | 14.1421i | −0.920575 | − | 0.920575i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 18.0000 | 1.16677 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.0000 | −1.03065 | −0.515325 | − | 0.856995i | \(-0.672329\pi\) | ||||
−0.515325 | + | 0.856995i | \(0.672329\pi\) | |||||||
\(242\) | −14.1421 | −0.909091 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4.00000 | − | 4.00000i | 0.256074 | − | 0.256074i | ||||
\(245\) | −1.41421 | − | 1.41421i | −0.0903508 | − | 0.0903508i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 20.0000i | − | 1.27257i | ||||||
\(248\) | − | 2.82843i | − | 0.179605i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −9.00000 | − | 9.00000i | −0.569210 | − | 0.569210i | ||||
\(251\) | 7.07107 | + | 7.07107i | 0.446322 | + | 0.446322i | 0.894130 | − | 0.447808i | \(-0.147795\pi\) |
−0.447808 | + | 0.894130i | \(0.647795\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.00000 | + | 4.00000i | −0.251478 | + | 0.251478i | ||||
\(254\) | − | 24.0416i | − | 1.50851i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 1.00000 | ||||||||
\(257\) | 21.2132 | 1.32324 | 0.661622 | − | 0.749838i | \(-0.269869\pi\) | ||||
0.661622 | + | 0.749838i | \(0.269869\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −12.0000 | + | 12.0000i | −0.745644 | + | 0.745644i | ||||
\(260\) | 14.1421 | 0.877058 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 19.0000 | + | 19.0000i | 1.17382 | + | 1.17382i | ||||
\(263\) | 14.1421i | 0.872041i | 0.899937 | + | 0.436021i | \(0.143613\pi\) | ||||
−0.899937 | + | 0.436021i | \(0.856387\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 11.0000i | − | 0.675725i | ||||||
\(266\) | −8.48528 | + | 8.48528i | −0.520266 | + | 0.520266i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 10.0000 | − | 10.0000i | 0.610847 | − | 0.610847i | ||||
\(269\) | 5.65685 | − | 5.65685i | 0.344904 | − | 0.344904i | −0.513303 | − | 0.858207i | \(-0.671578\pi\) |
0.858207 | + | 0.513303i | \(0.171578\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.0000 | −1.15417 | −0.577084 | − | 0.816685i | \(-0.695809\pi\) | ||||
−0.577084 | + | 0.816685i | \(0.695809\pi\) | |||||||
\(272\) | 16.9706 | 1.02899 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.00000 | 0.120824 | ||||||||
\(275\) | 2.82843 | − | 2.82843i | 0.170561 | − | 0.170561i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.00000 | − | 8.00000i | −0.480673 | − | 0.480673i | 0.424673 | − | 0.905347i | \(-0.360389\pi\) |
−0.905347 | + | 0.424673i | \(0.860389\pi\) | |||||||
\(278\) | −19.7990 | + | 19.7990i | −1.18746 | + | 1.18746i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −6.00000 | − | 6.00000i | −0.358569 | − | 0.358569i | ||||
\(281\) | 18.3848i | 1.09674i | 0.836235 | + | 0.548372i | \(0.184752\pi\) | ||||
−0.836235 | + | 0.548372i | \(0.815248\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.0000 | + | 10.0000i | 0.594438 | + | 0.594438i | 0.938827 | − | 0.344389i | \(-0.111914\pi\) |
−0.344389 | + | 0.938827i | \(0.611914\pi\) | |||||||
\(284\) | − | 2.82843i | − | 0.167836i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 10.0000i | 0.591312i | ||||||||
\(287\) | 8.48528 | 0.500870 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | − | 11.3137i | − | 0.664364i | ||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 6.00000i | − | 0.351123i | ||||||
\(293\) | 2.82843 | + | 2.82843i | 0.165238 | + | 0.165238i | 0.784883 | − | 0.619644i | \(-0.212723\pi\) |
−0.619644 | + | 0.784883i | \(0.712723\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.0000i | 0.582223i | ||||||||
\(296\) | −11.3137 | + | 11.3137i | −0.657596 | + | 0.657596i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −5.00000 | + | 5.00000i | −0.289642 | + | 0.289642i | ||||
\(299\) | −28.2843 | − | 28.2843i | −1.63572 | − | 1.63572i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.00000 | + | 3.00000i | −0.172917 | + | 0.172917i | ||||
\(302\) | 21.2132 | 1.22068 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −8.00000 | + | 8.00000i | −0.458831 | + | 0.458831i | ||||
\(305\) | −2.82843 | −0.161955 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.00000 | + | 5.00000i | −0.285365 | + | 0.285365i | −0.835244 | − | 0.549879i | \(-0.814674\pi\) |
0.549879 | + | 0.835244i | \(0.314674\pi\) | |||||||
\(308\) | 4.24264 | − | 4.24264i | 0.241747 | − | 0.241747i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.00000 | + | 1.00000i | −0.0567962 | + | 0.0567962i | ||||
\(311\) | − | 28.2843i | − | 1.60385i | −0.597422 | − | 0.801927i | \(-0.703808\pi\) | ||
0.597422 | − | 0.801927i | \(-0.296192\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.00000i | 0.508710i | 0.967111 | + | 0.254355i | \(0.0818632\pi\) | ||||
−0.967111 | + | 0.254355i | \(0.918137\pi\) | |||||||
\(314\) | 2.82843 | + | 2.82843i | 0.159617 | + | 0.159617i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −28.0000 | −1.57512 | ||||||||
\(317\) | −9.19239 | + | 9.19239i | −0.516296 | + | 0.516296i | −0.916449 | − | 0.400153i | \(-0.868957\pi\) |
0.400153 | + | 0.916449i | \(0.368957\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.00000 | 0.447914 | ||||||||
\(320\) | −5.65685 | − | 5.65685i | −0.316228 | − | 0.316228i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 24.0000i | 1.33747i | ||||||||
\(323\) | −8.48528 | + | 8.48528i | −0.472134 | + | 0.472134i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 20.0000 | + | 20.0000i | 1.10940 | + | 1.10940i | ||||
\(326\) | −9.89949 | − | 9.89949i | −0.548282 | − | 0.548282i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 8.00000 | 0.441726 | ||||||||
\(329\) | − | 12.7279i | − | 0.701713i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.00000 | + | 1.00000i | 0.0549650 | + | 0.0549650i | 0.734055 | − | 0.679090i | \(-0.237625\pi\) |
−0.679090 | + | 0.734055i | \(0.737625\pi\) | |||||||
\(332\) | 9.89949 | − | 9.89949i | 0.543305 | − | 0.543305i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −22.0000 | −1.20379 | ||||||||
\(335\) | −7.07107 | −0.386334 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.00000 | 0.435788 | 0.217894 | − | 0.975972i | \(-0.430081\pi\) | ||||
0.217894 | + | 0.975972i | \(0.430081\pi\) | |||||||
\(338\) | −52.3259 | −2.84615 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −6.00000 | − | 6.00000i | −0.325396 | − | 0.325396i | ||||
\(341\) | −0.707107 | − | 0.707107i | −0.0382920 | − | 0.0382920i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.0000i | 0.809924i | ||||||||
\(344\) | −2.82843 | + | 2.82843i | −0.152499 | + | 0.152499i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −11.0000 | − | 11.0000i | −0.591364 | − | 0.591364i | ||||
\(347\) | −3.53553 | − | 3.53553i | −0.189797 | − | 0.189797i | 0.605811 | − | 0.795609i | \(-0.292849\pi\) |
−0.795609 | + | 0.605811i | \(0.792849\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.0000 | + | 14.0000i | −0.749403 | + | 0.749403i | −0.974367 | − | 0.224964i | \(-0.927773\pi\) |
0.224964 | + | 0.974367i | \(0.427773\pi\) | |||||||
\(350\) | − | 16.9706i | − | 0.907115i | ||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.00000 | − | 4.00000i | 0.213201 | − | 0.213201i | ||||
\(353\) | −25.4558 | −1.35488 | −0.677439 | − | 0.735579i | \(-0.736910\pi\) | ||||
−0.677439 | + | 0.735579i | \(0.736910\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.00000 | + | 1.00000i | −0.0530745 | + | 0.0530745i | ||||
\(356\) | 31.1127i | 1.64897i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −17.0000 | − | 17.0000i | −0.898478 | − | 0.898478i | ||||
\(359\) | − | 24.0416i | − | 1.26887i | −0.772977 | − | 0.634434i | \(-0.781233\pi\) | ||
0.772977 | − | 0.634434i | \(-0.218767\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.0000i | 0.578947i | ||||||||
\(362\) | 5.65685 | − | 5.65685i | 0.297318 | − | 0.297318i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 30.0000 | + | 30.0000i | 1.57243 | + | 1.57243i | ||||
\(365\) | −2.12132 | + | 2.12132i | −0.111035 | + | 0.111035i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.00000 | 0.260998 | 0.130499 | − | 0.991448i | \(-0.458342\pi\) | ||||
0.130499 | + | 0.991448i | \(0.458342\pi\) | |||||||
\(368\) | 22.6274i | 1.17954i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 8.00000 | 0.415900 | ||||||||
\(371\) | 23.3345 | − | 23.3345i | 1.21147 | − | 1.21147i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.00000 | − | 5.00000i | −0.258890 | − | 0.258890i | 0.565712 | − | 0.824603i | \(-0.308601\pi\) |
−0.824603 | + | 0.565712i | \(0.808601\pi\) | |||||||
\(374\) | 4.24264 | − | 4.24264i | 0.219382 | − | 0.219382i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 12.0000i | − | 0.618853i | ||||||
\(377\) | 56.5685i | 2.91343i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.0000 | − | 14.0000i | −0.719132 | − | 0.719132i | 0.249296 | − | 0.968427i | \(-0.419801\pi\) |
−0.968427 | + | 0.249296i | \(0.919801\pi\) | |||||||
\(380\) | 5.65685 | 0.290191 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 30.0000i | − | 1.53493i | ||||||
\(383\) | −21.2132 | −1.08394 | −0.541972 | − | 0.840397i | \(-0.682322\pi\) | ||||
−0.541972 | + | 0.840397i | \(0.682322\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.00000 | −0.152894 | ||||||||
\(386\) | − | 24.0416i | − | 1.22369i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −10.0000 | −0.507673 | ||||||||
\(389\) | 0.707107 | + | 0.707107i | 0.0358517 | + | 0.0358517i | 0.724805 | − | 0.688954i | \(-0.241930\pi\) |
−0.688954 | + | 0.724805i | \(0.741930\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.0000i | 1.21373i | ||||||||
\(392\) | − | 5.65685i | − | 0.285714i | ||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 13.0000 | − | 13.0000i | 0.654931 | − | 0.654931i | ||||
\(395\) | 9.89949 | + | 9.89949i | 0.498098 | + | 0.498098i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.0000 | + | 11.0000i | −0.552074 | + | 0.552074i | −0.927039 | − | 0.374965i | \(-0.877655\pi\) |
0.374965 | + | 0.927039i | \(0.377655\pi\) | |||||||
\(398\) | −29.6985 | −1.48865 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | − | 16.0000i | − | 0.800000i | ||||||
\(401\) | −8.48528 | −0.423735 | −0.211867 | − | 0.977298i | \(-0.567954\pi\) | ||||
−0.211867 | + | 0.977298i | \(0.567954\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.00000 | − | 5.00000i | 0.249068 | − | 0.249068i | ||||
\(404\) | −9.89949 | − | 9.89949i | −0.492518 | − | 0.492518i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 24.0000 | − | 24.0000i | 1.19110 | − | 1.19110i | ||||
\(407\) | 5.65685i | 0.280400i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 21.0000i | 1.03838i | 0.854658 | + | 0.519192i | \(0.173767\pi\) | ||||
−0.854658 | + | 0.519192i | \(0.826233\pi\) | |||||||
\(410\) | −2.82843 | − | 2.82843i | −0.139686 | − | 0.139686i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 12.0000i | − | 0.591198i | ||||||
\(413\) | −21.2132 | + | 21.2132i | −1.04383 | + | 1.04383i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.00000 | −0.343616 | ||||||||
\(416\) | 28.2843 | + | 28.2843i | 1.38675 | + | 1.38675i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 4.00000i | 0.195646i | ||||||||
\(419\) | 18.3848 | − | 18.3848i | 0.898155 | − | 0.898155i | −0.0971178 | − | 0.995273i | \(-0.530962\pi\) |
0.995273 | + | 0.0971178i | \(0.0309624\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.00000 | − | 8.00000i | −0.389896 | − | 0.389896i | 0.484754 | − | 0.874650i | \(-0.338909\pi\) |
−0.874650 | + | 0.484754i | \(0.838909\pi\) | |||||||
\(422\) | −14.1421 | − | 14.1421i | −0.688428 | − | 0.688428i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 22.0000 | − | 22.0000i | 1.06841 | − | 1.06841i | ||||
\(425\) | − | 16.9706i | − | 0.823193i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.00000 | − | 6.00000i | −0.290360 | − | 0.290360i | ||||
\(428\) | 24.0416 | + | 24.0416i | 1.16210 | + | 1.16210i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.00000 | 0.0964486 | ||||||||
\(431\) | 4.24264 | 0.204361 | 0.102180 | − | 0.994766i | \(-0.467418\pi\) | ||||
0.102180 | + | 0.994766i | \(0.467418\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17.0000 | 0.816968 | 0.408484 | − | 0.912766i | \(-0.366058\pi\) | ||||
0.408484 | + | 0.912766i | \(0.366058\pi\) | |||||||
\(434\) | −4.24264 | −0.203653 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 16.0000 | − | 16.0000i | 0.766261 | − | 0.766261i | ||||
\(437\) | −11.3137 | − | 11.3137i | −0.541208 | − | 0.541208i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.0000i | 0.715911i | 0.933739 | + | 0.357955i | \(0.116526\pi\) | ||||
−0.933739 | + | 0.357955i | \(0.883474\pi\) | |||||||
\(440\) | −2.82843 | −0.134840 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 30.0000 | + | 30.0000i | 1.42695 | + | 1.42695i | ||||
\(443\) | −18.3848 | − | 18.3848i | −0.873487 | − | 0.873487i | 0.119364 | − | 0.992851i | \(-0.461915\pi\) |
−0.992851 | + | 0.119364i | \(0.961915\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11.0000 | − | 11.0000i | 0.521450 | − | 0.521450i | ||||
\(446\) | − | 2.82843i | − | 0.133930i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − | 24.0000i | − | 1.13389i | ||||||
\(449\) | 8.48528 | 0.400445 | 0.200223 | − | 0.979750i | \(-0.435833\pi\) | ||||
0.200223 | + | 0.979750i | \(0.435833\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.00000 | − | 2.00000i | 0.0941763 | − | 0.0941763i | ||||
\(452\) | −33.9411 | −1.59646 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −14.0000 | − | 14.0000i | −0.657053 | − | 0.657053i | ||||
\(455\) | − | 21.2132i | − | 0.994490i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.0000i | 0.701670i | 0.936437 | + | 0.350835i | \(0.114102\pi\) | ||||
−0.936437 | + | 0.350835i | \(0.885898\pi\) | |||||||
\(458\) | 9.89949 | − | 9.89949i | 0.462573 | − | 0.462573i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 8.00000 | − | 8.00000i | 0.373002 | − | 0.373002i | ||||
\(461\) | 16.2635 | − | 16.2635i | 0.757465 | − | 0.757465i | −0.218396 | − | 0.975860i | \(-0.570082\pi\) |
0.975860 | + | 0.218396i | \(0.0700823\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.00000 | −0.0464739 | −0.0232370 | − | 0.999730i | \(-0.507397\pi\) | ||||
−0.0232370 | + | 0.999730i | \(0.507397\pi\) | |||||||
\(464\) | 22.6274 | − | 22.6274i | 1.05045 | − | 1.05045i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.00000 | 0.0926482 | ||||||||
\(467\) | −9.19239 | + | 9.19239i | −0.425373 | + | 0.425373i | −0.887049 | − | 0.461676i | \(-0.847248\pi\) |
0.461676 | + | 0.887049i | \(0.347248\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.0000 | − | 15.0000i | −0.692636 | − | 0.692636i | ||||
\(470\) | −4.24264 | + | 4.24264i | −0.195698 | + | 0.195698i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −20.0000 | + | 20.0000i | −0.920575 | + | 0.920575i | ||||
\(473\) | 1.41421i | 0.0650256i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.00000 | + | 8.00000i | 0.367065 | + | 0.367065i | ||||
\(476\) | − | 25.4558i | − | 1.16677i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.24264 | 0.193851 | 0.0969256 | − | 0.995292i | \(-0.469099\pi\) | ||||
0.0969256 | + | 0.995292i | \(0.469099\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −40.0000 | −1.82384 | ||||||||
\(482\) | 22.6274i | 1.03065i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 20.0000i | 0.909091i | ||||||||
\(485\) | 3.53553 | + | 3.53553i | 0.160540 | + | 0.160540i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 12.0000i | − | 0.543772i | −0.962329 | − | 0.271886i | \(-0.912353\pi\) | ||
0.962329 | − | 0.271886i | \(-0.0876473\pi\) | |||||||
\(488\) | −5.65685 | − | 5.65685i | −0.256074 | − | 0.256074i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.00000 | + | 2.00000i | −0.0903508 | + | 0.0903508i | ||||
\(491\) | 9.19239 | + | 9.19239i | 0.414847 | + | 0.414847i | 0.883423 | − | 0.468576i | \(-0.155233\pi\) |
−0.468576 | + | 0.883423i | \(0.655233\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 24.0000 | − | 24.0000i | 1.08091 | − | 1.08091i | ||||
\(494\) | −28.2843 | −1.27257 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.00000 | −0.179605 | ||||||||
\(497\) | −4.24264 | −0.190308 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.0000 | + | 17.0000i | −0.761025 | + | 0.761025i | −0.976508 | − | 0.215483i | \(-0.930867\pi\) |
0.215483 | + | 0.976508i | \(0.430867\pi\) | |||||||
\(500\) | −12.7279 | + | 12.7279i | −0.569210 | + | 0.569210i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 10.0000 | − | 10.0000i | 0.446322 | − | 0.446322i | ||||
\(503\) | 14.1421i | 0.630567i | 0.948998 | + | 0.315283i | \(0.102100\pi\) | ||||
−0.948998 | + | 0.315283i | \(0.897900\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.00000i | 0.311496i | ||||||||
\(506\) | 5.65685 | + | 5.65685i | 0.251478 | + | 0.251478i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −34.0000 | −1.50851 | ||||||||
\(509\) | −21.9203 | + | 21.9203i | −0.971601 | + | 0.971601i | −0.999608 | − | 0.0280071i | \(-0.991084\pi\) |
0.0280071 | + | 0.999608i | \(0.491084\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.00000 | −0.398137 | ||||||||
\(512\) | − | 22.6274i | − | 1.00000i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 30.0000i | − | 1.32324i | ||||||
\(515\) | −4.24264 | + | 4.24264i | −0.186953 | + | 0.186953i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.00000 | − | 3.00000i | −0.131940 | − | 0.131940i | ||||
\(518\) | 16.9706 | + | 16.9706i | 0.745644 | + | 0.745644i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | − | 20.0000i | − | 0.877058i | ||||||
\(521\) | − | 15.5563i | − | 0.681536i | −0.940147 | − | 0.340768i | \(-0.889313\pi\) | ||
0.940147 | − | 0.340768i | \(-0.110687\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 25.0000 | + | 25.0000i | 1.09317 | + | 1.09317i | 0.995188 | + | 0.0979859i | \(0.0312400\pi\) |
0.0979859 | + | 0.995188i | \(0.468760\pi\) | |||||||
\(524\) | 26.8701 | − | 26.8701i | 1.17382 | − | 1.17382i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 20.0000 | 0.872041 | ||||||||
\(527\) | −4.24264 | −0.184812 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.00000 | −0.391304 | ||||||||
\(530\) | −15.5563 | −0.675725 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 12.0000 | + | 12.0000i | 0.520266 | + | 0.520266i | ||||
\(533\) | 14.1421 | + | 14.1421i | 0.612564 | + | 0.612564i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 17.0000i | − | 0.734974i | ||||||
\(536\) | −14.1421 | − | 14.1421i | −0.610847 | − | 0.610847i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −8.00000 | − | 8.00000i | −0.344904 | − | 0.344904i | ||||
\(539\) | −1.41421 | − | 1.41421i | −0.0609145 | − | 0.0609145i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.0000 | − | 22.0000i | 0.945854 | − | 0.945854i | −0.0527537 | − | 0.998608i | \(-0.516800\pi\) |
0.998608 | + | 0.0527537i | \(0.0167998\pi\) | |||||||
\(542\) | 26.8701i | 1.15417i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 24.0000i | − | 1.02899i | ||||||
\(545\) | −11.3137 | −0.484626 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.00000 | + | 5.00000i | −0.213785 | + | 0.213785i | −0.805873 | − | 0.592088i | \(-0.798304\pi\) |
0.592088 | + | 0.805873i | \(0.298304\pi\) | |||||||
\(548\) | − | 2.82843i | − | 0.120824i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4.00000 | − | 4.00000i | −0.170561 | − | 0.170561i | ||||
\(551\) | 22.6274i | 0.963960i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 42.0000i | 1.78602i | ||||||||
\(554\) | −11.3137 | + | 11.3137i | −0.480673 | + | 0.480673i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 28.0000 | + | 28.0000i | 1.18746 | + | 1.18746i | ||||
\(557\) | 16.2635 | − | 16.2635i | 0.689105 | − | 0.689105i | −0.272929 | − | 0.962034i | \(-0.587993\pi\) |
0.962034 | + | 0.272929i | \(0.0879925\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.0000 | −0.422955 | ||||||||
\(560\) | −8.48528 | + | 8.48528i | −0.358569 | + | 0.358569i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 26.0000 | 1.09674 | ||||||||
\(563\) | −13.4350 | + | 13.4350i | −0.566219 | + | 0.566219i | −0.931067 | − | 0.364848i | \(-0.881121\pi\) |
0.364848 | + | 0.931067i | \(0.381121\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 12.0000 | + | 12.0000i | 0.504844 | + | 0.504844i | ||||
\(566\) | 14.1421 | − | 14.1421i | 0.594438 | − | 0.594438i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.00000 | −0.167836 | ||||||||
\(569\) | 39.5980i | 1.66003i | 0.557738 | + | 0.830017i | \(0.311669\pi\) | ||||
−0.557738 | + | 0.830017i | \(0.688331\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.00000 | + | 7.00000i | 0.292941 | + | 0.292941i | 0.838241 | − | 0.545300i | \(-0.183584\pi\) |
−0.545300 | + | 0.838241i | \(0.683584\pi\) | |||||||
\(572\) | 14.1421 | 0.591312 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 12.0000i | − | 0.500870i | ||||||
\(575\) | 22.6274 | 0.943629 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −28.0000 | −1.16566 | −0.582828 | − | 0.812596i | \(-0.698054\pi\) | ||||
−0.582828 | + | 0.812596i | \(0.698054\pi\) | |||||||
\(578\) | − | 1.41421i | − | 0.0588235i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −16.0000 | −0.664364 | ||||||||
\(581\) | −14.8492 | − | 14.8492i | −0.616050 | − | 0.616050i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 11.0000i | − | 0.455573i | ||||||
\(584\) | −8.48528 | −0.351123 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.00000 | − | 4.00000i | 0.165238 | − | 0.165238i | ||||
\(587\) | 4.94975 | + | 4.94975i | 0.204298 | + | 0.204298i | 0.801839 | − | 0.597541i | \(-0.203855\pi\) |
−0.597541 | + | 0.801839i | \(0.703855\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.00000 | − | 2.00000i | 0.0824086 | − | 0.0824086i | ||||
\(590\) | 14.1421 | 0.582223 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 16.0000 | + | 16.0000i | 0.657596 | + | 0.657596i | ||||
\(593\) | 4.24264 | 0.174224 | 0.0871122 | − | 0.996199i | \(-0.472236\pi\) | ||||
0.0871122 | + | 0.996199i | \(0.472236\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.00000 | + | 9.00000i | −0.368964 | + | 0.368964i | ||||
\(596\) | 7.07107 | + | 7.07107i | 0.289642 | + | 0.289642i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −40.0000 | + | 40.0000i | −1.63572 | + | 1.63572i | ||||
\(599\) | − | 32.5269i | − | 1.32901i | −0.747282 | − | 0.664507i | \(-0.768642\pi\) | ||
0.747282 | − | 0.664507i | \(-0.231358\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.00000i | 0.367118i | 0.983009 | + | 0.183559i | \(0.0587618\pi\) | ||||
−0.983009 | + | 0.183559i | \(0.941238\pi\) | |||||||
\(602\) | 4.24264 | + | 4.24264i | 0.172917 | + | 0.172917i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 30.0000i | − | 1.22068i | ||||||
\(605\) | 7.07107 | − | 7.07107i | 0.287480 | − | 0.287480i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −28.0000 | −1.13648 | −0.568242 | − | 0.822861i | \(-0.692376\pi\) | ||||
−0.568242 | + | 0.822861i | \(0.692376\pi\) | |||||||
\(608\) | 11.3137 | + | 11.3137i | 0.458831 | + | 0.458831i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.00000i | 0.161955i | ||||||||
\(611\) | 21.2132 | − | 21.2132i | 0.858194 | − | 0.858194i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.00000 | + | 1.00000i | 0.0403896 | + | 0.0403896i | 0.727013 | − | 0.686624i | \(-0.240908\pi\) |
−0.686624 | + | 0.727013i | \(0.740908\pi\) | |||||||
\(614\) | 7.07107 | + | 7.07107i | 0.285365 | + | 0.285365i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −6.00000 | − | 6.00000i | −0.241747 | − | 0.241747i | ||||
\(617\) | − | 45.2548i | − | 1.82189i | −0.412527 | − | 0.910946i | \(-0.635354\pi\) | ||
0.412527 | − | 0.910946i | \(-0.364646\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 25.0000 | + | 25.0000i | 1.00483 | + | 1.00483i | 0.999988 | + | 0.00484658i | \(0.00154272\pi\) |
0.00484658 | + | 0.999988i | \(0.498457\pi\) | |||||||
\(620\) | 1.41421 | + | 1.41421i | 0.0567962 | + | 0.0567962i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −40.0000 | −1.60385 | ||||||||
\(623\) | 46.6690 | 1.86976 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.0000 | −0.440000 | ||||||||
\(626\) | 12.7279 | 0.508710 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.00000 | − | 4.00000i | 0.159617 | − | 0.159617i | ||||
\(629\) | 16.9706 | + | 16.9706i | 0.676661 | + | 0.676661i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 15.0000i | − | 0.597141i | −0.954388 | − | 0.298570i | \(-0.903490\pi\) | ||
0.954388 | − | 0.298570i | \(-0.0965097\pi\) | |||||||
\(632\) | 39.5980i | 1.57512i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 13.0000 | + | 13.0000i | 0.516296 | + | 0.516296i | ||||
\(635\) | 12.0208 | + | 12.0208i | 0.477032 | + | 0.477032i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 10.0000 | − | 10.0000i | 0.396214 | − | 0.396214i | ||||
\(638\) | − | 11.3137i | − | 0.447914i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −8.00000 | + | 8.00000i | −0.316228 | + | 0.316228i | ||||
\(641\) | −16.9706 | −0.670297 | −0.335148 | − | 0.942165i | \(-0.608786\pi\) | ||||
−0.335148 | + | 0.942165i | \(0.608786\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.0000 | − | 22.0000i | 0.867595 | − | 0.867595i | −0.124610 | − | 0.992206i | \(-0.539768\pi\) |
0.992206 | + | 0.124610i | \(0.0397681\pi\) | |||||||
\(644\) | 33.9411 | 1.33747 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 12.0000 | + | 12.0000i | 0.472134 | + | 0.472134i | ||||
\(647\) | 39.5980i | 1.55676i | 0.627795 | + | 0.778379i | \(0.283958\pi\) | ||||
−0.627795 | + | 0.778379i | \(0.716042\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.0000i | 0.392534i | ||||||||
\(650\) | 28.2843 | − | 28.2843i | 1.10940 | − | 1.10940i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −14.0000 | + | 14.0000i | −0.548282 | + | 0.548282i | ||||
\(653\) | −4.94975 | + | 4.94975i | −0.193699 | + | 0.193699i | −0.797292 | − | 0.603594i | \(-0.793735\pi\) |
0.603594 | + | 0.797292i | \(0.293735\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −19.0000 | −0.742391 | ||||||||
\(656\) | − | 11.3137i | − | 0.441726i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −18.0000 | −0.701713 | ||||||||
\(659\) | −13.4350 | + | 13.4350i | −0.523354 | + | 0.523354i | −0.918583 | − | 0.395228i | \(-0.870665\pi\) |
0.395228 | + | 0.918583i | \(0.370665\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.00000 | − | 2.00000i | −0.0777910 | − | 0.0777910i | 0.667141 | − | 0.744932i | \(-0.267518\pi\) |
−0.744932 | + | 0.667141i | \(0.767518\pi\) | |||||||
\(662\) | 1.41421 | − | 1.41421i | 0.0549650 | − | 0.0549650i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −14.0000 | − | 14.0000i | −0.543305 | − | 0.543305i | ||||
\(665\) | − | 8.48528i | − | 0.329045i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 32.0000 | + | 32.0000i | 1.23904 | + | 1.23904i | ||||
\(668\) | 31.1127i | 1.20379i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 10.0000i | 0.386334i | ||||||||
\(671\) | −2.82843 | −0.109190 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 41.0000 | 1.58043 | 0.790217 | − | 0.612827i | \(-0.209968\pi\) | ||||
0.790217 | + | 0.612827i | \(0.209968\pi\) | |||||||
\(674\) | − | 11.3137i | − | 0.435788i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 74.0000i | 2.84615i | ||||||||
\(677\) | 19.7990 | + | 19.7990i | 0.760937 | + | 0.760937i | 0.976492 | − | 0.215555i | \(-0.0691560\pi\) |
−0.215555 | + | 0.976492i | \(0.569156\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 15.0000i | 0.575647i | ||||||||
\(680\) | −8.48528 | + | 8.48528i | −0.325396 | + | 0.325396i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.00000 | + | 1.00000i | −0.0382920 | + | 0.0382920i | ||||
\(683\) | −5.65685 | − | 5.65685i | −0.216454 | − | 0.216454i | 0.590549 | − | 0.807002i | \(-0.298911\pi\) |
−0.807002 | + | 0.590549i | \(0.798911\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.00000 | + | 1.00000i | −0.0382080 | + | 0.0382080i | ||||
\(686\) | 21.2132 | 0.809924 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.00000 | + | 4.00000i | 0.152499 | + | 0.152499i | ||||
\(689\) | 77.7817 | 2.96325 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.0000 | − | 28.0000i | 1.06517 | − | 1.06517i | 0.0674474 | − | 0.997723i | \(-0.478515\pi\) |
0.997723 | − | 0.0674474i | \(-0.0214855\pi\) | |||||||
\(692\) | −15.5563 | + | 15.5563i | −0.591364 | + | 0.591364i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −5.00000 | + | 5.00000i | −0.189797 | + | 0.189797i | ||||
\(695\) | − | 19.7990i | − | 0.751018i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 12.0000i | − | 0.454532i | ||||||
\(698\) | 19.7990 | + | 19.7990i | 0.749403 | + | 0.749403i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −24.0000 | −0.907115 | ||||||||
\(701\) | −17.6777 | + | 17.6777i | −0.667676 | + | 0.667676i | −0.957178 | − | 0.289501i | \(-0.906511\pi\) |
0.289501 | + | 0.957178i | \(0.406511\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16.0000 | −0.603451 | ||||||||
\(704\) | −5.65685 | − | 5.65685i | −0.213201 | − | 0.213201i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 36.0000i | 1.35488i | ||||||||
\(707\) | −14.8492 | + | 14.8492i | −0.558463 | + | 0.558463i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14.0000 | − | 14.0000i | −0.525781 | − | 0.525781i | 0.393531 | − | 0.919312i | \(-0.371254\pi\) |
−0.919312 | + | 0.393531i | \(0.871254\pi\) | |||||||
\(710\) | 1.41421 | + | 1.41421i | 0.0530745 | + | 0.0530745i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 44.0000 | 1.64897 | ||||||||
\(713\) | − | 5.65685i | − | 0.211851i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.00000 | − | 5.00000i | −0.186989 | − | 0.186989i | ||||
\(716\) | −24.0416 | + | 24.0416i | −0.898478 | + | 0.898478i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −34.0000 | −1.26887 | ||||||||
\(719\) | −16.9706 | −0.632895 | −0.316448 | − | 0.948610i | \(-0.602490\pi\) | ||||
−0.316448 | + | 0.948610i | \(0.602490\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −18.0000 | −0.670355 | ||||||||
\(722\) | 15.5563 | 0.578947 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −8.00000 | − | 8.00000i | −0.297318 | − | 0.297318i | ||||
\(725\) | −22.6274 | − | 22.6274i | −0.840361 | − | 0.840361i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 45.0000i | − | 1.66896i | −0.551040 | − | 0.834479i | \(-0.685769\pi\) | ||
0.551040 | − | 0.834479i | \(-0.314231\pi\) | |||||||
\(728\) | 42.4264 | − | 42.4264i | 1.57243 | − | 1.57243i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 3.00000 | + | 3.00000i | 0.111035 | + | 0.111035i | ||||
\(731\) | 4.24264 | + | 4.24264i | 0.156920 | + | 0.156920i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.00000 | − | 4.00000i | 0.147743 | − | 0.147743i | −0.629366 | − | 0.777109i | \(-0.716685\pi\) |
0.777109 | + | 0.629366i | \(0.216685\pi\) | |||||||
\(734\) | − | 7.07107i | − | 0.260998i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 32.0000 | 1.17954 | ||||||||
\(737\) | −7.07107 | −0.260466 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 31.0000 | − | 31.0000i | 1.14035 | − | 1.14035i | 0.151968 | − | 0.988385i | \(-0.451439\pi\) |
0.988385 | − | 0.151968i | \(-0.0485611\pi\) | |||||||
\(740\) | − | 11.3137i | − | 0.415900i | ||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −33.0000 | − | 33.0000i | −1.21147 | − | 1.21147i | ||||
\(743\) | − | 7.07107i | − | 0.259412i | −0.991552 | − | 0.129706i | \(-0.958597\pi\) | ||
0.991552 | − | 0.129706i | \(-0.0414034\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 5.00000i | − | 0.183186i | ||||||
\(746\) | −7.07107 | + | 7.07107i | −0.258890 | + | 0.258890i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −6.00000 | − | 6.00000i | −0.219382 | − | 0.219382i | ||||
\(749\) | 36.0624 | − | 36.0624i | 1.31769 | − | 1.31769i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −43.0000 | −1.56909 | −0.784546 | − | 0.620070i | \(-0.787104\pi\) | ||||
−0.784546 | + | 0.620070i | \(0.787104\pi\) | |||||||
\(752\) | −16.9706 | −0.618853 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 80.0000 | 2.91343 | ||||||||
\(755\) | −10.6066 | + | 10.6066i | −0.386014 | + | 0.386014i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11.0000 | − | 11.0000i | −0.399802 | − | 0.399802i | 0.478361 | − | 0.878163i | \(-0.341231\pi\) |
−0.878163 | + | 0.478361i | \(0.841231\pi\) | |||||||
\(758\) | −19.7990 | + | 19.7990i | −0.719132 | + | 0.719132i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | − | 8.00000i | − | 0.290191i | ||||||
\(761\) | − | 2.82843i | − | 0.102530i | −0.998685 | − | 0.0512652i | \(-0.983675\pi\) | ||
0.998685 | − | 0.0512652i | \(-0.0163254\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −24.0000 | − | 24.0000i | −0.868858 | − | 0.868858i | ||||
\(764\) | −42.4264 | −1.53493 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 30.0000i | 1.08394i | ||||||||
\(767\) | −70.7107 | −2.55321 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 35.0000 | 1.26213 | 0.631066 | − | 0.775729i | \(-0.282618\pi\) | ||||
0.631066 | + | 0.775729i | \(0.282618\pi\) | |||||||
\(770\) | 4.24264i | 0.152894i | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −34.0000 | −1.22369 | ||||||||
\(773\) | 24.0416 | + | 24.0416i | 0.864717 | + | 0.864717i | 0.991882 | − | 0.127164i | \(-0.0405876\pi\) |
−0.127164 | + | 0.991882i | \(0.540588\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.00000i | 0.143684i | ||||||||
\(776\) | 14.1421i | 0.507673i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.00000 | − | 1.00000i | 0.0358517 | − | 0.0358517i | ||||
\(779\) | 5.65685 | + | 5.65685i | 0.202678 | + | 0.202678i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.00000 | + | 1.00000i | −0.0357828 | + | 0.0357828i | ||||
\(782\) | 33.9411 | 1.21373 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −8.00000 | −0.285714 | ||||||||
\(785\) | −2.82843 | −0.100951 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.0000 | + | 14.0000i | −0.499046 | + | 0.499046i | −0.911141 | − | 0.412095i | \(-0.864797\pi\) |
0.412095 | + | 0.911141i | \(0.364797\pi\) | |||||||
\(788\) | −18.3848 | − | 18.3848i | −0.654931 | − | 0.654931i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 14.0000 | − | 14.0000i | 0.498098 | − | 0.498098i | ||||
\(791\) | 50.9117i | 1.81021i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 20.0000i | − | 0.710221i | ||||||
\(794\) | 15.5563 | + | 15.5563i | 0.552074 | + | 0.552074i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 42.0000i | 1.48865i | ||||||||
\(797\) | 7.77817 | − | 7.77817i | 0.275517 | − | 0.275517i | −0.555799 | − | 0.831316i | \(-0.687588\pi\) |
0.831316 | + | 0.555799i | \(0.187588\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.0000 | −0.636794 | ||||||||
\(800\) | −22.6274 | −0.800000 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 12.0000i | 0.423735i | ||||||||
\(803\) | −2.12132 | + | 2.12132i | −0.0748598 | + | 0.0748598i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −12.0000 | − | 12.0000i | −0.422944 | − | 0.422944i | ||||
\(806\) | −7.07107 | − | 7.07107i | −0.249068 | − | 0.249068i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −14.0000 | + | 14.0000i | −0.492518 | + | 0.492518i | ||||
\(809\) | − | 15.5563i | − | 0.546932i | −0.961882 | − | 0.273466i | \(-0.911830\pi\) | ||
0.961882 | − | 0.273466i | \(-0.0881701\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8.00000 | − | 8.00000i | −0.280918 | − | 0.280918i | 0.552557 | − | 0.833475i | \(-0.313652\pi\) |
−0.833475 | + | 0.552557i | \(0.813652\pi\) | |||||||
\(812\) | −33.9411 | − | 33.9411i | −1.19110 | − | 1.19110i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 8.00000 | 0.280400 | ||||||||
\(815\) | 9.89949 | 0.346764 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.00000 | −0.139942 | ||||||||
\(818\) | 29.6985 | 1.03838 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.00000 | + | 4.00000i | −0.139686 | + | 0.139686i | ||||
\(821\) | −35.3553 | − | 35.3553i | −1.23391 | − | 1.23391i | −0.962450 | − | 0.271460i | \(-0.912493\pi\) |
−0.271460 | − | 0.962450i | \(-0.587507\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 9.00000i | − | 0.313720i | −0.987621 | − | 0.156860i | \(-0.949863\pi\) | ||
0.987621 | − | 0.156860i | \(-0.0501372\pi\) | |||||||
\(824\) | −16.9706 | −0.591198 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 30.0000 | + | 30.0000i | 1.04383 | + | 1.04383i | ||||
\(827\) | −9.89949 | − | 9.89949i | −0.344239 | − | 0.344239i | 0.513719 | − | 0.857958i | \(-0.328267\pi\) |
−0.857958 | + | 0.513719i | \(0.828267\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.0000 | − | 13.0000i | 0.451509 | − | 0.451509i | −0.444346 | − | 0.895855i | \(-0.646564\pi\) |
0.895855 | + | 0.444346i | \(0.146564\pi\) | |||||||
\(830\) | 9.89949i | 0.343616i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 40.0000 | − | 40.0000i | 1.38675 | − | 1.38675i | ||||
\(833\) | −8.48528 | −0.293998 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 11.0000 | − | 11.0000i | 0.380671 | − | 0.380671i | ||||
\(836\) | 5.65685 | 0.195646 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −26.0000 | − | 26.0000i | −0.898155 | − | 0.898155i | ||||
\(839\) | 9.89949i | 0.341769i | 0.985291 | + | 0.170884i | \(0.0546624\pi\) | ||||
−0.985291 | + | 0.170884i | \(0.945338\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 35.0000i | − | 1.20690i | ||||||
\(842\) | −11.3137 | + | 11.3137i | −0.389896 | + | 0.389896i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −20.0000 | + | 20.0000i | −0.688428 | + | 0.688428i | ||||
\(845\) | 26.1630 | − | 26.1630i | 0.900033 | − | 0.900033i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 30.0000 | 1.03081 | ||||||||
\(848\) | −31.1127 | − | 31.1127i | −1.06841 | − | 1.06841i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −24.0000 | −0.823193 | ||||||||
\(851\) | −22.6274 | + | 22.6274i | −0.775658 | + | 0.775658i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 31.0000 | + | 31.0000i | 1.06142 | + | 1.06142i | 0.997986 | + | 0.0634337i | \(0.0202051\pi\) |
0.0634337 | + | 0.997986i | \(0.479795\pi\) | |||||||
\(854\) | −8.48528 | + | 8.48528i | −0.290360 | + | 0.290360i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 34.0000 | − | 34.0000i | 1.16210 | − | 1.16210i | ||||
\(857\) | − | 24.0416i | − | 0.821246i | −0.911805 | − | 0.410623i | \(-0.865311\pi\) | ||
0.911805 | − | 0.410623i | \(-0.134689\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 28.0000 | + | 28.0000i | 0.955348 | + | 0.955348i | 0.999045 | − | 0.0436972i | \(-0.0139137\pi\) |
−0.0436972 | + | 0.999045i | \(0.513914\pi\) | |||||||
\(860\) | − | 2.82843i | − | 0.0964486i | ||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 6.00000i | − | 0.204361i | ||||||
\(863\) | −16.9706 | −0.577685 | −0.288842 | − | 0.957377i | \(-0.593270\pi\) | ||||
−0.288842 | + | 0.957377i | \(0.593270\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 11.0000 | 0.374011 | ||||||||
\(866\) | − | 24.0416i | − | 0.816968i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 6.00000i | 0.203653i | ||||||||
\(869\) | 9.89949 | + | 9.89949i | 0.335817 | + | 0.335817i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 50.0000i | − | 1.69419i | ||||||
\(872\) | −22.6274 | − | 22.6274i | −0.766261 | − | 0.766261i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −16.0000 | + | 16.0000i | −0.541208 | + | 0.541208i | ||||
\(875\) | 19.0919 | + | 19.0919i | 0.645423 | + | 0.645423i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 25.0000 | − | 25.0000i | 0.844190 | − | 0.844190i | −0.145211 | − | 0.989401i | \(-0.546386\pi\) |
0.989401 | + | 0.145211i | \(0.0463860\pi\) | |||||||
\(878\) | 21.2132 | 0.715911 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4.00000i | 0.134840i | ||||||||
\(881\) | 12.7279 | 0.428815 | 0.214407 | − | 0.976744i | \(-0.431218\pi\) | ||||
0.214407 | + | 0.976744i | \(0.431218\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.0000 | − | 28.0000i | 0.942275 | − | 0.942275i | −0.0561475 | − | 0.998422i | \(-0.517882\pi\) |
0.998422 | + | 0.0561475i | \(0.0178817\pi\) | |||||||
\(884\) | 42.4264 | − | 42.4264i | 1.42695 | − | 1.42695i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −26.0000 | + | 26.0000i | −0.873487 | + | 0.873487i | ||||
\(887\) | − | 7.07107i | − | 0.237423i | −0.992929 | − | 0.118712i | \(-0.962124\pi\) | ||
0.992929 | − | 0.118712i | \(-0.0378764\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 51.0000i | 1.71049i | ||||||||
\(890\) | −15.5563 | − | 15.5563i | −0.521450 | − | 0.521450i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4.00000 | −0.133930 | ||||||||
\(893\) | 8.48528 | − | 8.48528i | 0.283949 | − | 0.283949i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 17.0000 | 0.568247 | ||||||||
\(896\) | −33.9411 | −1.13389 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 12.0000i | − | 0.400445i | ||||||
\(899\) | −5.65685 | + | 5.65685i | −0.188667 | + | 0.188667i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −33.0000 | − | 33.0000i | −1.09939 | − | 1.09939i | ||||
\(902\) | −2.82843 | − | 2.82843i | −0.0941763 | − | 0.0941763i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 48.0000i | 1.59646i | ||||||||
\(905\) | 5.65685i | 0.188040i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.00000 | − | 2.00000i | −0.0664089 | − | 0.0664089i | 0.673122 | − | 0.739531i | \(-0.264953\pi\) |
−0.739531 | + | 0.673122i | \(0.764953\pi\) | |||||||
\(908\) | −19.7990 | + | 19.7990i | −0.657053 | + | 0.657053i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −30.0000 | −0.994490 | ||||||||
\(911\) | 12.7279 | 0.421695 | 0.210847 | − | 0.977519i | \(-0.432378\pi\) | ||||
0.210847 | + | 0.977519i | \(0.432378\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.00000 | −0.231666 | ||||||||
\(914\) | 21.2132 | 0.701670 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −14.0000 | − | 14.0000i | −0.462573 | − | 0.462573i | ||||
\(917\) | −40.3051 | − | 40.3051i | −1.33099 | − | 1.33099i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 21.0000i | 0.692726i | 0.938101 | + | 0.346363i | \(0.112583\pi\) | ||||
−0.938101 | + | 0.346363i | \(0.887417\pi\) | |||||||
\(920\) | −11.3137 | − | 11.3137i | −0.373002 | − | 0.373002i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −23.0000 | − | 23.0000i | −0.757465 | − | 0.757465i | ||||
\(923\) | −7.07107 | − | 7.07107i | −0.232747 | − | 0.232747i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 16.0000 | − | 16.0000i | 0.526077 | − | 0.526077i | ||||
\(926\) | 1.41421i | 0.0464739i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −32.0000 | − | 32.0000i | −1.05045 | − | 1.05045i | ||||
\(929\) | −59.3970 | −1.94875 | −0.974376 | − | 0.224927i | \(-0.927786\pi\) | ||||
−0.974376 | + | 0.224927i | \(0.927786\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.00000 | − | 4.00000i | 0.131095 | − | 0.131095i | ||||
\(932\) | − | 2.82843i | − | 0.0926482i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 13.0000 | + | 13.0000i | 0.425373 | + | 0.425373i | ||||
\(935\) | 4.24264i | 0.138749i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 15.0000i | 0.490029i | 0.969519 | + | 0.245014i | \(0.0787927\pi\) | ||||
−0.969519 | + | 0.245014i | \(0.921207\pi\) | |||||||
\(938\) | −21.2132 | + | 21.2132i | −0.692636 | + | 0.692636i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 6.00000 | + | 6.00000i | 0.195698 | + | 0.195698i | ||||
\(941\) | −4.94975 | + | 4.94975i | −0.161357 | + | 0.161357i | −0.783168 | − | 0.621811i | \(-0.786397\pi\) |
0.621811 | + | 0.783168i | \(0.286397\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16.0000 | 0.521032 | ||||||||
\(944\) | 28.2843 | + | 28.2843i | 0.920575 | + | 0.920575i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.00000 | 0.0650256 | ||||||||
\(947\) | −13.4350 | + | 13.4350i | −0.436580 | + | 0.436580i | −0.890859 | − | 0.454279i | \(-0.849897\pi\) |
0.454279 | + | 0.890859i | \(0.349897\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15.0000 | − | 15.0000i | −0.486921 | − | 0.486921i | ||||
\(950\) | 11.3137 | − | 11.3137i | 0.367065 | − | 0.367065i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −36.0000 | −1.16677 | ||||||||
\(953\) | 5.65685i | 0.183243i | 0.995794 | + | 0.0916217i | \(0.0292051\pi\) | ||||
−0.995794 | + | 0.0916217i | \(0.970795\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 15.0000 | + | 15.0000i | 0.485389 | + | 0.485389i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 6.00000i | − | 0.193851i | ||||||
\(959\) | −4.24264 | −0.137002 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.0000 | −0.967742 | ||||||||
\(962\) | 56.5685i | 1.82384i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 32.0000 | 1.03065 | ||||||||
\(965\) | 12.0208 | + | 12.0208i | 0.386964 | + | 0.386964i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 33.0000i | − | 1.06121i | −0.847620 | − | 0.530604i | \(-0.821965\pi\) | ||
0.847620 | − | 0.530604i | \(-0.178035\pi\) | |||||||
\(968\) | 28.2843 | 0.909091 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 5.00000 | − | 5.00000i | 0.160540 | − | 0.160540i | ||||
\(971\) | 4.94975 | + | 4.94975i | 0.158845 | + | 0.158845i | 0.782055 | − | 0.623210i | \(-0.214172\pi\) |
−0.623210 | + | 0.782055i | \(0.714172\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 42.0000 | − | 42.0000i | 1.34646 | − | 1.34646i | ||||
\(974\) | −16.9706 | −0.543772 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.00000 | + | 8.00000i | −0.256074 | + | 0.256074i | ||||
\(977\) | 12.7279 | 0.407202 | 0.203601 | − | 0.979054i | \(-0.434735\pi\) | ||||
0.203601 | + | 0.979054i | \(0.434735\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11.0000 | − | 11.0000i | 0.351562 | − | 0.351562i | ||||
\(980\) | 2.82843 | + | 2.82843i | 0.0903508 | + | 0.0903508i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 13.0000 | − | 13.0000i | 0.414847 | − | 0.414847i | ||||
\(983\) | 26.8701i | 0.857022i | 0.903537 | + | 0.428511i | \(0.140962\pi\) | ||||
−0.903537 | + | 0.428511i | \(0.859038\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.0000i | 0.414214i | ||||||||
\(986\) | −33.9411 | − | 33.9411i | −1.08091 | − | 1.08091i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 40.0000i | 1.27257i | ||||||||
\(989\) | −5.65685 | + | 5.65685i | −0.179878 | + | 0.179878i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.0000 | −0.412959 | −0.206479 | − | 0.978451i | \(-0.566201\pi\) | ||||
−0.206479 | + | 0.978451i | \(0.566201\pi\) | |||||||
\(992\) | 5.65685i | 0.179605i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 6.00000i | 0.190308i | ||||||||
\(995\) | 14.8492 | − | 14.8492i | 0.470753 | − | 0.470753i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.00000 | + | 1.00000i | 0.0316703 | + | 0.0316703i | 0.722765 | − | 0.691094i | \(-0.242871\pi\) |
−0.691094 | + | 0.722765i | \(0.742871\pi\) | |||||||
\(998\) | 24.0416 | + | 24.0416i | 0.761025 | + | 0.761025i | ||||
\(999\) | 0 | 0 |
(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 | 432.2.k.a.325.1 | yes | 4 | |
3.2 | odd | 2 | inner | 432.2.k.a.325.2 | yes | 4 | |
4.3 | odd | 2 | 1728.2.k.a.433.2 | 4 | |||
12.11 | even | 2 | 1728.2.k.a.433.1 | 4 | |||
16.3 | odd | 4 | 1728.2.k.a.1297.2 | 4 | |||
16.13 | even | 4 | inner | 432.2.k.a.109.2 | yes | 4 | |
48.29 | odd | 4 | inner | 432.2.k.a.109.1 | ✓ | 4 | |
48.35 | even | 4 | 1728.2.k.a.1297.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
432.2.k.a.109.1 | ✓ | 4 | 48.29 | odd | 4 | inner | |
432.2.k.a.109.2 | yes | 4 | 16.13 | even | 4 | inner | |
432.2.k.a.325.1 | yes | 4 | 1.1 | even | 1 | trivial | |
432.2.k.a.325.2 | yes | 4 | 3.2 | odd | 2 | inner | |
1728.2.k.a.433.1 | 4 | 12.11 | even | 2 | |||
1728.2.k.a.433.2 | 4 | 4.3 | odd | 2 | |||
1728.2.k.a.1297.1 | 4 | 48.35 | even | 4 | |||
1728.2.k.a.1297.2 | 4 | 16.3 | odd | 4 |