Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [315,2,Mod(118,315)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(315, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("315.118");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.p (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: | \(2.51528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(i, \sqrt{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 35) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 118.1 | ||
Root | \(-1.58114 + 1.58114i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 315.118 |
Dual form | 315.2.p.c.307.1 |
$q$-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 \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(136\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | − | 1.00000i | 0.707107 | − | 0.707107i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.58114 | + | 1.58114i | −0.707107 | + | 0.707107i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.58114 | + | 0.581139i | 0.975579 | + | 0.219650i | ||||
\(8\) | 2.00000 | + | 2.00000i | 0.707107 | + | 0.707107i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.16228i | 1.00000i | ||||||||
\(11\) | 1.00000 | 0.301511 | 0.150756 | − | 0.988571i | \(-0.451829\pi\) | ||||
0.150756 | + | 0.988571i | \(0.451829\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.58114 | − | 1.58114i | 0.438529 | − | 0.438529i | −0.452988 | − | 0.891517i | \(-0.649642\pi\) |
0.891517 | + | 0.452988i | \(0.149642\pi\) | |||||||
\(14\) | 3.16228 | − | 2.00000i | 0.845154 | − | 0.534522i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 1.00000 | ||||||||
\(17\) | 1.58114 | + | 1.58114i | 0.383482 | + | 0.383482i | 0.872355 | − | 0.488873i | \(-0.162592\pi\) |
−0.488873 | + | 0.872355i | \(0.662592\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.16228 | −0.725476 | −0.362738 | − | 0.931891i | \(-0.618158\pi\) | ||||
−0.362738 | + | 0.931891i | \(0.618158\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | − | 1.00000i | 0.213201 | − | 0.213201i | ||||
\(23\) | −2.00000 | − | 2.00000i | −0.417029 | − | 0.417029i | 0.467150 | − | 0.884178i | \(-0.345281\pi\) |
−0.884178 | + | 0.467150i | \(0.845281\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 5.00000i | − | 1.00000i | ||||||
\(26\) | − | 3.16228i | − | 0.620174i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.00000i | 0.557086i | 0.960424 | + | 0.278543i | \(0.0898515\pi\) | ||||
−0.960424 | + | 0.278543i | \(0.910149\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 3.16228i | − | 0.567962i | −0.958830 | − | 0.283981i | \(-0.908345\pi\) | ||
0.958830 | − | 0.283981i | \(-0.0916552\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.16228 | 0.542326 | ||||||||
\(35\) | −5.00000 | + | 3.16228i | −0.845154 | + | 0.534522i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.00000 | + | 6.00000i | −0.986394 | + | 0.986394i | −0.999909 | − | 0.0135147i | \(-0.995698\pi\) |
0.0135147 | + | 0.999909i | \(0.495698\pi\) | |||||||
\(38\) | −3.16228 | + | 3.16228i | −0.512989 | + | 0.512989i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −6.32456 | −1.00000 | ||||||||
\(41\) | − | 9.48683i | − | 1.48159i | −0.671729 | − | 0.740797i | \(-0.734448\pi\) | ||
0.671729 | − | 0.740797i | \(-0.265552\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.00000 | − | 3.00000i | −0.457496 | − | 0.457496i | 0.440337 | − | 0.897833i | \(-0.354859\pi\) |
−0.897833 | + | 0.440337i | \(0.854859\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.00000 | −0.589768 | ||||||||
\(47\) | −4.74342 | − | 4.74342i | −0.691898 | − | 0.691898i | 0.270751 | − | 0.962649i | \(-0.412728\pi\) |
−0.962649 | + | 0.270751i | \(0.912728\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.32456 | + | 3.00000i | 0.903508 | + | 0.428571i | ||||
\(50\) | −5.00000 | − | 5.00000i | −0.707107 | − | 0.707107i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.00000 | − | 1.00000i | −0.137361 | − | 0.137361i | 0.635083 | − | 0.772444i | \(-0.280966\pi\) |
−0.772444 | + | 0.635083i | \(0.780966\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.58114 | + | 1.58114i | −0.213201 | + | 0.213201i | ||||
\(56\) | 4.00000 | + | 6.32456i | 0.534522 | + | 0.845154i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.00000 | + | 3.00000i | 0.393919 | + | 0.393919i | ||||
\(59\) | 9.48683 | 1.23508 | 0.617540 | − | 0.786539i | \(-0.288129\pi\) | ||||
0.617540 | + | 0.786539i | \(0.288129\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 6.32456i | − | 0.809776i | −0.914366 | − | 0.404888i | \(-0.867310\pi\) | ||
0.914366 | − | 0.404888i | \(-0.132690\pi\) | |||||||
\(62\) | −3.16228 | − | 3.16228i | −0.401610 | − | 0.401610i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000i | 1.00000i | ||||||||
\(65\) | 5.00000i | 0.620174i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.00000 | + | 1.00000i | −0.122169 | + | 0.122169i | −0.765548 | − | 0.643379i | \(-0.777532\pi\) |
0.643379 | + | 0.765548i | \(0.277532\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.83772 | + | 8.16228i | −0.219650 | + | 0.975579i | ||||
\(71\) | 6.00000 | 0.712069 | 0.356034 | − | 0.934473i | \(-0.384129\pi\) | ||||
0.356034 | + | 0.934473i | \(0.384129\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(74\) | 12.0000i | 1.39497i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.58114 | + | 0.581139i | 0.294148 | + | 0.0662269i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 13.0000i | − | 1.46261i | −0.682048 | − | 0.731307i | \(-0.738911\pi\) | ||
0.682048 | − | 0.731307i | \(-0.261089\pi\) | |||||||
\(80\) | −6.32456 | + | 6.32456i | −0.707107 | + | 0.707107i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −9.48683 | − | 9.48683i | −1.04765 | − | 1.04765i | ||||
\(83\) | −3.16228 | + | 3.16228i | −0.347105 | + | 0.347105i | −0.859030 | − | 0.511925i | \(-0.828933\pi\) |
0.511925 | + | 0.859030i | \(0.328933\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.00000 | −0.542326 | ||||||||
\(86\) | −6.00000 | −0.646997 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.00000 | + | 2.00000i | 0.213201 | + | 0.213201i | ||||
\(89\) | −6.32456 | −0.670402 | −0.335201 | − | 0.942147i | \(-0.608804\pi\) | ||||
−0.335201 | + | 0.942147i | \(0.608804\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.00000 | − | 3.16228i | 0.524142 | − | 0.331497i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −9.48683 | −0.978492 | ||||||||
\(95\) | 5.00000 | − | 5.00000i | 0.512989 | − | 0.512989i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.58114 | + | 1.58114i | 0.160540 | + | 0.160540i | 0.782806 | − | 0.622266i | \(-0.213788\pi\) |
−0.622266 | + | 0.782806i | \(0.713788\pi\) | |||||||
\(98\) | 9.32456 | − | 3.32456i | 0.941922 | − | 0.335831i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 3.16228i | − | 0.314658i | −0.987546 | − | 0.157329i | \(-0.949712\pi\) | ||
0.987546 | − | 0.157329i | \(-0.0502884\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.0680 | + | 11.0680i | −1.09056 | + | 1.09056i | −0.0950911 | + | 0.995469i | \(0.530314\pi\) |
−0.995469 | + | 0.0950911i | \(0.969686\pi\) | |||||||
\(104\) | 6.32456 | 0.620174 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.00000 | −0.194257 | ||||||||
\(107\) | 3.00000 | − | 3.00000i | 0.290021 | − | 0.290021i | −0.547068 | − | 0.837088i | \(-0.684256\pi\) |
0.837088 | + | 0.547068i | \(0.184256\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.00000i | 0.670478i | 0.942133 | + | 0.335239i | \(0.108817\pi\) | ||||
−0.942133 | + | 0.335239i | \(0.891183\pi\) | |||||||
\(110\) | 3.16228i | 0.301511i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 10.3246 | + | 2.32456i | 0.975579 | + | 0.219650i | ||||
\(113\) | −12.0000 | − | 12.0000i | −1.12887 | − | 1.12887i | −0.990362 | − | 0.138503i | \(-0.955771\pi\) |
−0.138503 | − | 0.990362i | \(-0.544229\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.32456 | 0.589768 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 9.48683 | − | 9.48683i | 0.873334 | − | 0.873334i | ||||
\(119\) | 3.16228 | + | 5.00000i | 0.289886 | + | 0.458349i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.0000 | −0.909091 | ||||||||
\(122\) | −6.32456 | − | 6.32456i | −0.572598 | − | 0.572598i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.90569 | + | 7.90569i | 0.707107 | + | 0.707107i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.00000 | − | 9.00000i | 0.798621 | − | 0.798621i | −0.184257 | − | 0.982878i | \(-0.558988\pi\) |
0.982878 | + | 0.184257i | \(0.0589879\pi\) | |||||||
\(128\) | 8.00000 | + | 8.00000i | 0.707107 | + | 0.707107i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 5.00000 | + | 5.00000i | 0.438529 | + | 0.438529i | ||||
\(131\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.16228 | − | 1.83772i | −0.707759 | − | 0.159351i | ||||
\(134\) | 2.00000i | 0.172774i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.32456i | 0.542326i | ||||||||
\(137\) | −2.00000 | + | 2.00000i | −0.170872 | + | 0.170872i | −0.787362 | − | 0.616491i | \(-0.788554\pi\) |
0.616491 | + | 0.787362i | \(0.288554\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.9737 | 1.60933 | 0.804663 | − | 0.593732i | \(-0.202346\pi\) | ||||
0.804663 | + | 0.593732i | \(0.202346\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 6.00000 | − | 6.00000i | 0.503509 | − | 0.503509i | ||||
\(143\) | 1.58114 | − | 1.58114i | 0.132221 | − | 0.132221i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.74342 | − | 4.74342i | −0.393919 | − | 0.393919i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 12.0000i | − | 0.983078i | −0.870855 | − | 0.491539i | \(-0.836434\pi\) | ||
0.870855 | − | 0.491539i | \(-0.163566\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.00000 | 0.732410 | 0.366205 | − | 0.930534i | \(-0.380657\pi\) | ||||
0.366205 | + | 0.930534i | \(0.380657\pi\) | |||||||
\(152\) | −6.32456 | − | 6.32456i | −0.512989 | − | 0.512989i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.16228 | − | 2.00000i | 0.254824 | − | 0.161165i | ||||
\(155\) | 5.00000 | + | 5.00000i | 0.401610 | + | 0.401610i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.32456 | − | 6.32456i | −0.504754 | − | 0.504754i | 0.408157 | − | 0.912912i | \(-0.366172\pi\) |
−0.912912 | + | 0.408157i | \(0.866172\pi\) | |||||||
\(158\) | −13.0000 | − | 13.0000i | −1.03422 | − | 1.03422i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.00000 | − | 6.32456i | −0.315244 | − | 0.498445i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.00000 | + | 6.00000i | 0.469956 | + | 0.469956i | 0.901900 | − | 0.431944i | \(-0.142172\pi\) |
−0.431944 | + | 0.901900i | \(0.642172\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.32456i | 0.490881i | ||||||||
\(167\) | 11.0680 | + | 11.0680i | 0.856465 | + | 0.856465i | 0.990920 | − | 0.134454i | \(-0.0429282\pi\) |
−0.134454 | + | 0.990920i | \(0.542928\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.00000i | 0.615385i | ||||||||
\(170\) | −5.00000 | + | 5.00000i | −0.383482 | + | 0.383482i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −11.0680 | + | 11.0680i | −0.841482 | + | 0.841482i | −0.989052 | − | 0.147569i | \(-0.952855\pi\) |
0.147569 | + | 0.989052i | \(0.452855\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.90569 | − | 12.9057i | 0.219650 | − | 0.975579i | ||||
\(176\) | 4.00000 | 0.301511 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −6.32456 | + | 6.32456i | −0.474045 | + | 0.474045i | ||||
\(179\) | − | 6.00000i | − | 0.448461i | −0.974536 | − | 0.224231i | \(-0.928013\pi\) | ||
0.974536 | − | 0.224231i | \(-0.0719869\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.1359i | 1.64535i | 0.568511 | + | 0.822676i | \(0.307520\pi\) | ||||
−0.568511 | + | 0.822676i | \(0.692480\pi\) | |||||||
\(182\) | 1.83772 | − | 8.16228i | 0.136221 | − | 0.605028i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 8.00000i | − | 0.589768i | ||||||
\(185\) | − | 18.9737i | − | 1.39497i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.58114 | + | 1.58114i | 0.115624 | + | 0.115624i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | − | 10.0000i | − | 0.725476i | ||||||
\(191\) | 3.00000 | 0.217072 | 0.108536 | − | 0.994092i | \(-0.465384\pi\) | ||||
0.108536 | + | 0.994092i | \(0.465384\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.00000 | − | 8.00000i | −0.575853 | − | 0.575853i | 0.357905 | − | 0.933758i | \(-0.383491\pi\) |
−0.933758 | + | 0.357905i | \(0.883491\pi\) | |||||||
\(194\) | 3.16228 | 0.227038 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.00000 | − | 1.00000i | 0.0712470 | − | 0.0712470i | −0.670585 | − | 0.741832i | \(-0.733957\pi\) |
0.741832 | + | 0.670585i | \(0.233957\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.48683 | 0.672504 | 0.336252 | − | 0.941772i | \(-0.390841\pi\) | ||||
0.336252 | + | 0.941772i | \(0.390841\pi\) | |||||||
\(200\) | 10.0000 | − | 10.0000i | 0.707107 | − | 0.707107i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3.16228 | − | 3.16228i | −0.222497 | − | 0.222497i | ||||
\(203\) | −1.74342 | + | 7.74342i | −0.122364 | + | 0.543481i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 15.0000 | + | 15.0000i | 1.04765 | + | 1.04765i | ||||
\(206\) | 22.1359i | 1.54228i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 6.32456 | − | 6.32456i | 0.438529 | − | 0.438529i | ||||
\(209\) | −3.16228 | −0.218739 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.0000 | 1.17033 | 0.585164 | − | 0.810915i | \(-0.301030\pi\) | ||||
0.585164 | + | 0.810915i | \(0.301030\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 6.00000i | − | 0.410152i | ||||||
\(215\) | 9.48683 | 0.646997 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.83772 | − | 8.16228i | 0.124753 | − | 0.554092i | ||||
\(218\) | 7.00000 | + | 7.00000i | 0.474100 | + | 0.474100i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.00000 | 0.336336 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.2302 | + | 14.2302i | −0.952928 | + | 0.952928i | −0.998941 | − | 0.0460129i | \(-0.985348\pi\) |
0.0460129 | + | 0.998941i | \(0.485348\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −24.0000 | −1.59646 | ||||||||
\(227\) | −1.58114 | − | 1.58114i | −0.104944 | − | 0.104944i | 0.652685 | − | 0.757629i | \(-0.273642\pi\) |
−0.757629 | + | 0.652685i | \(0.773642\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.8114 | −1.04485 | −0.522423 | − | 0.852686i | \(-0.674972\pi\) | ||||
−0.522423 | + | 0.852686i | \(0.674972\pi\) | |||||||
\(230\) | 6.32456 | − | 6.32456i | 0.417029 | − | 0.417029i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.00000 | + | 6.00000i | −0.393919 | + | 0.393919i | ||||
\(233\) | 18.0000 | + | 18.0000i | 1.17922 | + | 1.17922i | 0.979943 | + | 0.199276i | \(0.0638589\pi\) |
0.199276 | + | 0.979943i | \(0.436141\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 15.0000 | 0.978492 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 8.16228 | + | 1.83772i | 0.529082 | + | 0.119122i | ||||
\(239\) | 19.0000i | 1.22901i | 0.788914 | + | 0.614504i | \(0.210644\pi\) | ||||
−0.788914 | + | 0.614504i | \(0.789356\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 25.2982i | − | 1.62960i | −0.579741 | − | 0.814801i | \(-0.696846\pi\) | ||
0.579741 | − | 0.814801i | \(-0.303154\pi\) | |||||||
\(242\) | −10.0000 | + | 10.0000i | −0.642824 | + | 0.642824i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −14.7434 | + | 5.25658i | −0.941922 | + | 0.335831i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.00000 | + | 5.00000i | −0.318142 | + | 0.318142i | ||||
\(248\) | 6.32456 | − | 6.32456i | 0.401610 | − | 0.401610i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 15.8114 | 1.00000 | ||||||||
\(251\) | 12.6491i | 0.798405i | 0.916863 | + | 0.399202i | \(0.130713\pi\) | ||||
−0.916863 | + | 0.399202i | \(0.869287\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.00000 | − | 2.00000i | −0.125739 | − | 0.125739i | ||||
\(254\) | − | 18.0000i | − | 1.12942i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12.6491 | + | 12.6491i | 0.789030 | + | 0.789030i | 0.981335 | − | 0.192305i | \(-0.0615964\pi\) |
−0.192305 | + | 0.981335i | \(0.561596\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −18.9737 | + | 12.0000i | −1.17897 | + | 0.745644i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.00000 | − | 7.00000i | −0.431638 | − | 0.431638i | 0.457547 | − | 0.889185i | \(-0.348728\pi\) |
−0.889185 | + | 0.457547i | \(0.848728\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.16228 | 0.194257 | ||||||||
\(266\) | −10.0000 | + | 6.32456i | −0.613139 | + | 0.387783i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −18.9737 | −1.15684 | −0.578422 | − | 0.815737i | \(-0.696331\pi\) | ||||
−0.578422 | + | 0.815737i | \(0.696331\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.6491i | 0.768379i | 0.923254 | + | 0.384189i | \(0.125519\pi\) | ||||
−0.923254 | + | 0.384189i | \(0.874481\pi\) | |||||||
\(272\) | 6.32456 | + | 6.32456i | 0.383482 | + | 0.383482i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.00000i | 0.241649i | ||||||||
\(275\) | − | 5.00000i | − | 0.301511i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.0000 | + | 18.0000i | −1.08152 | + | 1.08152i | −0.0851468 | + | 0.996368i | \(0.527136\pi\) |
−0.996368 | + | 0.0851468i | \(0.972864\pi\) | |||||||
\(278\) | 18.9737 | − | 18.9737i | 1.13796 | − | 1.13796i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −16.3246 | − | 3.67544i | −0.975579 | − | 0.219650i | ||||
\(281\) | −9.00000 | −0.536895 | −0.268447 | − | 0.963294i | \(-0.586511\pi\) | ||||
−0.268447 | + | 0.963294i | \(0.586511\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.74342 | − | 4.74342i | 0.281967 | − | 0.281967i | −0.551926 | − | 0.833893i | \(-0.686107\pi\) |
0.833893 | + | 0.551926i | \(0.186107\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 3.16228i | − | 0.186989i | ||||||
\(287\) | 5.51317 | − | 24.4868i | 0.325432 | − | 1.44541i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 12.0000i | − | 0.705882i | ||||||
\(290\) | −9.48683 | −0.557086 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.90569 | + | 7.90569i | −0.461856 | + | 0.461856i | −0.899263 | − | 0.437408i | \(-0.855897\pi\) |
0.437408 | + | 0.899263i | \(0.355897\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −15.0000 | + | 15.0000i | −0.873334 | + | 0.873334i | ||||
\(296\) | −24.0000 | −1.39497 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −12.0000 | − | 12.0000i | −0.695141 | − | 0.695141i | ||||
\(299\) | −6.32456 | −0.365758 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.00000 | − | 9.48683i | −0.345834 | − | 0.546812i | ||||
\(302\) | 9.00000 | − | 9.00000i | 0.517892 | − | 0.517892i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −12.6491 | −0.725476 | ||||||||
\(305\) | 10.0000 | + | 10.0000i | 0.572598 | + | 0.572598i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.74342 | + | 4.74342i | 0.270721 | + | 0.270721i | 0.829390 | − | 0.558669i | \(-0.188688\pi\) |
−0.558669 | + | 0.829390i | \(0.688688\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 10.0000 | 0.567962 | ||||||||
\(311\) | − | 22.1359i | − | 1.25521i | −0.778530 | − | 0.627607i | \(-0.784034\pi\) | ||
0.778530 | − | 0.627607i | \(-0.215966\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.2302 | − | 14.2302i | 0.804341 | − | 0.804341i | −0.179430 | − | 0.983771i | \(-0.557425\pi\) |
0.983771 | + | 0.179430i | \(0.0574252\pi\) | |||||||
\(314\) | −12.6491 | −0.713831 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −19.0000 | + | 19.0000i | −1.06715 | + | 1.06715i | −0.0695692 | + | 0.997577i | \(0.522162\pi\) |
−0.997577 | + | 0.0695692i | \(0.977838\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.00000i | 0.167968i | ||||||||
\(320\) | −12.6491 | − | 12.6491i | −0.707107 | − | 0.707107i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −10.3246 | − | 2.32456i | −0.575365 | − | 0.129542i | ||||
\(323\) | −5.00000 | − | 5.00000i | −0.278207 | − | 0.278207i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.90569 | − | 7.90569i | −0.438529 | − | 0.438529i | ||||
\(326\) | 12.0000 | 0.664619 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 18.9737 | − | 18.9737i | 1.04765 | − | 1.04765i | ||||
\(329\) | −9.48683 | − | 15.0000i | −0.523026 | − | 0.826977i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.00000 | −0.329790 | −0.164895 | − | 0.986311i | \(-0.552728\pi\) | ||||
−0.164895 | + | 0.986311i | \(0.552728\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 22.1359 | 1.21122 | ||||||||
\(335\) | − | 3.16228i | − | 0.172774i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.00000 | + | 8.00000i | −0.435788 | + | 0.435788i | −0.890592 | − | 0.454804i | \(-0.849709\pi\) |
0.454804 | + | 0.890592i | \(0.349709\pi\) | |||||||
\(338\) | 8.00000 | + | 8.00000i | 0.435143 | + | 0.435143i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 3.16228i | − | 0.171247i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.5811 | + | 11.4189i | 0.787307 | + | 0.616561i | ||||
\(344\) | − | 12.0000i | − | 0.646997i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 22.1359i | 1.19004i | ||||||||
\(347\) | −24.0000 | + | 24.0000i | −1.28839 | + | 1.28839i | −0.352621 | + | 0.935766i | \(0.614710\pi\) |
−0.935766 | + | 0.352621i | \(0.885290\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −34.7851 | −1.86200 | −0.931001 | − | 0.365018i | \(-0.881063\pi\) | ||||
−0.931001 | + | 0.365018i | \(0.881063\pi\) | |||||||
\(350\) | −10.0000 | − | 15.8114i | −0.534522 | − | 0.845154i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 14.2302 | − | 14.2302i | 0.757400 | − | 0.757400i | −0.218449 | − | 0.975848i | \(-0.570100\pi\) |
0.975848 | + | 0.218449i | \(0.0700996\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.48683 | + | 9.48683i | −0.503509 | + | 0.503509i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6.00000 | − | 6.00000i | −0.317110 | − | 0.317110i | ||||
\(359\) | − | 22.0000i | − | 1.16112i | −0.814219 | − | 0.580558i | \(-0.802835\pi\) | ||
0.814219 | − | 0.580558i | \(-0.197165\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.00000 | −0.473684 | ||||||||
\(362\) | 22.1359 | + | 22.1359i | 1.16344 | + | 1.16344i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.3925 | + | 17.3925i | 0.907883 | + | 0.907883i | 0.996101 | − | 0.0882186i | \(-0.0281174\pi\) |
−0.0882186 | + | 0.996101i | \(0.528117\pi\) | |||||||
\(368\) | −8.00000 | − | 8.00000i | −0.417029 | − | 0.417029i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −18.9737 | − | 18.9737i | −0.986394 | − | 0.986394i | ||||
\(371\) | −2.00000 | − | 3.16228i | −0.103835 | − | 0.164177i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.0000 | + | 12.0000i | 0.621336 | + | 0.621336i | 0.945873 | − | 0.324537i | \(-0.105208\pi\) |
−0.324537 | + | 0.945873i | \(0.605208\pi\) | |||||||
\(374\) | 3.16228 | 0.163517 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 18.9737i | − | 0.978492i | ||||||
\(377\) | 4.74342 | + | 4.74342i | 0.244298 | + | 0.244298i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 8.00000i | − | 0.410932i | −0.978664 | − | 0.205466i | \(-0.934129\pi\) | ||
0.978664 | − | 0.205466i | \(-0.0658711\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3.00000 | − | 3.00000i | 0.153493 | − | 0.153493i | ||||
\(383\) | −15.8114 | + | 15.8114i | −0.807924 | + | 0.807924i | −0.984319 | − | 0.176395i | \(-0.943556\pi\) |
0.176395 | + | 0.984319i | \(0.443556\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.00000 | + | 3.16228i | −0.254824 | + | 0.161165i | ||||
\(386\) | −16.0000 | −0.814379 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 23.0000i | 1.16615i | 0.812420 | + | 0.583073i | \(0.198150\pi\) | ||||
−0.812420 | + | 0.583073i | \(0.801850\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 6.32456i | − | 0.319847i | ||||||
\(392\) | 6.64911 | + | 18.6491i | 0.335831 | + | 0.941922i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 2.00000i | − | 0.100759i | ||||||
\(395\) | 20.5548 | + | 20.5548i | 1.03422 | + | 1.03422i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 23.7171 | + | 23.7171i | 1.19033 | + | 1.19033i | 0.976976 | + | 0.213351i | \(0.0684376\pi\) |
0.213351 | + | 0.976976i | \(0.431562\pi\) | |||||||
\(398\) | 9.48683 | − | 9.48683i | 0.475532 | − | 0.475532i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | − | 20.0000i | − | 1.00000i | ||||||
\(401\) | 1.00000 | 0.0499376 | 0.0249688 | − | 0.999688i | \(-0.492051\pi\) | ||||
0.0249688 | + | 0.999688i | \(0.492051\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.00000 | − | 5.00000i | −0.249068 | − | 0.249068i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.00000 | + | 9.48683i | 0.297775 | + | 0.470824i | ||||
\(407\) | −6.00000 | + | 6.00000i | −0.297409 | + | 0.297409i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.16228 | −0.156365 | −0.0781823 | − | 0.996939i | \(-0.524912\pi\) | ||||
−0.0781823 | + | 0.996939i | \(0.524912\pi\) | |||||||
\(410\) | 30.0000 | 1.48159 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 24.4868 | + | 5.51317i | 1.20492 | + | 0.271285i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 10.0000i | − | 0.490881i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3.16228 | + | 3.16228i | −0.154672 | + | 0.154672i | ||||
\(419\) | −15.8114 | −0.772437 | −0.386218 | − | 0.922407i | \(-0.626219\pi\) | ||||
−0.386218 | + | 0.922407i | \(0.626219\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.0000 | 0.926003 | 0.463002 | − | 0.886357i | \(-0.346772\pi\) | ||||
0.463002 | + | 0.886357i | \(0.346772\pi\) | |||||||
\(422\) | 17.0000 | − | 17.0000i | 0.827547 | − | 0.827547i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 4.00000i | − | 0.194257i | ||||||
\(425\) | 7.90569 | − | 7.90569i | 0.383482 | − | 0.383482i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.67544 | − | 16.3246i | 0.177867 | − | 0.790001i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 9.48683 | − | 9.48683i | 0.457496 | − | 0.457496i | ||||
\(431\) | 23.0000 | 1.10787 | 0.553936 | − | 0.832560i | \(-0.313125\pi\) | ||||
0.553936 | + | 0.832560i | \(0.313125\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.48683 | + | 9.48683i | −0.455908 | + | 0.455908i | −0.897310 | − | 0.441402i | \(-0.854481\pi\) |
0.441402 | + | 0.897310i | \(0.354481\pi\) | |||||||
\(434\) | −6.32456 | − | 10.0000i | −0.303588 | − | 0.480015i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.32456 | + | 6.32456i | 0.302545 | + | 0.302545i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.6491 | 0.603709 | 0.301855 | − | 0.953354i | \(-0.402394\pi\) | ||||
0.301855 | + | 0.953354i | \(0.402394\pi\) | |||||||
\(440\) | −6.32456 | −0.301511 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5.00000 | − | 5.00000i | 0.237826 | − | 0.237826i | ||||
\(443\) | −1.00000 | − | 1.00000i | −0.0475114 | − | 0.0475114i | 0.682952 | − | 0.730463i | \(-0.260696\pi\) |
−0.730463 | + | 0.682952i | \(0.760696\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.0000 | − | 10.0000i | 0.474045 | − | 0.474045i | ||||
\(446\) | 28.4605i | 1.34764i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −4.64911 | + | 20.6491i | −0.219650 | + | 0.975579i | ||||
\(449\) | − | 17.0000i | − | 0.802280i | −0.916017 | − | 0.401140i | \(-0.868614\pi\) | ||
0.916017 | − | 0.401140i | \(-0.131386\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 9.48683i | − | 0.446718i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3.16228 | −0.148413 | ||||||||
\(455\) | −2.90569 | + | 12.9057i | −0.136221 | + | 0.605028i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.00000 | + | 1.00000i | −0.0467780 | + | 0.0467780i | −0.730109 | − | 0.683331i | \(-0.760531\pi\) |
0.683331 | + | 0.730109i | \(0.260531\pi\) | |||||||
\(458\) | −15.8114 | + | 15.8114i | −0.738818 | + | 0.738818i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 6.32456i | − | 0.294564i | −0.989095 | − | 0.147282i | \(-0.952948\pi\) | ||
0.989095 | − | 0.147282i | \(-0.0470525\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.00000 | − | 4.00000i | −0.185896 | − | 0.185896i | 0.608023 | − | 0.793919i | \(-0.291963\pi\) |
−0.793919 | + | 0.608023i | \(0.791963\pi\) | |||||||
\(464\) | 12.0000i | 0.557086i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 36.0000 | 1.66767 | ||||||||
\(467\) | −11.0680 | − | 11.0680i | −0.512165 | − | 0.512165i | 0.403025 | − | 0.915189i | \(-0.367959\pi\) |
−0.915189 | + | 0.403025i | \(0.867959\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.16228 | + | 2.00000i | −0.146020 | + | 0.0923514i | ||||
\(470\) | 15.0000 | − | 15.0000i | 0.691898 | − | 0.691898i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 18.9737 | + | 18.9737i | 0.873334 | + | 0.873334i | ||||
\(473\) | −3.00000 | − | 3.00000i | −0.137940 | − | 0.137940i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 15.8114i | 0.725476i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 19.0000 | + | 19.0000i | 0.869040 | + | 0.869040i | ||||
\(479\) | −6.32456 | −0.288976 | −0.144488 | − | 0.989507i | \(-0.546154\pi\) | ||||
−0.144488 | + | 0.989507i | \(0.546154\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.9737i | 0.865125i | ||||||||
\(482\) | −25.2982 | − | 25.2982i | −1.15230 | − | 1.15230i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5.00000 | −0.227038 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.00000 | − | 4.00000i | 0.181257 | − | 0.181257i | −0.610646 | − | 0.791904i | \(-0.709090\pi\) |
0.791904 | + | 0.610646i | \(0.209090\pi\) | |||||||
\(488\) | 12.6491 | − | 12.6491i | 0.572598 | − | 0.572598i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −9.48683 | + | 20.0000i | −0.428571 | + | 0.903508i | ||||
\(491\) | 41.0000 | 1.85030 | 0.925152 | − | 0.379597i | \(-0.123937\pi\) | ||||
0.925152 | + | 0.379597i | \(0.123937\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.74342 | + | 4.74342i | −0.213633 | + | 0.213633i | ||||
\(494\) | 10.0000i | 0.449921i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 12.6491i | − | 0.567962i | ||||||
\(497\) | 15.4868 | + | 3.48683i | 0.694679 | + | 0.156406i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 19.0000i | − | 0.850557i | −0.905063 | − | 0.425278i | \(-0.860176\pi\) | ||
0.905063 | − | 0.425278i | \(-0.139824\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 12.6491 | + | 12.6491i | 0.564557 | + | 0.564557i | ||||
\(503\) | 7.90569 | − | 7.90569i | 0.352497 | − | 0.352497i | −0.508541 | − | 0.861038i | \(-0.669815\pi\) |
0.861038 | + | 0.508541i | \(0.169815\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.00000 | + | 5.00000i | 0.222497 | + | 0.222497i | ||||
\(506\) | −4.00000 | −0.177822 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 18.9737 | 0.840993 | 0.420496 | − | 0.907294i | \(-0.361856\pi\) | ||||
0.420496 | + | 0.907294i | \(0.361856\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −16.0000 | + | 16.0000i | −0.707107 | + | 0.707107i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 25.2982 | 1.11586 | ||||||||
\(515\) | − | 35.0000i | − | 1.54228i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.74342 | − | 4.74342i | −0.208615 | − | 0.208615i | ||||
\(518\) | −6.97367 | + | 30.9737i | −0.306405 | + | 1.36090i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −10.0000 | + | 10.0000i | −0.438529 | + | 0.438529i | ||||
\(521\) | 41.1096i | 1.80104i | 0.434810 | + | 0.900522i | \(0.356816\pi\) | ||||
−0.434810 | + | 0.900522i | \(0.643184\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18.9737 | − | 18.9737i | 0.829660 | − | 0.829660i | −0.157809 | − | 0.987470i | \(-0.550443\pi\) |
0.987470 | + | 0.157809i | \(0.0504431\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −14.0000 | −0.610429 | ||||||||
\(527\) | 5.00000 | − | 5.00000i | 0.217803 | − | 0.217803i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 15.0000i | − | 0.652174i | ||||||
\(530\) | 3.16228 | − | 3.16228i | 0.137361 | − | 0.137361i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −15.0000 | − | 15.0000i | −0.649722 | − | 0.649722i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.48683i | 0.410152i | ||||||||
\(536\) | −4.00000 | −0.172774 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −18.9737 | + | 18.9737i | −0.818013 | + | 0.818013i | ||||
\(539\) | 6.32456 | + | 3.00000i | 0.272418 | + | 0.129219i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.00000 | 0.386940 | 0.193470 | − | 0.981106i | \(-0.438026\pi\) | ||||
0.193470 | + | 0.981106i | \(0.438026\pi\) | |||||||
\(542\) | 12.6491 | + | 12.6491i | 0.543326 | + | 0.543326i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −11.0680 | − | 11.0680i | −0.474100 | − | 0.474100i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.0000 | − | 14.0000i | 0.598597 | − | 0.598597i | −0.341342 | − | 0.939939i | \(-0.610882\pi\) |
0.939939 | + | 0.341342i | \(0.110882\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −5.00000 | − | 5.00000i | −0.213201 | − | 0.213201i | ||||
\(551\) | − | 9.48683i | − | 0.404153i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.55480 | − | 33.5548i | 0.321263 | − | 1.42690i | ||||
\(554\) | 36.0000i | 1.52949i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.00000 | − | 6.00000i | 0.254228 | − | 0.254228i | −0.568473 | − | 0.822702i | \(-0.692466\pi\) |
0.822702 | + | 0.568473i | \(0.192466\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.48683 | −0.401250 | ||||||||
\(560\) | −20.0000 | + | 12.6491i | −0.845154 | + | 0.534522i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −9.00000 | + | 9.00000i | −0.379642 | + | 0.379642i | ||||
\(563\) | 9.48683 | − | 9.48683i | 0.399822 | − | 0.399822i | −0.478348 | − | 0.878170i | \(-0.658764\pi\) |
0.878170 | + | 0.478348i | \(0.158764\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 37.9473 | 1.59646 | ||||||||
\(566\) | − | 9.48683i | − | 0.398761i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 12.0000 | + | 12.0000i | 0.503509 | + | 0.503509i | ||||
\(569\) | − | 32.0000i | − | 1.34151i | −0.741679 | − | 0.670755i | \(-0.765970\pi\) | ||
0.741679 | − | 0.670755i | \(-0.234030\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −26.0000 | −1.08807 | −0.544033 | − | 0.839064i | \(-0.683103\pi\) | ||||
−0.544033 | + | 0.839064i | \(0.683103\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −18.9737 | − | 30.0000i | −0.791946 | − | 1.25218i | ||||
\(575\) | −10.0000 | + | 10.0000i | −0.417029 | + | 0.417029i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −20.5548 | − | 20.5548i | −0.855708 | − | 0.855708i | 0.135121 | − | 0.990829i | \(-0.456858\pi\) |
−0.990829 | + | 0.135121i | \(0.956858\pi\) | |||||||
\(578\) | −12.0000 | − | 12.0000i | −0.499134 | − | 0.499134i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.0000 | + | 6.32456i | −0.414870 | + | 0.262387i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.00000 | − | 1.00000i | −0.0414158 | − | 0.0414158i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 15.8114i | 0.653162i | ||||||||
\(587\) | −15.8114 | − | 15.8114i | −0.652606 | − | 0.652606i | 0.301014 | − | 0.953620i | \(-0.402675\pi\) |
−0.953620 | + | 0.301014i | \(0.902675\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.0000i | 0.412043i | ||||||||
\(590\) | 30.0000i | 1.23508i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −24.0000 | + | 24.0000i | −0.986394 | + | 0.986394i | ||||
\(593\) | 20.5548 | − | 20.5548i | 0.844085 | − | 0.844085i | −0.145303 | − | 0.989387i | \(-0.546416\pi\) |
0.989387 | + | 0.145303i | \(0.0464156\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12.9057 | − | 2.90569i | −0.529082 | − | 0.119122i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −6.32456 | + | 6.32456i | −0.258630 | + | 0.258630i | ||||
\(599\) | 13.0000i | 0.531166i | 0.964088 | + | 0.265583i | \(0.0855644\pi\) | ||||
−0.964088 | + | 0.265583i | \(0.914436\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 22.1359i | − | 0.902944i | −0.892285 | − | 0.451472i | \(-0.850899\pi\) | ||
0.892285 | − | 0.451472i | \(-0.149101\pi\) | |||||||
\(602\) | −15.4868 | − | 3.48683i | −0.631196 | − | 0.142113i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 15.8114 | − | 15.8114i | 0.642824 | − | 0.642824i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.2302 | − | 14.2302i | −0.577588 | − | 0.577588i | 0.356650 | − | 0.934238i | \(-0.383919\pi\) |
−0.934238 | + | 0.356650i | \(0.883919\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 20.0000 | 0.809776 | ||||||||
\(611\) | −15.0000 | −0.606835 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17.0000 | + | 17.0000i | 0.686624 | + | 0.686624i | 0.961484 | − | 0.274861i | \(-0.0886317\pi\) |
−0.274861 | + | 0.961484i | \(0.588632\pi\) | |||||||
\(614\) | 9.48683 | 0.382857 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.00000 | + | 6.32456i | 0.161165 | + | 0.254824i | ||||
\(617\) | −4.00000 | + | 4.00000i | −0.161034 | + | 0.161034i | −0.783025 | − | 0.621991i | \(-0.786324\pi\) |
0.621991 | + | 0.783025i | \(0.286324\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 25.2982 | 1.01682 | 0.508411 | − | 0.861115i | \(-0.330233\pi\) | ||||
0.508411 | + | 0.861115i | \(0.330233\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −22.1359 | − | 22.1359i | −0.887570 | − | 0.887570i | ||||
\(623\) | −16.3246 | − | 3.67544i | −0.654029 | − | 0.147254i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −25.0000 | −1.00000 | ||||||||
\(626\) | − | 28.4605i | − | 1.13751i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −18.9737 | −0.756530 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.0000 | −1.23409 | −0.617045 | − | 0.786928i | \(-0.711670\pi\) | ||||
−0.617045 | + | 0.786928i | \(0.711670\pi\) | |||||||
\(632\) | 26.0000 | − | 26.0000i | 1.03422 | − | 1.03422i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 38.0000i | 1.50917i | ||||||||
\(635\) | 28.4605i | 1.12942i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 14.7434 | − | 5.25658i | 0.584155 | − | 0.208273i | ||||
\(638\) | 3.00000 | + | 3.00000i | 0.118771 | + | 0.118771i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −25.2982 | −1.00000 | ||||||||
\(641\) | −44.0000 | −1.73790 | −0.868948 | − | 0.494904i | \(-0.835203\pi\) | ||||
−0.868948 | + | 0.494904i | \(0.835203\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.74342 | + | 4.74342i | −0.187062 | + | 0.187062i | −0.794425 | − | 0.607363i | \(-0.792228\pi\) |
0.607363 | + | 0.794425i | \(0.292228\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −10.0000 | −0.393445 | ||||||||
\(647\) | 12.6491 | + | 12.6491i | 0.497288 | + | 0.497288i | 0.910593 | − | 0.413305i | \(-0.135626\pi\) |
−0.413305 | + | 0.910593i | \(0.635626\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.48683 | 0.372391 | ||||||||
\(650\) | −15.8114 | −0.620174 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19.0000 | + | 19.0000i | 0.743527 | + | 0.743527i | 0.973255 | − | 0.229728i | \(-0.0737835\pi\) |
−0.229728 | + | 0.973255i | \(0.573784\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 37.9473i | − | 1.48159i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −24.4868 | − | 5.51317i | −0.954596 | − | 0.214926i | ||||
\(659\) | − | 1.00000i | − | 0.0389545i | −0.999810 | − | 0.0194772i | \(-0.993800\pi\) | ||
0.999810 | − | 0.0194772i | \(-0.00620019\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.6491i | 0.491993i | 0.969271 | + | 0.245997i | \(0.0791152\pi\) | ||||
−0.969271 | + | 0.245997i | \(0.920885\pi\) | |||||||
\(662\) | −6.00000 | + | 6.00000i | −0.233197 | + | 0.233197i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −12.6491 | −0.490881 | ||||||||
\(665\) | 15.8114 | − | 10.0000i | 0.613139 | − | 0.387783i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.00000 | − | 6.00000i | 0.232321 | − | 0.232321i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −3.16228 | − | 3.16228i | −0.122169 | − | 0.122169i | ||||
\(671\) | − | 6.32456i | − | 0.244157i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24.0000 | − | 24.0000i | −0.925132 | − | 0.925132i | 0.0722542 | − | 0.997386i | \(-0.476981\pi\) |
−0.997386 | + | 0.0722542i | \(0.976981\pi\) | |||||||
\(674\) | 16.0000i | 0.616297i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14.2302 | − | 14.2302i | −0.546913 | − | 0.546913i | 0.378634 | − | 0.925547i | \(-0.376394\pi\) |
−0.925547 | + | 0.378634i | \(0.876394\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.16228 | + | 5.00000i | 0.121357 | + | 0.191882i | ||||
\(680\) | −10.0000 | − | 10.0000i | −0.383482 | − | 0.383482i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3.16228 | − | 3.16228i | −0.121090 | − | 0.121090i | ||||
\(683\) | −32.0000 | − | 32.0000i | −1.22445 | − | 1.22445i | −0.966035 | − | 0.258411i | \(-0.916801\pi\) |
−0.258411 | − | 0.966035i | \(-0.583199\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 6.32456i | − | 0.241649i | ||||||
\(686\) | 26.0000 | − | 3.16228i | 0.992685 | − | 0.120736i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −12.0000 | − | 12.0000i | −0.457496 | − | 0.457496i | ||||
\(689\) | −3.16228 | −0.120473 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 31.6228i | − | 1.20299i | −0.798878 | − | 0.601494i | \(-0.794573\pi\) | ||
0.798878 | − | 0.601494i | \(-0.205427\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 48.0000i | 1.82206i | ||||||||
\(695\) | −30.0000 | + | 30.0000i | −1.13796 | + | 1.13796i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15.0000 | − | 15.0000i | 0.568166 | − | 0.568166i | ||||
\(698\) | −34.7851 | + | 34.7851i | −1.31663 | + | 1.31663i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.0000 | 0.491003 | 0.245502 | − | 0.969396i | \(-0.421047\pi\) | ||||
0.245502 | + | 0.969396i | \(0.421047\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18.9737 | − | 18.9737i | 0.715605 | − | 0.715605i | ||||
\(704\) | 8.00000i | 0.301511i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 28.4605i | − | 1.07113i | ||||||
\(707\) | 1.83772 | − | 8.16228i | 0.0691147 | − | 0.306974i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 9.00000i | − | 0.338002i | −0.985616 | − | 0.169001i | \(-0.945946\pi\) | ||
0.985616 | − | 0.169001i | \(-0.0540541\pi\) | |||||||
\(710\) | 18.9737i | 0.712069i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −12.6491 | − | 12.6491i | −0.474045 | − | 0.474045i | ||||
\(713\) | −6.32456 | + | 6.32456i | −0.236856 | + | 0.236856i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.00000i | 0.186989i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −22.0000 | − | 22.0000i | −0.821033 | − | 0.821033i | ||||
\(719\) | 31.6228 | 1.17933 | 0.589665 | − | 0.807648i | \(-0.299260\pi\) | ||||
0.589665 | + | 0.807648i | \(0.299260\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −35.0000 | + | 22.1359i | −1.30347 | + | 0.824386i | ||||
\(722\) | −9.00000 | + | 9.00000i | −0.334945 | + | 0.334945i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 15.0000 | 0.557086 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.48683 | − | 9.48683i | −0.351847 | − | 0.351847i | 0.508949 | − | 0.860796i | \(-0.330034\pi\) |
−0.860796 | + | 0.508949i | \(0.830034\pi\) | |||||||
\(728\) | 16.3246 | + | 3.67544i | 0.605028 | + | 0.136221i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 9.48683i | − | 0.350883i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17.3925 | + | 17.3925i | −0.642408 | + | 0.642408i | −0.951147 | − | 0.308739i | \(-0.900093\pi\) |
0.308739 | + | 0.951147i | \(0.400093\pi\) | |||||||
\(734\) | 34.7851 | 1.28394 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.00000 | + | 1.00000i | −0.0368355 | + | 0.0368355i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 37.0000i | 1.36107i | 0.732717 | + | 0.680534i | \(0.238252\pi\) | ||||
−0.732717 | + | 0.680534i | \(0.761748\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5.16228 | − | 1.16228i | −0.189513 | − | 0.0426686i | ||||
\(743\) | 9.00000 | + | 9.00000i | 0.330178 | + | 0.330178i | 0.852654 | − | 0.522476i | \(-0.174992\pi\) |
−0.522476 | + | 0.852654i | \(0.674992\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 18.9737 | + | 18.9737i | 0.695141 | + | 0.695141i | ||||
\(746\) | 24.0000 | 0.878702 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.48683 | − | 6.00000i | 0.346641 | − | 0.219235i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 37.0000 | 1.35015 | 0.675075 | − | 0.737749i | \(-0.264111\pi\) | ||||
0.675075 | + | 0.737749i | \(0.264111\pi\) | |||||||
\(752\) | −18.9737 | − | 18.9737i | −0.691898 | − | 0.691898i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 9.48683 | 0.345490 | ||||||||
\(755\) | −14.2302 | + | 14.2302i | −0.517892 | + | 0.517892i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16.0000 | + | 16.0000i | −0.581530 | + | 0.581530i | −0.935324 | − | 0.353794i | \(-0.884892\pi\) |
0.353794 | + | 0.935324i | \(0.384892\pi\) | |||||||
\(758\) | −8.00000 | − | 8.00000i | −0.290573 | − | 0.290573i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 20.0000 | 0.725476 | ||||||||
\(761\) | 25.2982i | 0.917060i | 0.888679 | + | 0.458530i | \(0.151624\pi\) | ||||
−0.888679 | + | 0.458530i | \(0.848376\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.06797 | + | 18.0680i | −0.147270 | + | 0.654104i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 31.6228i | 1.14258i | ||||||||
\(767\) | 15.0000 | − | 15.0000i | 0.541619 | − | 0.541619i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.1359 | 0.798243 | 0.399121 | − | 0.916898i | \(-0.369315\pi\) | ||||
0.399121 | + | 0.916898i | \(0.369315\pi\) | |||||||
\(770\) | −1.83772 | + | 8.16228i | −0.0662269 | + | 0.294148i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −36.3662 | + | 36.3662i | −1.30800 | + | 1.30800i | −0.385145 | + | 0.922856i | \(0.625849\pi\) |
−0.922856 | + | 0.385145i | \(0.874151\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −15.8114 | −0.567962 | ||||||||
\(776\) | 6.32456i | 0.227038i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 23.0000 | + | 23.0000i | 0.824590 | + | 0.824590i | ||||
\(779\) | 30.0000i | 1.07486i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.00000 | 0.214697 | ||||||||
\(782\) | −6.32456 | − | 6.32456i | −0.226166 | − | 0.226166i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 25.2982 | + | 12.0000i | 0.903508 | + | 0.428571i | ||||
\(785\) | 20.0000 | 0.713831 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17.3925 | − | 17.3925i | −0.619977 | − | 0.619977i | 0.325549 | − | 0.945525i | \(-0.394451\pi\) |
−0.945525 | + | 0.325549i | \(0.894451\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 41.1096 | 1.46261 | ||||||||
\(791\) | −24.0000 | − | 37.9473i | −0.853342 | − | 1.34925i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.0000 | − | 10.0000i | −0.355110 | − | 0.355110i | ||||
\(794\) | 47.4342 | 1.68338 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.58114 | + | 1.58114i | 0.0560068 | + | 0.0560068i | 0.734555 | − | 0.678549i | \(-0.237391\pi\) |
−0.678549 | + | 0.734555i | \(0.737391\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 15.0000i | − | 0.530662i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.00000 | − | 1.00000i | 0.0353112 | − | 0.0353112i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 16.3246 | + | 3.67544i | 0.575365 | + | 0.129542i | ||||
\(806\) | −10.0000 | −0.352235 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 6.32456 | − | 6.32456i | 0.222497 | − | 0.222497i | ||||
\(809\) | 3.00000i | 0.105474i | 0.998608 | + | 0.0527372i | \(0.0167946\pi\) | ||||
−0.998608 | + | 0.0527372i | \(0.983205\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 37.9473i | 1.33251i | 0.745724 | + | 0.666256i | \(0.232104\pi\) | ||||
−0.745724 | + | 0.666256i | \(0.767896\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 12.0000i | 0.420600i | ||||||||
\(815\) | −18.9737 | −0.664619 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.48683 | + | 9.48683i | 0.331902 | + | 0.331902i | ||||
\(818\) | −3.16228 | + | 3.16228i | −0.110566 | + | 0.110566i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 23.0000 | 0.802706 | 0.401353 | − | 0.915924i | \(-0.368540\pi\) | ||||
0.401353 | + | 0.915924i | \(0.368540\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.00000 | − | 3.00000i | −0.104573 | − | 0.104573i | 0.652884 | − | 0.757458i | \(-0.273559\pi\) |
−0.757458 | + | 0.652884i | \(0.773559\pi\) | |||||||
\(824\) | −44.2719 | −1.54228 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 30.0000 | − | 18.9737i | 1.04383 | − | 0.660178i | ||||
\(827\) | 26.0000 | − | 26.0000i | 0.904109 | − | 0.904109i | −0.0916799 | − | 0.995789i | \(-0.529224\pi\) |
0.995789 | + | 0.0916799i | \(0.0292237\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −28.4605 | −0.988474 | −0.494237 | − | 0.869327i | \(-0.664552\pi\) | ||||
−0.494237 | + | 0.869327i | \(0.664552\pi\) | |||||||
\(830\) | −10.0000 | − | 10.0000i | −0.347105 | − | 0.347105i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 12.6491 | + | 12.6491i | 0.438529 | + | 0.438529i | ||||
\(833\) | 5.25658 | + | 14.7434i | 0.182130 | + | 0.510829i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −35.0000 | −1.21122 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −15.8114 | + | 15.8114i | −0.546195 | + | 0.546195i | ||||
\(839\) | 50.5964 | 1.74678 | 0.873392 | − | 0.487019i | \(-0.161916\pi\) | ||||
0.873392 | + | 0.487019i | \(0.161916\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20.0000 | 0.689655 | ||||||||
\(842\) | 19.0000 | − | 19.0000i | 0.654783 | − | 0.654783i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −12.6491 | − | 12.6491i | −0.435143 | − | 0.435143i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −25.8114 | − | 5.81139i | −0.886890 | − | 0.199682i | ||||
\(848\) | −4.00000 | − | 4.00000i | −0.137361 | − | 0.137361i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − | 15.8114i | − | 0.542326i | ||||||
\(851\) | 24.0000 | 0.822709 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(854\) | −12.6491 | − | 20.0000i | −0.432844 | − | 0.684386i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 12.0000 | 0.410152 | ||||||||
\(857\) | −31.6228 | − | 31.6228i | −1.08021 | − | 1.08021i | −0.996489 | − | 0.0837245i | \(-0.973318\pi\) |
−0.0837245 | − | 0.996489i | \(-0.526682\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.6491 | −0.431582 | −0.215791 | − | 0.976440i | \(-0.569233\pi\) | ||||
−0.215791 | + | 0.976440i | \(0.569233\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 23.0000 | − | 23.0000i | 0.783383 | − | 0.783383i | ||||
\(863\) | 13.0000 | + | 13.0000i | 0.442525 | + | 0.442525i | 0.892860 | − | 0.450335i | \(-0.148695\pi\) |
−0.450335 | + | 0.892860i | \(0.648695\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 35.0000i | − | 1.19004i | ||||||
\(866\) | 18.9737i | 0.644751i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 13.0000i | − | 0.440995i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.16228i | 0.107150i | ||||||||
\(872\) | −14.0000 | + | 14.0000i | −0.474100 | + | 0.474100i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 12.6491 | 0.427863 | ||||||||
\(875\) | 15.8114 | + | 25.0000i | 0.534522 | + | 0.845154i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17.0000 | − | 17.0000i | 0.574049 | − | 0.574049i | −0.359208 | − | 0.933257i | \(-0.616953\pi\) |
0.933257 | + | 0.359208i | \(0.116953\pi\) | |||||||
\(878\) | 12.6491 | − | 12.6491i | 0.426887 | − | 0.426887i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −6.32456 | + | 6.32456i | −0.213201 | + | 0.213201i | ||||
\(881\) | 37.9473i | 1.27848i | 0.769008 | + | 0.639239i | \(0.220751\pi\) | ||||
−0.769008 | + | 0.639239i | \(0.779249\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −18.0000 | − | 18.0000i | −0.605748 | − | 0.605748i | 0.336084 | − | 0.941832i | \(-0.390897\pi\) |
−0.941832 | + | 0.336084i | \(0.890897\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.00000 | −0.0671913 | ||||||||
\(887\) | 3.16228 | + | 3.16228i | 0.106179 | + | 0.106179i | 0.758200 | − | 0.652022i | \(-0.226079\pi\) |
−0.652022 | + | 0.758200i | \(0.726079\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 28.4605 | − | 18.0000i | 0.954534 | − | 0.603701i | ||||
\(890\) | − | 20.0000i | − | 0.670402i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 15.0000 | + | 15.0000i | 0.501956 | + | 0.501956i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.48683 | + | 9.48683i | 0.317110 | + | 0.317110i | ||||
\(896\) | 16.0000 | + | 25.2982i | 0.534522 | + | 0.845154i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −17.0000 | − | 17.0000i | −0.567297 | − | 0.567297i | ||||
\(899\) | 9.48683 | 0.316404 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 3.16228i | − | 0.105351i | ||||||
\(902\) | −9.48683 | − | 9.48683i | −0.315877 | − | 0.315877i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 48.0000i | − | 1.59646i | ||||||
\(905\) | −35.0000 | − | 35.0000i | −1.16344 | − | 1.16344i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22.0000 | − | 22.0000i | 0.730498 | − | 0.730498i | −0.240220 | − | 0.970718i | \(-0.577220\pi\) |
0.970718 | + | 0.240220i | \(0.0772197\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 10.0000 | + | 15.8114i | 0.331497 | + | 0.524142i | ||||
\(911\) | −54.0000 | −1.78910 | −0.894550 | − | 0.446968i | \(-0.852504\pi\) | ||||
−0.894550 | + | 0.446968i | \(0.852504\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.16228 | + | 3.16228i | −0.104656 | + | 0.104656i | ||||
\(914\) | 2.00000i | 0.0661541i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 27.0000i | 0.890648i | 0.895370 | + | 0.445324i | \(0.146911\pi\) | ||||
−0.895370 | + | 0.445324i | \(0.853089\pi\) | |||||||
\(920\) | 12.6491 | + | 12.6491i | 0.417029 | + | 0.417029i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −6.32456 | − | 6.32456i | −0.208288 | − | 0.208288i | ||||
\(923\) | 9.48683 | − | 9.48683i | 0.312263 | − | 0.312263i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 30.0000 | + | 30.0000i | 0.986394 | + | 0.986394i | ||||
\(926\) | −8.00000 | −0.262896 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.16228 | 0.103751 | 0.0518755 | − | 0.998654i | \(-0.483480\pi\) | ||||
0.0518755 | + | 0.998654i | \(0.483480\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −20.0000 | − | 9.48683i | −0.655474 | − | 0.310918i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −22.1359 | −0.724310 | ||||||||
\(935\) | −5.00000 | −0.163517 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.2302 | + | 14.2302i | 0.464882 | + | 0.464882i | 0.900252 | − | 0.435370i | \(-0.143382\pi\) |
−0.435370 | + | 0.900252i | \(0.643382\pi\) | |||||||
\(938\) | −1.16228 | + | 5.16228i | −0.0379497 | + | 0.168554i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 37.9473i | − | 1.23705i | −0.785766 | − | 0.618524i | \(-0.787731\pi\) | ||
0.785766 | − | 0.618524i | \(-0.212269\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −18.9737 | + | 18.9737i | −0.617868 | + | 0.617868i | ||||
\(944\) | 37.9473 | 1.23508 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.00000 | −0.195077 | ||||||||
\(947\) | −7.00000 | + | 7.00000i | −0.227469 | + | 0.227469i | −0.811635 | − | 0.584165i | \(-0.801422\pi\) |
0.584165 | + | 0.811635i | \(0.301422\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 15.8114 | + | 15.8114i | 0.512989 | + | 0.512989i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.67544 | + | 16.3246i | −0.119122 | + | 0.529082i | ||||
\(953\) | 3.00000 | + | 3.00000i | 0.0971795 | + | 0.0971795i | 0.754025 | − | 0.656846i | \(-0.228110\pi\) |
−0.656846 | + | 0.754025i | \(0.728110\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.74342 | + | 4.74342i | −0.153493 | + | 0.153493i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −6.32456 | + | 6.32456i | −0.204337 | + | 0.204337i | ||||
\(959\) | −6.32456 | + | 4.00000i | −0.204231 | + | 0.129167i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 21.0000 | 0.677419 | ||||||||
\(962\) | 18.9737 | + | 18.9737i | 0.611736 | + | 0.611736i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 25.2982 | 0.814379 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −33.0000 | + | 33.0000i | −1.06121 | + | 1.06121i | −0.0632081 | + | 0.998000i | \(0.520133\pi\) |
−0.998000 | + | 0.0632081i | \(0.979867\pi\) | |||||||
\(968\) | −20.0000 | − | 20.0000i | −0.642824 | − | 0.642824i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −5.00000 | + | 5.00000i | −0.160540 | + | 0.160540i | ||||
\(971\) | − | 34.7851i | − | 1.11631i | −0.829738 | − | 0.558153i | \(-0.811510\pi\) | ||
0.829738 | − | 0.558153i | \(-0.188490\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 48.9737 | + | 11.0263i | 1.57002 | + | 0.353488i | ||||
\(974\) | − | 8.00000i | − | 0.256337i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 25.2982i | − | 0.809776i | ||||||
\(977\) | 1.00000 | − | 1.00000i | 0.0319928 | − | 0.0319928i | −0.690929 | − | 0.722922i | \(-0.742798\pi\) |
0.722922 | + | 0.690929i | \(0.242798\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.32456 | −0.202134 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 41.0000 | − | 41.0000i | 1.30836 | − | 1.30836i | ||||
\(983\) | −20.5548 | + | 20.5548i | −0.655596 | + | 0.655596i | −0.954335 | − | 0.298739i | \(-0.903434\pi\) |
0.298739 | + | 0.954335i | \(0.403434\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.16228i | 0.100759i | ||||||||
\(986\) | 9.48683i | 0.302122i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12.0000i | 0.381578i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.00000 | 0.127064 | 0.0635321 | − | 0.997980i | \(-0.479763\pi\) | ||||
0.0635321 | + | 0.997980i | \(0.479763\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 18.9737 | − | 12.0000i | 0.601808 | − | 0.380617i | ||||
\(995\) | −15.0000 | + | 15.0000i | −0.475532 | + | 0.475532i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14.2302 | − | 14.2302i | −0.450677 | − | 0.450677i | 0.444902 | − | 0.895579i | \(-0.353238\pi\) |
−0.895579 | + | 0.444902i | \(0.853238\pi\) | |||||||
\(998\) | −19.0000 | − | 19.0000i | −0.601434 | − | 0.601434i | ||||
\(999\) | 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 | 315.2.p.c.118.1 | 4 | ||
3.2 | odd | 2 | 35.2.f.a.13.1 | ✓ | 4 | ||
5.2 | odd | 4 | inner | 315.2.p.c.307.2 | 4 | ||
7.6 | odd | 2 | inner | 315.2.p.c.118.2 | 4 | ||
12.11 | even | 2 | 560.2.bj.a.433.2 | 4 | |||
15.2 | even | 4 | 35.2.f.a.27.2 | yes | 4 | ||
15.8 | even | 4 | 175.2.f.c.132.1 | 4 | |||
15.14 | odd | 2 | 175.2.f.c.118.2 | 4 | |||
21.2 | odd | 6 | 245.2.l.c.178.1 | 8 | |||
21.5 | even | 6 | 245.2.l.c.178.2 | 8 | |||
21.11 | odd | 6 | 245.2.l.c.68.2 | 8 | |||
21.17 | even | 6 | 245.2.l.c.68.1 | 8 | |||
21.20 | even | 2 | 35.2.f.a.13.2 | yes | 4 | ||
35.27 | even | 4 | inner | 315.2.p.c.307.1 | 4 | ||
60.47 | odd | 4 | 560.2.bj.a.97.1 | 4 | |||
84.83 | odd | 2 | 560.2.bj.a.433.1 | 4 | |||
105.2 | even | 12 | 245.2.l.c.227.1 | 8 | |||
105.17 | odd | 12 | 245.2.l.c.117.1 | 8 | |||
105.32 | even | 12 | 245.2.l.c.117.2 | 8 | |||
105.47 | odd | 12 | 245.2.l.c.227.2 | 8 | |||
105.62 | odd | 4 | 35.2.f.a.27.1 | yes | 4 | ||
105.83 | odd | 4 | 175.2.f.c.132.2 | 4 | |||
105.104 | even | 2 | 175.2.f.c.118.1 | 4 | |||
420.167 | even | 4 | 560.2.bj.a.97.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.2.f.a.13.1 | ✓ | 4 | 3.2 | odd | 2 | ||
35.2.f.a.13.2 | yes | 4 | 21.20 | even | 2 | ||
35.2.f.a.27.1 | yes | 4 | 105.62 | odd | 4 | ||
35.2.f.a.27.2 | yes | 4 | 15.2 | even | 4 | ||
175.2.f.c.118.1 | 4 | 105.104 | even | 2 | |||
175.2.f.c.118.2 | 4 | 15.14 | odd | 2 | |||
175.2.f.c.132.1 | 4 | 15.8 | even | 4 | |||
175.2.f.c.132.2 | 4 | 105.83 | odd | 4 | |||
245.2.l.c.68.1 | 8 | 21.17 | even | 6 | |||
245.2.l.c.68.2 | 8 | 21.11 | odd | 6 | |||
245.2.l.c.117.1 | 8 | 105.17 | odd | 12 | |||
245.2.l.c.117.2 | 8 | 105.32 | even | 12 | |||
245.2.l.c.178.1 | 8 | 21.2 | odd | 6 | |||
245.2.l.c.178.2 | 8 | 21.5 | even | 6 | |||
245.2.l.c.227.1 | 8 | 105.2 | even | 12 | |||
245.2.l.c.227.2 | 8 | 105.47 | odd | 12 | |||
315.2.p.c.118.1 | 4 | 1.1 | even | 1 | trivial | ||
315.2.p.c.118.2 | 4 | 7.6 | odd | 2 | inner | ||
315.2.p.c.307.1 | 4 | 35.27 | even | 4 | inner | ||
315.2.p.c.307.2 | 4 | 5.2 | odd | 4 | inner | ||
560.2.bj.a.97.1 | 4 | 60.47 | odd | 4 | |||
560.2.bj.a.97.2 | 4 | 420.167 | even | 4 | |||
560.2.bj.a.433.1 | 4 | 84.83 | odd | 2 | |||
560.2.bj.a.433.2 | 4 | 12.11 | even | 2 |