Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [560,2,Mod(97,560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(560, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("560.97");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 560 = 2^{4} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 560.bj (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.47162251319\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 35) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 97.1 | ||
Root | \(-1.58114 - 1.58114i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 560.97 |
Dual form | 560.2.bj.a.433.1 |
$q$-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 \(\left(\mathbb{Z}/560\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(337\) | \(351\) | \(421\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.58114 | − | 1.58114i | −0.912871 | − | 0.912871i | 0.0836263 | − | 0.996497i | \(-0.473350\pi\) |
−0.996497 | + | 0.0836263i | \(0.973350\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.58114 | − | 1.58114i | −0.707107 | − | 0.707107i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.581139 | − | 2.58114i | 0.219650 | − | 0.975579i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.00000i | 0.666667i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 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 | \(-0.350358\pi\) |
−0.891517 | + | 0.452988i | \(0.850358\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.00000i | 1.29099i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.58114 | − | 1.58114i | 0.383482 | − | 0.383482i | −0.488873 | − | 0.872355i | \(-0.662592\pi\) |
0.872355 | + | 0.488873i | \(0.162592\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.16228 | −0.725476 | −0.362738 | − | 0.931891i | \(-0.618158\pi\) | ||||
−0.362738 | + | 0.931891i | \(0.618158\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.00000 | + | 3.16228i | −1.09109 | + | 0.690066i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.00000 | + | 2.00000i | −0.417029 | + | 0.417029i | −0.884178 | − | 0.467150i | \(-0.845281\pi\) |
0.467150 | + | 0.884178i | \(0.345281\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.00000i | 1.00000i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.58114 | + | 1.58114i | −0.304290 | + | 0.304290i | ||||
\(28\) | 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 | \(0.0916552\pi\) | ||||
−0.958830 | + | 0.283981i | \(0.908345\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.58114 | − | 1.58114i | −0.275241 | − | 0.275241i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.00000 | + | 3.16228i | −0.845154 | + | 0.534522i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.00000 | − | 6.00000i | −0.986394 | − | 0.986394i | 0.0135147 | − | 0.999909i | \(-0.495698\pi\) |
−0.999909 | + | 0.0135147i | \(0.995698\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.00000i | 0.800641i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.48683i | 1.48159i | 0.671729 | + | 0.740797i | \(0.265552\pi\) | ||||
−0.671729 | + | 0.740797i | \(0.734448\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.00000 | − | 3.00000i | 0.457496 | − | 0.457496i | −0.440337 | − | 0.897833i | \(-0.645141\pi\) |
0.897833 | + | 0.440337i | \(0.145141\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.16228 | − | 3.16228i | 0.471405 | − | 0.471405i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.74342 | − | 4.74342i | 0.691898 | − | 0.691898i | −0.270751 | − | 0.962649i | \(-0.587272\pi\) |
0.962649 | + | 0.270751i | \(0.0872720\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.32456 | − | 3.00000i | −0.903508 | − | 0.428571i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.00000 | −0.700140 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.00000 | − | 1.00000i | 0.137361 | − | 0.137361i | −0.635083 | − | 0.772444i | \(-0.719034\pi\) |
0.772444 | + | 0.635083i | \(0.219034\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.58114 | − | 1.58114i | −0.213201 | − | 0.213201i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.00000 | + | 5.00000i | 0.662266 | + | 0.662266i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.48683 | −1.23508 | −0.617540 | − | 0.786539i | \(-0.711871\pi\) | ||||
−0.617540 | + | 0.786539i | \(0.711871\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 6.32456i | − | 0.809776i | −0.914366 | − | 0.404888i | \(-0.867310\pi\) | ||
0.914366 | − | 0.404888i | \(-0.132690\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.16228 | + | 1.16228i | 0.650386 | + | 0.146433i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.00000i | 0.620174i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.00000 | + | 1.00000i | 0.122169 | + | 0.122169i | 0.765548 | − | 0.643379i | \(-0.222468\pi\) |
−0.643379 | + | 0.765548i | \(0.722468\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.32456 | 0.761387 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 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 | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 7.90569 | − | 7.90569i | 0.912871 | − | 0.912871i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.581139 | − | 2.58114i | 0.0662269 | − | 0.294148i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 13.0000i | − | 1.46261i | −0.682048 | − | 0.731307i | \(-0.738911\pi\) | ||
0.682048 | − | 0.731307i | \(-0.261089\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 11.0000 | 1.22222 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.16228 | + | 3.16228i | 0.347105 | + | 0.347105i | 0.859030 | − | 0.511925i | \(-0.171067\pi\) |
−0.511925 | + | 0.859030i | \(0.671067\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.00000 | −0.542326 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.74342 | − | 4.74342i | 0.508548 | − | 0.508548i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −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 | ||||||||
\(93\) | 5.00000 | − | 5.00000i | 0.518476 | − | 0.518476i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.00000 | + | 5.00000i | 0.512989 | + | 0.512989i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.58114 | + | 1.58114i | −0.160540 | + | 0.160540i | −0.782806 | − | 0.622266i | \(-0.786212\pi\) |
0.622266 | + | 0.782806i | \(0.286212\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.00000i | 0.201008i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.16228i | 0.314658i | 0.987546 | + | 0.157329i | \(0.0502884\pi\) | ||||
−0.987546 | + | 0.157329i | \(0.949712\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.0680 | − | 11.0680i | −1.09056 | − | 1.09056i | −0.995469 | − | 0.0950911i | \(-0.969686\pi\) |
−0.0950911 | − | 0.995469i | \(-0.530314\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 12.9057 | + | 2.90569i | 1.25947 | + | 0.283567i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.00000 | + | 3.00000i | 0.290021 | + | 0.290021i | 0.837088 | − | 0.547068i | \(-0.184256\pi\) |
−0.547068 | + | 0.837088i | \(0.684256\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 7.00000i | − | 0.670478i | −0.942133 | − | 0.335239i | \(-0.891183\pi\) | ||
0.942133 | − | 0.335239i | \(-0.108817\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 18.9737i | 1.80090i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.0000 | − | 12.0000i | 1.12887 | − | 1.12887i | 0.138503 | − | 0.990362i | \(-0.455771\pi\) |
0.990362 | − | 0.138503i | \(-0.0442291\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.32456 | 0.589768 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.16228 | − | 3.16228i | 0.292353 | − | 0.292353i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.16228 | − | 5.00000i | −0.289886 | − | 0.458349i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.0000 | −0.909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 15.0000 | − | 15.0000i | 1.35250 | − | 1.35250i | ||||
\(124\) | 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 | \(-0.441012\pi\) |
−0.982878 | + | 0.184257i | \(0.941012\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.48683 | −0.835269 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.83772 | + | 8.16228i | −0.159351 | + | 0.707759i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.00000 | 0.430331 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.00000 | + | 2.00000i | 0.170872 | + | 0.170872i | 0.787362 | − | 0.616491i | \(-0.211446\pi\) |
−0.616491 | + | 0.787362i | \(0.711446\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.9737 | 1.60933 | 0.804663 | − | 0.593732i | \(-0.202346\pi\) | ||||
0.804663 | + | 0.593732i | \(0.202346\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −15.0000 | −1.26323 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.58114 | − | 1.58114i | −0.132221 | − | 0.132221i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.74342 | − | 4.74342i | 0.393919 | − | 0.393919i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.25658 | + | 14.7434i | 0.433556 | + | 1.21602i | ||||
\(148\) | 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 | \(-0.619343\pi\) | ||||
−0.366205 | + | 0.930534i | \(0.619343\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.16228 | + | 3.16228i | 0.255655 | + | 0.255655i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.00000 | − | 5.00000i | 0.401610 | − | 0.401610i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.32456 | − | 6.32456i | 0.504754 | − | 0.504754i | −0.408157 | − | 0.912912i | \(-0.633828\pi\) |
0.912912 | + | 0.408157i | \(0.133828\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.16228 | −0.250785 | ||||||||
\(160\) | 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 | \(-0.857828\pi\) |
0.431944 | + | 0.901900i | \(0.357828\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.00000i | 0.389249i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −11.0680 | + | 11.0680i | −0.856465 | + | 0.856465i | −0.990920 | − | 0.134454i | \(-0.957072\pi\) |
0.134454 | + | 0.990920i | \(0.457072\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 8.00000i | − | 0.615385i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 6.32456i | − | 0.483651i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −11.0680 | − | 11.0680i | −0.841482 | − | 0.841482i | 0.147569 | − | 0.989052i | \(-0.452855\pi\) |
−0.989052 | + | 0.147569i | \(0.952855\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 12.9057 | + | 2.90569i | 0.975579 | + | 0.219650i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 15.0000 | + | 15.0000i | 1.12747 | + | 1.12747i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.00000i | 0.448461i | 0.974536 | + | 0.224231i | \(0.0719869\pi\) | ||||
−0.974536 | + | 0.224231i | \(0.928013\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.1359i | 1.64535i | 0.568511 | + | 0.822676i | \(0.307520\pi\) | ||||
−0.568511 | + | 0.822676i | \(0.692480\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.0000 | + | 10.0000i | −0.739221 | + | 0.739221i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 18.9737i | 1.39497i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.58114 | − | 1.58114i | 0.115624 | − | 0.115624i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.16228 | + | 5.00000i | 0.230022 | + | 0.363696i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 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 | −0.933758 | − | 0.357905i | \(-0.883491\pi\) |
0.357905 | + | 0.933758i | \(0.383491\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 7.90569 | − | 7.90569i | 0.566139 | − | 0.566139i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.00000 | − | 1.00000i | −0.0712470 | − | 0.0712470i | 0.670585 | − | 0.741832i | \(-0.266043\pi\) |
−0.741832 | + | 0.670585i | \(0.766043\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.48683 | 0.672504 | 0.336252 | − | 0.941772i | \(-0.390841\pi\) | ||||
0.336252 | + | 0.941772i | \(0.390841\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 3.16228i | − | 0.223050i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.74342 | + | 1.74342i | 0.543481 | + | 0.122364i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 15.0000 | − | 15.0000i | 1.04765 | − | 1.04765i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.00000 | − | 4.00000i | −0.278019 | − | 0.278019i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.16228 | −0.218739 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.0000 | −1.17033 | −0.585164 | − | 0.810915i | \(-0.698970\pi\) | ||||
−0.585164 | + | 0.810915i | \(0.698970\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −9.48683 | − | 9.48683i | −0.650027 | − | 0.650027i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −9.48683 | −0.646997 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.16228 | + | 1.83772i | 0.554092 | + | 0.124753i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.00000 | −0.336336 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.2302 | − | 14.2302i | −0.952928 | − | 0.952928i | 0.0460129 | − | 0.998941i | \(-0.485348\pi\) |
−0.998941 | + | 0.0460129i | \(0.985348\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −10.0000 | −0.666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.58114 | − | 1.58114i | 0.104944 | − | 0.104944i | −0.652685 | − | 0.757629i | \(-0.726358\pi\) |
0.757629 | + | 0.652685i | \(0.226358\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.8114 | 1.04485 | 0.522423 | − | 0.852686i | \(-0.325028\pi\) | ||||
0.522423 | + | 0.852686i | \(0.325028\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.00000 | + | 3.16228i | −0.328976 | + | 0.208063i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.0000 | + | 18.0000i | −1.17922 | + | 1.17922i | −0.199276 | + | 0.979943i | \(0.563859\pi\) |
−0.979943 | + | 0.199276i | \(0.936141\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −15.0000 | −0.978492 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −20.5548 | + | 20.5548i | −1.33518 | + | 1.33518i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 19.0000i | − | 1.22901i | −0.788914 | − | 0.614504i | \(-0.789356\pi\) | ||
0.788914 | − | 0.614504i | \(-0.210644\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 25.2982i | − | 1.62960i | −0.579741 | − | 0.814801i | \(-0.696846\pi\) | ||
0.579741 | − | 0.814801i | \(-0.303154\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −12.6491 | − | 12.6491i | −0.811441 | − | 0.811441i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.25658 | + | 14.7434i | 0.335831 | + | 0.941922i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.00000 | + | 5.00000i | 0.318142 | + | 0.318142i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 10.0000i | − | 0.633724i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 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 | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 7.90569 | + | 7.90569i | 0.495074 | + | 0.495074i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12.6491 | − | 12.6491i | 0.789030 | − | 0.789030i | −0.192305 | − | 0.981335i | \(-0.561596\pi\) |
0.981335 | + | 0.192305i | \(0.0615964\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −18.9737 | + | 12.0000i | −1.17897 | + | 0.745644i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.00000 | −0.371391 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.00000 | + | 7.00000i | −0.431638 | + | 0.431638i | −0.889185 | − | 0.457547i | \(-0.848728\pi\) |
0.457547 | + | 0.889185i | \(0.348728\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.16228 | −0.194257 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.0000 | + | 10.0000i | 0.611990 | + | 0.611990i | ||||
\(268\) | 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 | \(-0.874481\pi\) | ||
0.923254 | − | 0.384189i | \(-0.125519\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 12.9057 | + | 2.90569i | 0.781088 | + | 0.175861i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.00000i | 0.301511i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.0000 | − | 18.0000i | −1.08152 | − | 1.08152i | −0.996368 | − | 0.0851468i | \(-0.972864\pi\) |
−0.0851468 | − | 0.996368i | \(-0.527136\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.32456 | −0.378641 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.00000 | 0.536895 | 0.268447 | − | 0.963294i | \(-0.413489\pi\) | ||||
0.268447 | + | 0.963294i | \(0.413489\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.74342 | + | 4.74342i | 0.281967 | + | 0.281967i | 0.833893 | − | 0.551926i | \(-0.186107\pi\) |
−0.551926 | + | 0.833893i | \(0.686107\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − | 15.8114i | − | 0.936586i | ||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 24.4868 | + | 5.51317i | 1.44541 | + | 0.325432i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12.0000i | 0.705882i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.00000 | 0.293105 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.90569 | − | 7.90569i | −0.461856 | − | 0.461856i | 0.437408 | − | 0.899263i | \(-0.355897\pi\) |
−0.899263 | + | 0.437408i | \(0.855897\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 15.0000 | + | 15.0000i | 0.873334 | + | 0.873334i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.58114 | + | 1.58114i | −0.0917470 | + | 0.0917470i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.32456 | 0.365758 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.00000 | − | 9.48683i | −0.345834 | − | 0.546812i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.00000 | − | 5.00000i | 0.287242 | − | 0.287242i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −10.0000 | + | 10.0000i | −0.572598 | + | 0.572598i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.74342 | − | 4.74342i | 0.270721 | − | 0.270721i | −0.558669 | − | 0.829390i | \(-0.688688\pi\) |
0.829390 | + | 0.558669i | \(0.188688\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 35.0000i | 1.99108i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 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 | \(-0.442575\pi\) |
−0.983771 | + | 0.179430i | \(0.942575\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −6.32456 | − | 10.0000i | −0.356348 | − | 0.563436i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 19.0000 | + | 19.0000i | 1.06715 | + | 1.06715i | 0.997577 | + | 0.0695692i | \(0.0221625\pi\) |
0.0695692 | + | 0.997577i | \(0.477838\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.00000i | 0.167968i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 9.48683i | − | 0.529503i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.00000 | + | 5.00000i | −0.278207 | + | 0.278207i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.90569 | − | 7.90569i | 0.438529 | − | 0.438529i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −11.0680 | + | 11.0680i | −0.612060 | + | 0.612060i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9.48683 | − | 15.0000i | −0.523026 | − | 0.826977i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.00000 | 0.329790 | 0.164895 | − | 0.986311i | \(-0.447272\pi\) | ||||
0.164895 | + | 0.986311i | \(0.447272\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 12.0000 | − | 12.0000i | 0.657596 | − | 0.657596i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 3.16228i | − | 0.172774i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.00000 | − | 8.00000i | −0.435788 | − | 0.435788i | 0.454804 | − | 0.890592i | \(-0.349709\pi\) |
−0.890592 | + | 0.454804i | \(0.849709\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −37.9473 | −2.06102 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.16228i | 0.171247i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −11.4189 | + | 14.5811i | −0.616561 | + | 0.787307i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −10.0000 | − | 10.0000i | −0.538382 | − | 0.538382i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −24.0000 | − | 24.0000i | −1.28839 | − | 1.28839i | −0.935766 | − | 0.352621i | \(-0.885290\pi\) |
−0.352621 | − | 0.935766i | \(-0.614710\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 34.7851 | 1.86200 | 0.931001 | − | 0.365018i | \(-0.118937\pi\) | ||||
0.931001 | + | 0.365018i | \(0.118937\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.00000 | 0.266880 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 14.2302 | + | 14.2302i | 0.757400 | + | 0.757400i | 0.975848 | − | 0.218449i | \(-0.0700996\pi\) |
−0.218449 | + | 0.975848i | \(0.570100\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.48683 | − | 9.48683i | −0.503509 | − | 0.503509i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.90569 | + | 12.9057i | −0.153786 | + | 0.683042i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 22.0000i | 1.16112i | 0.814219 | + | 0.580558i | \(0.197165\pi\) | ||||
−0.814219 | + | 0.580558i | \(0.802835\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.00000 | −0.473684 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 15.8114 | + | 15.8114i | 0.829883 | + | 0.829883i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.3925 | − | 17.3925i | 0.907883 | − | 0.907883i | −0.0882186 | − | 0.996101i | \(-0.528117\pi\) |
0.996101 | + | 0.0882186i | \(0.0281174\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −18.9737 | −0.987730 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.00000 | − | 3.16228i | −0.103835 | − | 0.164177i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.0000 | − | 12.0000i | 0.621336 | − | 0.621336i | −0.324537 | − | 0.945873i | \(-0.605208\pi\) |
0.945873 | + | 0.324537i | \(0.105208\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −25.0000 | −1.29099 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 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 | ||||||||
\(381\) | 28.4605i | 1.45808i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 15.8114 | + | 15.8114i | 0.807924 | + | 0.807924i | 0.984319 | − | 0.176395i | \(-0.0564437\pi\) |
−0.176395 | + | 0.984319i | \(0.556444\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.00000 | + | 3.16228i | −0.254824 | + | 0.161165i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.00000 | + | 6.00000i | 0.304997 | + | 0.304997i | ||||
\(388\) | 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 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −20.5548 | + | 20.5548i | −1.03422 | + | 1.03422i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −23.7171 | + | 23.7171i | −1.19033 | + | 1.19033i | −0.213351 | + | 0.976976i | \(0.568438\pi\) |
−0.976976 | + | 0.213351i | \(0.931562\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 15.8114 | − | 10.0000i | 0.791559 | − | 0.500626i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.00000 | −0.0499376 | −0.0249688 | − | 0.999688i | \(-0.507949\pi\) | ||||
−0.0249688 | + | 0.999688i | \(0.507949\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.00000 | − | 5.00000i | 0.249068 | − | 0.249068i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −17.3925 | − | 17.3925i | −0.864242 | − | 0.864242i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.00000 | − | 6.00000i | −0.297409 | − | 0.297409i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.16228 | 0.156365 | 0.0781823 | − | 0.996939i | \(-0.475088\pi\) | ||||
0.0781823 | + | 0.996939i | \(0.475088\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 6.32456i | − | 0.311967i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5.51317 | + | 24.4868i | −0.271285 | + | 1.20492i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 10.0000i | − | 0.490881i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −30.0000 | − | 30.0000i | −1.46911 | − | 1.46911i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.8114 | 0.772437 | 0.386218 | − | 0.922407i | \(-0.373781\pi\) | ||||
0.386218 | + | 0.922407i | \(0.373781\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.0000 | 0.926003 | 0.463002 | − | 0.886357i | \(-0.346772\pi\) | ||||
0.463002 | + | 0.886357i | \(0.346772\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9.48683 | + | 9.48683i | 0.461266 | + | 0.461266i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.90569 | + | 7.90569i | 0.383482 | + | 0.383482i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −16.3246 | − | 3.67544i | −0.790001 | − | 0.177867i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.00000i | 0.241402i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 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 | \(-0.145519\pi\) |
−0.441402 | + | 0.897310i | \(0.645519\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −15.0000 | −0.719195 | ||||||||
\(436\) | 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 | \(0.402394\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.00000 | − | 12.6491i | 0.285714 | − | 0.602339i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.00000 | + | 1.00000i | −0.0475114 | + | 0.0475114i | −0.730463 | − | 0.682952i | \(-0.760696\pi\) |
0.682952 | + | 0.730463i | \(0.260696\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.0000 | + | 10.0000i | 0.474045 | + | 0.474045i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −18.9737 | + | 18.9737i | −0.897424 | + | 0.897424i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 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 | ||||||||
\(453\) | 14.2302 | + | 14.2302i | 0.668595 | + | 0.668595i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 12.9057 | + | 2.90569i | 0.605028 | + | 0.136221i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.00000 | − | 1.00000i | −0.0467780 | − | 0.0467780i | 0.683331 | − | 0.730109i | \(-0.260531\pi\) |
−0.730109 | + | 0.683331i | \(0.760531\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.00000i | 0.233380i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.32456i | 0.294564i | 0.989095 | + | 0.147282i | \(0.0470525\pi\) | ||||
−0.989095 | + | 0.147282i | \(0.952948\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.00000 | − | 4.00000i | 0.185896 | − | 0.185896i | −0.608023 | − | 0.793919i | \(-0.708037\pi\) |
0.793919 | + | 0.608023i | \(0.208037\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −15.8114 | −0.733236 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11.0680 | − | 11.0680i | 0.512165 | − | 0.512165i | −0.403025 | − | 0.915189i | \(-0.632041\pi\) |
0.915189 | + | 0.403025i | \(0.132041\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.16228 | − | 2.00000i | 0.146020 | − | 0.0923514i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −20.0000 | −0.921551 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.00000 | − | 3.00000i | 0.137940 | − | 0.137940i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 15.8114i | − | 0.725476i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.00000 | + | 2.00000i | 0.0915737 | + | 0.0915737i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.32456 | 0.288976 | 0.144488 | − | 0.989507i | \(-0.453846\pi\) | ||||
0.144488 | + | 0.989507i | \(0.453846\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.9737i | 0.865125i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.67544 | − | 16.3246i | 0.167239 | − | 0.742793i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.00000 | 0.227038 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.00000 | − | 4.00000i | −0.181257 | − | 0.181257i | 0.610646 | − | 0.791904i | \(-0.290910\pi\) |
−0.791904 | + | 0.610646i | \(0.790910\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 18.9737 | 0.858019 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 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 | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.16228 | − | 3.16228i | 0.142134 | − | 0.142134i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.48683 | − | 15.4868i | 0.156406 | − | 0.694679i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 19.0000i | − | 0.850557i | −0.905063 | − | 0.425278i | \(-0.860176\pi\) | ||
0.905063 | − | 0.425278i | \(-0.139824\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 35.0000 | 1.56368 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7.90569 | − | 7.90569i | −0.352497 | − | 0.352497i | 0.508541 | − | 0.861038i | \(-0.330185\pi\) |
−0.861038 | + | 0.508541i | \(0.830185\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.00000 | − | 5.00000i | 0.222497 | − | 0.222497i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.6491 | + | 12.6491i | −0.561767 | + | 0.561767i | ||||
\(508\) | 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 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.00000 | − | 5.00000i | 0.220755 | − | 0.220755i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 35.0000i | 1.54228i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.74342 | − | 4.74342i | 0.208615 | − | 0.208615i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 35.0000i | 1.53633i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 41.1096i | − | 1.80104i | −0.434810 | − | 0.900522i | \(-0.643184\pi\) | ||
0.434810 | − | 0.900522i | \(-0.356816\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18.9737 | + | 18.9737i | 0.829660 | + | 0.829660i | 0.987470 | − | 0.157809i | \(-0.0504431\pi\) |
−0.157809 | + | 0.987470i | \(0.550443\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −15.8114 | − | 25.0000i | −0.690066 | − | 1.09109i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.00000 | + | 5.00000i | 0.217803 | + | 0.217803i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.0000i | 0.652174i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 18.9737i | − | 0.823387i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 15.0000 | − | 15.0000i | 0.649722 | − | 0.649722i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 9.48683i | − | 0.410152i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.48683 | − | 9.48683i | 0.409387 | − | 0.409387i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −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 | \(0.438026\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 35.0000 | − | 35.0000i | 1.50199 | − | 1.50199i | ||||
\(544\) | 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 | \(-0.389118\pi\) |
−0.939939 | + | 0.341342i | \(0.889118\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 12.6491 | 0.539851 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 9.48683i | − | 0.404153i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −33.5548 | − | 7.55480i | −1.42690 | − | 0.321263i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 30.0000 | − | 30.0000i | 1.27343 | − | 1.27343i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.00000 | − | 6.00000i | −0.254228 | − | 0.254228i | 0.568473 | − | 0.822702i | \(-0.307534\pi\) |
−0.822702 | + | 0.568473i | \(0.807534\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.48683 | −0.401250 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.00000 | −0.211100 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9.48683 | − | 9.48683i | −0.399822 | − | 0.399822i | 0.478348 | − | 0.878170i | \(-0.341236\pi\) |
−0.878170 | + | 0.478348i | \(0.841236\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −37.9473 | −1.59646 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 6.39253 | − | 28.3925i | 0.268461 | − | 1.19237i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 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 | \(-0.316897\pi\) | ||||
0.544033 | + | 0.839064i | \(0.316897\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.74342 | − | 4.74342i | −0.198159 | − | 0.198159i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −10.0000 | − | 10.0000i | −0.417029 | − | 0.417029i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20.5548 | − | 20.5548i | 0.855708 | − | 0.855708i | −0.135121 | − | 0.990829i | \(-0.543142\pi\) |
0.990829 | + | 0.135121i | \(0.0431424\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 25.2982 | 1.05136 | ||||||||
\(580\) | 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 | ||||||||
\(585\) | −10.0000 | −0.413449 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 15.8114 | − | 15.8114i | 0.652606 | − | 0.652606i | −0.301014 | − | 0.953620i | \(-0.597325\pi\) |
0.953620 | + | 0.301014i | \(0.0973251\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 10.0000i | − | 0.412043i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.16228i | 0.130079i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 20.5548 | + | 20.5548i | 0.844085 | + | 0.844085i | 0.989387 | − | 0.145303i | \(-0.0464156\pi\) |
−0.145303 | + | 0.989387i | \(0.546416\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.90569 | + | 12.9057i | −0.119122 | + | 0.529082i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −15.0000 | − | 15.0000i | −0.613909 | − | 0.613909i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 13.0000i | − | 0.531166i | −0.964088 | − | 0.265583i | \(-0.914436\pi\) | ||
0.964088 | − | 0.265583i | \(-0.0855644\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 22.1359i | − | 0.902944i | −0.892285 | − | 0.451472i | \(-0.850899\pi\) | ||
0.892285 | − | 0.451472i | \(-0.149101\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.00000 | + | 2.00000i | −0.0814463 | + | 0.0814463i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 15.8114 | + | 15.8114i | 0.642824 | + | 0.642824i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.2302 | + | 14.2302i | −0.577588 | + | 0.577588i | −0.934238 | − | 0.356650i | \(-0.883919\pi\) |
0.356650 | + | 0.934238i | \(0.383919\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −9.48683 | − | 15.0000i | −0.384426 | − | 0.607831i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −15.0000 | −0.606835 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17.0000 | − | 17.0000i | 0.686624 | − | 0.686624i | −0.274861 | − | 0.961484i | \(-0.588632\pi\) |
0.961484 | + | 0.274861i | \(0.0886317\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −47.4342 | −1.91273 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.00000 | + | 4.00000i | 0.161034 | + | 0.161034i | 0.783025 | − | 0.621991i | \(-0.213676\pi\) |
−0.621991 | + | 0.783025i | \(0.713676\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 25.2982 | 1.01682 | 0.508411 | − | 0.861115i | \(-0.330233\pi\) | ||||
0.508411 | + | 0.861115i | \(0.330233\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 6.32456i | − | 0.253796i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.67544 | + | 16.3246i | −0.147254 | + | 0.654029i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −25.0000 | −1.00000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.00000 | + | 5.00000i | 0.199681 | + | 0.199681i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −18.9737 | −0.756530 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 31.0000 | 1.23409 | 0.617045 | − | 0.786928i | \(-0.288330\pi\) | ||||
0.617045 | + | 0.786928i | \(0.288330\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 26.8794 | + | 26.8794i | 1.06836 | + | 1.06836i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 28.4605i | 1.12942i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.25658 | + | 14.7434i | 0.208273 | + | 0.584155i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12.0000i | 0.474713i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 44.0000 | 1.73790 | 0.868948 | − | 0.494904i | \(-0.164797\pi\) | ||||
0.868948 | + | 0.494904i | \(0.164797\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.74342 | − | 4.74342i | −0.187062 | − | 0.187062i | 0.607363 | − | 0.794425i | \(-0.292228\pi\) |
−0.794425 | + | 0.607363i | \(0.792228\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 15.0000 | + | 15.0000i | 0.590624 | + | 0.590624i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12.6491 | + | 12.6491i | −0.497288 | + | 0.497288i | −0.910593 | − | 0.413305i | \(-0.864374\pi\) |
0.413305 | + | 0.910593i | \(0.364374\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.48683 | −0.372391 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10.0000 | − | 15.8114i | −0.391931 | − | 0.619697i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −19.0000 | + | 19.0000i | −0.743527 | + | 0.743527i | −0.973255 | − | 0.229728i | \(-0.926216\pi\) |
0.229728 | + | 0.973255i | \(0.426216\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.00000i | 0.0389545i | 0.999810 | + | 0.0194772i | \(0.00620019\pi\) | ||||
−0.999810 | + | 0.0194772i | \(0.993800\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.6491i | 0.491993i | 0.969271 | + | 0.245997i | \(0.0791152\pi\) | ||||
−0.969271 | + | 0.245997i | \(0.920885\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 7.90569 | + | 7.90569i | 0.307032 | + | 0.307032i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 15.8114 | − | 10.0000i | 0.613139 | − | 0.387783i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.00000 | − | 6.00000i | −0.232321 | − | 0.232321i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 45.0000i | 1.73980i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 6.32456i | − | 0.244157i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24.0000 | + | 24.0000i | −0.925132 | + | 0.925132i | −0.997386 | − | 0.0722542i | \(-0.976981\pi\) |
0.0722542 | + | 0.997386i | \(0.476981\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −7.90569 | − | 7.90569i | −0.304290 | − | 0.304290i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14.2302 | + | 14.2302i | −0.546913 | + | 0.546913i | −0.925547 | − | 0.378634i | \(-0.876394\pi\) |
0.378634 | + | 0.925547i | \(0.376394\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.16228 | + | 5.00000i | 0.121357 | + | 0.191882i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.00000 | −0.191600 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −32.0000 | + | 32.0000i | −1.22445 | + | 1.22445i | −0.258411 | + | 0.966035i | \(0.583199\pi\) |
−0.966035 | + | 0.258411i | \(0.916801\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 6.32456i | − | 0.241649i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −25.0000 | − | 25.0000i | −0.953809 | − | 0.953809i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.16228 | −0.120473 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 31.6228i | 1.20299i | 0.798878 | + | 0.601494i | \(0.205427\pi\) | ||||
−0.798878 | + | 0.601494i | \(0.794573\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.16228 | + | 1.16228i | 0.196099 | + | 0.0441513i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −30.0000 | − | 30.0000i | −1.13796 | − | 1.13796i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15.0000 | + | 15.0000i | 0.568166 | + | 0.568166i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 56.9210 | 2.15295 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −13.0000 | −0.491003 | −0.245502 | − | 0.969396i | \(-0.578953\pi\) | ||||
−0.245502 | + | 0.969396i | \(0.578953\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18.9737 | + | 18.9737i | 0.715605 | + | 0.715605i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 23.7171 | + | 23.7171i | 0.893237 | + | 0.893237i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.16228 | + | 1.83772i | 0.306974 | + | 0.0691147i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.00000i | 0.338002i | 0.985616 | + | 0.169001i | \(0.0540541\pi\) | ||||
−0.985616 | + | 0.169001i | \(0.945946\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 26.0000 | 0.975076 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.32456 | − | 6.32456i | −0.236856 | − | 0.236856i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.00000i | 0.186989i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −30.0416 | + | 30.0416i | −1.12193 | + | 1.12193i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −31.6228 | −1.17933 | −0.589665 | − | 0.807648i | \(-0.700740\pi\) | ||||
−0.589665 | + | 0.807648i | \(0.700740\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −35.0000 | + | 22.1359i | −1.30347 | + | 0.824386i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −40.0000 | + | 40.0000i | −1.48762 | + | 1.48762i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −15.0000 | −0.557086 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.48683 | + | 9.48683i | −0.351847 | + | 0.351847i | −0.860796 | − | 0.508949i | \(-0.830034\pi\) |
0.508949 | + | 0.860796i | \(0.330034\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 7.00000i | 0.259259i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 9.48683i | − | 0.350883i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17.3925 | + | 17.3925i | 0.642408 | + | 0.642408i | 0.951147 | − | 0.308739i | \(-0.0999070\pi\) |
−0.308739 | + | 0.951147i | \(0.599907\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 15.0000 | − | 31.6228i | 0.553283 | − | 1.16642i | ||||
\(736\) | 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 | ||||||||
\(741\) | − | 15.8114i | − | 0.580846i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.00000 | − | 9.00000i | 0.330178 | − | 0.330178i | −0.522476 | − | 0.852654i | \(-0.674992\pi\) |
0.852654 | + | 0.522476i | \(0.174992\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −18.9737 | + | 18.9737i | −0.695141 | + | 0.695141i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.32456 | + | 6.32456i | −0.231403 | + | 0.231403i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.48683 | − | 6.00000i | 0.346641 | − | 0.219235i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −37.0000 | −1.35015 | −0.675075 | − | 0.737749i | \(-0.735889\pi\) | ||||
−0.675075 | + | 0.737749i | \(0.735889\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 20.0000 | − | 20.0000i | 0.728841 | − | 0.728841i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 14.2302 | + | 14.2302i | 0.517892 | + | 0.517892i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16.0000 | − | 16.0000i | −0.581530 | − | 0.581530i | 0.353794 | − | 0.935324i | \(-0.384892\pi\) |
−0.935324 | + | 0.353794i | \(0.884892\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.32456 | 0.229567 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 25.2982i | − | 0.917060i | −0.888679 | − | 0.458530i | \(-0.848376\pi\) | ||
0.888679 | − | 0.458530i | \(-0.151624\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −18.0680 | − | 4.06797i | −0.654104 | − | 0.147270i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − | 10.0000i | − | 0.361551i | ||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 15.0000 | + | 15.0000i | 0.541619 | + | 0.541619i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22.1359 | −0.798243 | −0.399121 | − | 0.916898i | \(-0.630685\pi\) | ||||
−0.399121 | + | 0.916898i | \(0.630685\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −40.0000 | −1.44056 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −36.3662 | − | 36.3662i | −1.30800 | − | 1.30800i | −0.922856 | − | 0.385145i | \(-0.874151\pi\) |
−0.385145 | − | 0.922856i | \(-0.625849\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −15.8114 | −0.567962 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 48.9737 | + | 11.0263i | 1.75692 | + | 0.395568i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 30.0000i | − | 1.07486i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.00000 | 0.214697 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.74342 | − | 4.74342i | −0.169516 | − | 0.169516i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −20.0000 | −0.713831 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17.3925 | + | 17.3925i | −0.619977 | + | 0.619977i | −0.945525 | − | 0.325549i | \(-0.894451\pi\) |
0.325549 | + | 0.945525i | \(0.394451\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 22.1359 | 0.788060 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −24.0000 | − | 37.9473i | −0.853342 | − | 1.34925i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.0000 | + | 10.0000i | −0.355110 | + | 0.355110i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5.00000 | + | 5.00000i | 0.177332 | + | 0.177332i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.58114 | − | 1.58114i | 0.0560068 | − | 0.0560068i | −0.678549 | − | 0.734555i | \(-0.737391\pi\) |
0.734555 | + | 0.678549i | \(0.237391\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 15.0000i | − | 0.530662i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 12.6491i | − | 0.446934i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.67544 | − | 16.3246i | 0.129542 | − | 0.575365i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 30.0000 | + | 30.0000i | 1.05605 | + | 1.05605i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 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 | \(-0.767896\pi\) | ||
0.745724 | − | 0.666256i | \(-0.232104\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −20.0000 | + | 20.0000i | −0.701431 | + | 0.701431i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 18.9737 | 0.664619 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.48683 | + | 9.48683i | −0.331902 | + | 0.331902i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.32456 | − | 10.0000i | −0.220998 | − | 0.349428i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −23.0000 | −0.802706 | −0.401353 | − | 0.915924i | \(-0.631460\pi\) | ||||
−0.401353 | + | 0.915924i | \(0.631460\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.00000 | − | 3.00000i | 0.104573 | − | 0.104573i | −0.652884 | − | 0.757458i | \(-0.726441\pi\) |
0.757458 | + | 0.652884i | \(0.226441\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7.90569 | − | 7.90569i | 0.275241 | − | 0.275241i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 26.0000 | + | 26.0000i | 0.904109 | + | 0.904109i | 0.995789 | − | 0.0916799i | \(-0.0292237\pi\) |
−0.0916799 | + | 0.995789i | \(0.529224\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 28.4605 | 0.988474 | 0.494237 | − | 0.869327i | \(-0.335448\pi\) | ||||
0.494237 | + | 0.869327i | \(0.335448\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 56.9210i | 1.97457i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −14.7434 | + | 5.25658i | −0.510829 | + | 0.182130i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 35.0000 | 1.21122 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.00000 | − | 5.00000i | −0.172825 | − | 0.172825i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −50.5964 | −1.74678 | −0.873392 | − | 0.487019i | \(-0.838084\pi\) | ||||
−0.873392 | + | 0.487019i | \(0.838084\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20.0000 | 0.689655 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −14.2302 | − | 14.2302i | −0.490116 | − | 0.490116i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −12.6491 | + | 12.6491i | −0.435143 | + | 0.435143i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.81139 | + | 25.8114i | −0.199682 | + | 0.886890i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 15.0000i | − | 0.514799i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 24.0000 | 0.822709 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −10.0000 | + | 10.0000i | −0.341993 | + | 0.341993i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −31.6228 | + | 31.6228i | −1.08021 | + | 1.08021i | −0.0837245 | + | 0.996489i | \(0.526682\pi\) |
−0.996489 | + | 0.0837245i | \(0.973318\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.6491 | −0.431582 | −0.215791 | − | 0.976440i | \(-0.569233\pi\) | ||||
−0.215791 | + | 0.976440i | \(0.569233\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −30.0000 | − | 47.4342i | −1.02240 | − | 1.61655i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 13.0000 | − | 13.0000i | 0.442525 | − | 0.442525i | −0.450335 | − | 0.892860i | \(-0.648695\pi\) |
0.892860 | + | 0.450335i | \(0.148695\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 35.0000i | 1.19004i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 18.9737 | − | 18.9737i | 0.644379 | − | 0.644379i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 13.0000i | − | 0.440995i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 3.16228i | − | 0.107150i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.16228 | − | 3.16228i | −0.107027 | − | 0.107027i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −15.8114 | − | 25.0000i | −0.534522 | − | 0.845154i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17.0000 | + | 17.0000i | 0.574049 | + | 0.574049i | 0.933257 | − | 0.359208i | \(-0.116953\pi\) |
−0.359208 | + | 0.933257i | \(0.616953\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 25.0000i | 0.843229i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 37.9473i | − | 1.27848i | −0.769008 | − | 0.639239i | \(-0.779249\pi\) | ||
0.769008 | − | 0.639239i | \(-0.220751\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.0000 | − | 18.0000i | 0.605748 | − | 0.605748i | −0.336084 | − | 0.941832i | \(-0.609103\pi\) |
0.941832 | + | 0.336084i | \(0.109103\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 47.4342i | − | 1.59448i | ||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.16228 | + | 3.16228i | −0.106179 | + | 0.106179i | −0.758200 | − | 0.652022i | \(-0.773921\pi\) |
0.652022 | + | 0.758200i | \(0.273921\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −28.4605 | + | 18.0000i | −0.954534 | + | 0.603701i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 11.0000 | 0.368514 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −15.0000 | + | 15.0000i | −0.501956 | + | 0.501956i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.48683 | − | 9.48683i | 0.317110 | − | 0.317110i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −10.0000 | − | 10.0000i | −0.333890 | − | 0.333890i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.48683 | −0.316404 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 3.16228i | − | 0.105351i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.51317 | + | 24.4868i | −0.183467 | + | 0.814871i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 35.0000 | − | 35.0000i | 1.16344 | − | 1.16344i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22.0000 | − | 22.0000i | −0.730498 | − | 0.730498i | 0.240220 | − | 0.970718i | \(-0.422780\pi\) |
−0.970718 | + | 0.240220i | \(0.922780\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.32456 | −0.209772 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −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 | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 31.6228 | 1.04542 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 27.0000i | 0.890648i | 0.895370 | + | 0.445324i | \(0.146911\pi\) | ||||
−0.895370 | + | 0.445324i | \(0.853089\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −15.0000 | −0.494267 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −9.48683 | − | 9.48683i | −0.312263 | − | 0.312263i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 30.0000 | − | 30.0000i | 0.986394 | − | 0.986394i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 22.1359 | − | 22.1359i | 0.727040 | − | 0.727040i | ||||
\(928\) | 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 | ||||||||
\(933\) | −35.0000 | + | 35.0000i | −1.14585 | + | 1.14585i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.00000 | −0.163517 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14.2302 | + | 14.2302i | −0.464882 | + | 0.464882i | −0.900252 | − | 0.435370i | \(-0.856618\pi\) |
0.435370 | + | 0.900252i | \(0.356618\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 45.0000i | 1.46852i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 37.9473i | 1.23705i | 0.785766 | + | 0.618524i | \(0.212269\pi\) | ||||
−0.785766 | + | 0.618524i | \(0.787731\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −18.9737 | − | 18.9737i | −0.617868 | − | 0.617868i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.90569 | − | 12.9057i | 0.0945222 | − | 0.419822i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −7.00000 | − | 7.00000i | −0.227469 | − | 0.227469i | 0.584165 | − | 0.811635i | \(-0.301422\pi\) |
−0.811635 | + | 0.584165i | \(0.801422\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 60.0833i | − | 1.94833i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.00000 | + | 3.00000i | −0.0971795 | + | 0.0971795i | −0.754025 | − | 0.656846i | \(-0.771890\pi\) |
0.656846 | + | 0.754025i | \(0.271890\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.74342 | − | 4.74342i | −0.153493 | − | 0.153493i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.74342 | − | 4.74342i | 0.153333 | − | 0.153333i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.32456 | − | 4.00000i | 0.204231 | − | 0.129167i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 21.0000 | 0.677419 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.00000 | + | 6.00000i | −0.193347 | + | 0.193347i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 25.2982 | 0.814379 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 33.0000 | + | 33.0000i | 1.06121 | + | 1.06121i | 0.998000 | + | 0.0632081i | \(0.0201332\pi\) |
0.0632081 | + | 0.998000i | \(0.479867\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 15.8114 | 0.507935 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 34.7851i | − | 1.11631i | −0.829738 | − | 0.558153i | \(-0.811510\pi\) | ||
0.829738 | − | 0.558153i | \(-0.188490\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.0263 | − | 48.9737i | 0.353488 | − | 1.57002i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −25.0000 | −0.800641 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.00000 | − | 1.00000i | −0.0319928 | − | 0.0319928i | 0.690929 | − | 0.722922i | \(-0.257202\pi\) |
−0.722922 | + | 0.690929i | \(0.757202\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.32456 | −0.202134 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.0000 | 0.446986 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 20.5548 | + | 20.5548i | 0.655596 | + | 0.655596i | 0.954335 | − | 0.298739i | \(-0.0965658\pi\) |
−0.298739 | + | 0.954335i | \(0.596566\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.16228i | 0.100759i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −8.71708 | + | 38.7171i | −0.277468 | + | 1.23238i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12.0000i | 0.381578i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.00000 | −0.127064 | −0.0635321 | − | 0.997980i | \(-0.520237\pi\) | ||||
−0.0635321 | + | 0.997980i | \(0.520237\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −9.48683 | − | 9.48683i | −0.301056 | − | 0.301056i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −15.0000 | − | 15.0000i | −0.475532 | − | 0.475532i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14.2302 | − | 14.2302i | 0.450677 | − | 0.450677i | −0.444902 | − | 0.895579i | \(-0.646762\pi\) |
0.895579 | + | 0.444902i | \(0.146762\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 18.9737 | 0.600300 |
(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 | 560.2.bj.a.97.1 | 4 | ||
4.3 | odd | 2 | 35.2.f.a.27.2 | yes | 4 | ||
5.3 | odd | 4 | inner | 560.2.bj.a.433.2 | 4 | ||
7.6 | odd | 2 | inner | 560.2.bj.a.97.2 | 4 | ||
12.11 | even | 2 | 315.2.p.c.307.2 | 4 | |||
20.3 | even | 4 | 35.2.f.a.13.1 | ✓ | 4 | ||
20.7 | even | 4 | 175.2.f.c.118.2 | 4 | |||
20.19 | odd | 2 | 175.2.f.c.132.1 | 4 | |||
28.3 | even | 6 | 245.2.l.c.117.1 | 8 | |||
28.11 | odd | 6 | 245.2.l.c.117.2 | 8 | |||
28.19 | even | 6 | 245.2.l.c.227.2 | 8 | |||
28.23 | odd | 6 | 245.2.l.c.227.1 | 8 | |||
28.27 | even | 2 | 35.2.f.a.27.1 | yes | 4 | ||
35.13 | even | 4 | inner | 560.2.bj.a.433.1 | 4 | ||
60.23 | odd | 4 | 315.2.p.c.118.1 | 4 | |||
84.83 | odd | 2 | 315.2.p.c.307.1 | 4 | |||
140.3 | odd | 12 | 245.2.l.c.68.1 | 8 | |||
140.23 | even | 12 | 245.2.l.c.178.1 | 8 | |||
140.27 | odd | 4 | 175.2.f.c.118.1 | 4 | |||
140.83 | odd | 4 | 35.2.f.a.13.2 | yes | 4 | ||
140.103 | odd | 12 | 245.2.l.c.178.2 | 8 | |||
140.123 | even | 12 | 245.2.l.c.68.2 | 8 | |||
140.139 | even | 2 | 175.2.f.c.132.2 | 4 | |||
420.83 | even | 4 | 315.2.p.c.118.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.2.f.a.13.1 | ✓ | 4 | 20.3 | even | 4 | ||
35.2.f.a.13.2 | yes | 4 | 140.83 | odd | 4 | ||
35.2.f.a.27.1 | yes | 4 | 28.27 | even | 2 | ||
35.2.f.a.27.2 | yes | 4 | 4.3 | odd | 2 | ||
175.2.f.c.118.1 | 4 | 140.27 | odd | 4 | |||
175.2.f.c.118.2 | 4 | 20.7 | even | 4 | |||
175.2.f.c.132.1 | 4 | 20.19 | odd | 2 | |||
175.2.f.c.132.2 | 4 | 140.139 | even | 2 | |||
245.2.l.c.68.1 | 8 | 140.3 | odd | 12 | |||
245.2.l.c.68.2 | 8 | 140.123 | even | 12 | |||
245.2.l.c.117.1 | 8 | 28.3 | even | 6 | |||
245.2.l.c.117.2 | 8 | 28.11 | odd | 6 | |||
245.2.l.c.178.1 | 8 | 140.23 | even | 12 | |||
245.2.l.c.178.2 | 8 | 140.103 | odd | 12 | |||
245.2.l.c.227.1 | 8 | 28.23 | odd | 6 | |||
245.2.l.c.227.2 | 8 | 28.19 | even | 6 | |||
315.2.p.c.118.1 | 4 | 60.23 | odd | 4 | |||
315.2.p.c.118.2 | 4 | 420.83 | even | 4 | |||
315.2.p.c.307.1 | 4 | 84.83 | odd | 2 | |||
315.2.p.c.307.2 | 4 | 12.11 | even | 2 | |||
560.2.bj.a.97.1 | 4 | 1.1 | even | 1 | trivial | ||
560.2.bj.a.97.2 | 4 | 7.6 | odd | 2 | inner | ||
560.2.bj.a.433.1 | 4 | 35.13 | even | 4 | inner | ||
560.2.bj.a.433.2 | 4 | 5.3 | odd | 4 | inner |