Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [900,2,Mod(307,900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(900, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("900.307");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 900.k (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.18653618192\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 300) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 343.4 | ||
Root | \(0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 900.343 |
Dual form | 900.2.k.l.307.3 |
$q$-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 \(\left(\mathbb{Z}/900\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(451\) | \(577\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.22474 | + | 0.707107i | 0.866025 | + | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | + | 1.73205i | 0.500000 | + | 0.866025i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.74238 | − | 1.74238i | −0.658559 | − | 0.658559i | 0.296480 | − | 0.955039i | \(-0.404187\pi\) |
−0.955039 | + | 0.296480i | \(0.904187\pi\) | |||||||
\(8\) | 2.82843i | 1.00000i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.00000i | 0.603023i | 0.953463 | + | 0.301511i | \(0.0974911\pi\) | ||||
−0.953463 | + | 0.301511i | \(0.902509\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.05317 | + | 4.05317i | 1.12415 | + | 1.12415i | 0.991111 | + | 0.133037i | \(0.0424728\pi\) |
0.133037 | + | 0.991111i | \(0.457527\pi\) | |||||||
\(14\) | −0.901924 | − | 3.36603i | −0.241049 | − | 0.899608i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | + | 3.46410i | −0.500000 | + | 0.866025i | ||||
\(17\) | −4.24264 | + | 4.24264i | −1.02899 | + | 1.02899i | −0.0294245 | + | 0.999567i | \(0.509367\pi\) |
−0.999567 | + | 0.0294245i | \(0.990633\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.19615 | 1.65091 | 0.825455 | − | 0.564467i | \(-0.190918\pi\) | ||||
0.825455 | + | 0.564467i | \(0.190918\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.41421 | + | 2.44949i | −0.301511 | + | 0.522233i | ||||
\(23\) | 0.378937 | − | 0.378937i | 0.0790139 | − | 0.0790139i | −0.666495 | − | 0.745509i | \(-0.732206\pi\) |
0.745509 | + | 0.666495i | \(0.232206\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.09808 | + | 7.83013i | 0.411467 | + | 1.53561i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.27551 | − | 4.76028i | 0.241049 | − | 0.899608i | ||||
\(29\) | 7.46410i | 1.38605i | 0.720914 | + | 0.693024i | \(0.243722\pi\) | ||||
−0.720914 | + | 0.693024i | \(0.756278\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 0.267949i | − | 0.0481251i | −0.999710 | − | 0.0240625i | \(-0.992340\pi\) | ||
0.999710 | − | 0.0240625i | \(-0.00766009\pi\) | |||||||
\(32\) | −4.89898 | + | 2.82843i | −0.866025 | + | 0.500000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −8.19615 | + | 2.19615i | −1.40563 | + | 0.376637i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.07055 | − | 2.07055i | 0.340397 | − | 0.340397i | −0.516120 | − | 0.856516i | \(-0.672624\pi\) |
0.856516 | + | 0.516120i | \(0.172624\pi\) | |||||||
\(38\) | 8.81345 | + | 5.08845i | 1.42973 | + | 0.825455i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.46410 | 0.853349 | 0.426675 | − | 0.904405i | \(-0.359685\pi\) | ||||
0.426675 | + | 0.904405i | \(0.359685\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.74238 | − | 1.74238i | 0.265711 | − | 0.265711i | −0.561658 | − | 0.827369i | \(-0.689836\pi\) |
0.827369 | + | 0.561658i | \(0.189836\pi\) | |||||||
\(44\) | −3.46410 | + | 2.00000i | −0.522233 | + | 0.301511i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.732051 | − | 0.196152i | 0.107935 | − | 0.0289211i | ||||
\(47\) | −9.14162 | − | 9.14162i | −1.33344 | − | 1.33344i | −0.902269 | − | 0.431173i | \(-0.858100\pi\) |
−0.431173 | − | 0.902269i | \(-0.641900\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 0.928203i | − | 0.132600i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.96713 | + | 11.0735i | −0.411467 | + | 1.53561i | ||||
\(53\) | −1.03528 | − | 1.03528i | −0.142206 | − | 0.142206i | 0.632420 | − | 0.774626i | \(-0.282062\pi\) |
−0.774626 | + | 0.632420i | \(0.782062\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.92820 | − | 4.92820i | 0.658559 | − | 0.658559i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.27792 | + | 9.14162i | −0.693024 | + | 1.20035i | ||||
\(59\) | 4.53590 | 0.590524 | 0.295262 | − | 0.955416i | \(-0.404593\pi\) | ||||
0.295262 | + | 0.955416i | \(0.404593\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.00000 | 0.384111 | 0.192055 | − | 0.981384i | \(-0.438485\pi\) | ||||
0.192055 | + | 0.981384i | \(0.438485\pi\) | |||||||
\(62\) | 0.189469 | − | 0.328169i | 0.0240625 | − | 0.0416776i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.81345 | − | 8.81345i | −1.07673 | − | 1.07673i | −0.996800 | − | 0.0799342i | \(-0.974529\pi\) |
−0.0799342 | − | 0.996800i | \(-0.525471\pi\) | |||||||
\(68\) | −11.5911 | − | 3.10583i | −1.40563 | − | 0.376637i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 9.46410i | − | 1.12318i | −0.827415 | − | 0.561591i | \(-0.810189\pi\) | ||
0.827415 | − | 0.561591i | \(-0.189811\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.82843 | − | 2.82843i | −0.331042 | − | 0.331042i | 0.521940 | − | 0.852982i | \(-0.325209\pi\) |
−0.852982 | + | 0.521940i | \(0.825209\pi\) | |||||||
\(74\) | 4.00000 | − | 1.07180i | 0.464991 | − | 0.124594i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.19615 | + | 12.4641i | 0.825455 | + | 1.42973i | ||||
\(77\) | 3.48477 | − | 3.48477i | 0.397126 | − | 0.397126i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.535898 | 0.0602933 | 0.0301466 | − | 0.999545i | \(-0.490403\pi\) | ||||
0.0301466 | + | 0.999545i | \(0.490403\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6.69213 | + | 3.86370i | 0.739022 | + | 0.426675i | ||||
\(83\) | 0.656339 | − | 0.656339i | 0.0720425 | − | 0.0720425i | −0.670167 | − | 0.742210i | \(-0.733778\pi\) |
0.742210 | + | 0.670167i | \(0.233778\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 3.36603 | − | 0.901924i | 0.362968 | − | 0.0972569i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −5.65685 | −0.603023 | ||||||||
\(89\) | − | 6.92820i | − | 0.734388i | −0.930144 | − | 0.367194i | \(-0.880318\pi\) | ||
0.930144 | − | 0.367194i | \(-0.119682\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 14.1244i | − | 1.48063i | ||||||
\(92\) | 1.03528 | + | 0.277401i | 0.107935 | + | 0.0289211i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.73205 | − | 17.6603i | −0.488074 | − | 1.82152i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.43211 | + | 4.43211i | −0.450013 | + | 0.450013i | −0.895359 | − | 0.445346i | \(-0.853081\pi\) |
0.445346 | + | 0.895359i | \(0.353081\pi\) | |||||||
\(98\) | 0.656339 | − | 1.13681i | 0.0663002 | − | 0.114835i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.46410 | 0.145684 | 0.0728418 | − | 0.997344i | \(-0.476793\pi\) | ||||
0.0728418 | + | 0.997344i | \(0.476793\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.89898 | + | 4.89898i | −0.482711 | + | 0.482711i | −0.905996 | − | 0.423286i | \(-0.860877\pi\) |
0.423286 | + | 0.905996i | \(0.360877\pi\) | |||||||
\(104\) | −11.4641 | + | 11.4641i | −1.12415 | + | 1.12415i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.535898 | − | 2.00000i | −0.0520511 | − | 0.194257i | ||||
\(107\) | 4.62158 | + | 4.62158i | 0.446785 | + | 0.446785i | 0.894284 | − | 0.447499i | \(-0.147685\pi\) |
−0.447499 | + | 0.894284i | \(0.647685\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.00000i | 0.670478i | 0.942133 | + | 0.335239i | \(0.108817\pi\) | ||||
−0.942133 | + | 0.335239i | \(0.891183\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 9.52056 | − | 2.55103i | 0.899608 | − | 0.241049i | ||||
\(113\) | 9.79796 | + | 9.79796i | 0.921714 | + | 0.921714i | 0.997151 | − | 0.0754362i | \(-0.0240349\pi\) |
−0.0754362 | + | 0.997151i | \(0.524035\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −12.9282 | + | 7.46410i | −1.20035 | + | 0.693024i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 5.55532 | + | 3.20736i | 0.511409 | + | 0.295262i | ||||
\(119\) | 14.7846 | 1.35530 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.00000 | 0.636364 | ||||||||
\(122\) | 3.67423 | + | 2.12132i | 0.332650 | + | 0.192055i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.464102 | − | 0.267949i | 0.0416776 | − | 0.0240625i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.07055 | − | 2.07055i | −0.183732 | − | 0.183732i | 0.609248 | − | 0.792980i | \(-0.291471\pi\) |
−0.792980 | + | 0.609248i | \(0.791471\pi\) | |||||||
\(128\) | −9.79796 | − | 5.65685i | −0.866025 | − | 0.500000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.46410i | 0.826882i | 0.910531 | + | 0.413441i | \(0.135673\pi\) | ||||
−0.910531 | + | 0.413441i | \(0.864327\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −12.5385 | − | 12.5385i | −1.08722 | − | 1.08722i | ||||
\(134\) | −4.56218 | − | 17.0263i | −0.394112 | − | 1.47085i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −12.0000 | − | 12.0000i | −1.02899 | − | 1.02899i | ||||
\(137\) | 6.03579 | − | 6.03579i | 0.515672 | − | 0.515672i | −0.400586 | − | 0.916259i | \(-0.631194\pi\) |
0.916259 | + | 0.400586i | \(0.131194\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19.4641 | 1.65092 | 0.825462 | − | 0.564458i | \(-0.190915\pi\) | ||||
0.825462 | + | 0.564458i | \(0.190915\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 6.69213 | − | 11.5911i | 0.561591 | − | 0.972704i | ||||
\(143\) | −8.10634 | + | 8.10634i | −0.677887 | + | 0.677887i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.46410 | − | 5.46410i | −0.121170 | − | 0.452212i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5.65685 | + | 1.51575i | 0.464991 | + | 0.124594i | ||||
\(149\) | − | 15.8564i | − | 1.29901i | −0.760358 | − | 0.649504i | \(-0.774977\pi\) | ||
0.760358 | − | 0.649504i | \(-0.225023\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 4.26795i | − | 0.347321i | −0.984806 | − | 0.173660i | \(-0.944440\pi\) | ||
0.984806 | − | 0.173660i | \(-0.0555595\pi\) | |||||||
\(152\) | 20.3538i | 1.65091i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 6.73205 | − | 1.80385i | 0.542484 | − | 0.145358i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.88160 | − | 6.88160i | 0.549211 | − | 0.549211i | −0.377001 | − | 0.926213i | \(-0.623045\pi\) |
0.926213 | + | 0.377001i | \(0.123045\pi\) | |||||||
\(158\) | 0.656339 | + | 0.378937i | 0.0522155 | + | 0.0301466i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.32051 | −0.104071 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.2277 | − | 10.2277i | 0.801092 | − | 0.801092i | −0.182174 | − | 0.983266i | \(-0.558313\pi\) |
0.983266 | + | 0.182174i | \(0.0583134\pi\) | |||||||
\(164\) | 5.46410 | + | 9.46410i | 0.426675 | + | 0.739022i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.26795 | − | 0.339746i | 0.0984119 | − | 0.0263694i | ||||
\(167\) | 3.10583 | + | 3.10583i | 0.240336 | + | 0.240336i | 0.816989 | − | 0.576653i | \(-0.195642\pi\) |
−0.576653 | + | 0.816989i | \(0.695642\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 19.8564i | 1.52742i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.76028 | + | 1.27551i | 0.362968 | + | 0.0972569i | ||||
\(173\) | −6.31319 | − | 6.31319i | −0.479983 | − | 0.479983i | 0.425143 | − | 0.905126i | \(-0.360224\pi\) |
−0.905126 | + | 0.425143i | \(0.860224\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −6.92820 | − | 4.00000i | −0.522233 | − | 0.301511i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 4.89898 | − | 8.48528i | 0.367194 | − | 0.635999i | ||||
\(179\) | −25.3205 | −1.89254 | −0.946272 | − | 0.323372i | \(-0.895183\pi\) | ||||
−0.946272 | + | 0.323372i | \(0.895183\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.9282 | −1.03528 | −0.517638 | − | 0.855600i | \(-0.673188\pi\) | ||||
−0.517638 | + | 0.855600i | \(0.673188\pi\) | |||||||
\(182\) | 9.98743 | − | 17.2987i | 0.740317 | − | 1.28227i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.07180 | + | 1.07180i | 0.0790139 | + | 0.0790139i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.48528 | − | 8.48528i | −0.620505 | − | 0.620505i | ||||
\(188\) | 6.69213 | − | 24.9754i | 0.488074 | − | 1.82152i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 16.9282i | − | 1.22488i | −0.790516 | − | 0.612441i | \(-0.790188\pi\) | ||
0.790516 | − | 0.612441i | \(-0.209812\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.71003 | + | 9.71003i | 0.698943 | + | 0.698943i | 0.964183 | − | 0.265240i | \(-0.0854510\pi\) |
−0.265240 | + | 0.964183i | \(0.585451\pi\) | |||||||
\(194\) | −8.56218 | + | 2.29423i | −0.614729 | + | 0.164716i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.60770 | − | 0.928203i | 0.114835 | − | 0.0663002i | ||||
\(197\) | 10.1769 | − | 10.1769i | 0.725074 | − | 0.725074i | −0.244560 | − | 0.969634i | \(-0.578644\pi\) |
0.969634 | + | 0.244560i | \(0.0786436\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.1244 | −1.00125 | −0.500625 | − | 0.865665i | \(-0.666896\pi\) | ||||
−0.500625 | + | 0.865665i | \(0.666896\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.79315 | + | 1.03528i | 0.126166 | + | 0.0728418i | ||||
\(203\) | 13.0053 | − | 13.0053i | 0.912795 | − | 0.912795i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −9.46410 | + | 2.53590i | −0.659395 | + | 0.176684i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −22.1469 | + | 5.93426i | −1.53561 | + | 0.411467i | ||||
\(209\) | 14.3923i | 0.995537i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.19615i | 0.495404i | 0.968836 | + | 0.247702i | \(0.0796753\pi\) | ||||
−0.968836 | + | 0.247702i | \(0.920325\pi\) | |||||||
\(212\) | 0.757875 | − | 2.82843i | 0.0520511 | − | 0.194257i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.39230 | + | 8.92820i | 0.163535 | + | 0.610319i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.466870 | + | 0.466870i | −0.0316932 | + | 0.0316932i | ||||
\(218\) | −4.94975 | + | 8.57321i | −0.335239 | + | 0.580651i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −34.3923 | −2.31348 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.05558 | − | 8.05558i | 0.539441 | − | 0.539441i | −0.383924 | − | 0.923365i | \(-0.625427\pi\) |
0.923365 | + | 0.383924i | \(0.125427\pi\) | |||||||
\(224\) | 13.4641 | + | 3.60770i | 0.899608 | + | 0.241049i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.07180 | + | 18.9282i | 0.337371 | + | 1.25909i | ||||
\(227\) | 8.76268 | + | 8.76268i | 0.581600 | + | 0.581600i | 0.935343 | − | 0.353743i | \(-0.115091\pi\) |
−0.353743 | + | 0.935343i | \(0.615091\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 24.8564i | − | 1.64256i | −0.570527 | − | 0.821279i | \(-0.693261\pi\) | ||
0.570527 | − | 0.821279i | \(-0.306739\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −21.1117 | −1.38605 | ||||||||
\(233\) | −8.76268 | − | 8.76268i | −0.574062 | − | 0.574062i | 0.359199 | − | 0.933261i | \(-0.383050\pi\) |
−0.933261 | + | 0.359199i | \(0.883050\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 4.53590 | + | 7.85641i | 0.295262 | + | 0.511409i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 18.1074 | + | 10.4543i | 1.17373 | + | 0.677651i | ||||
\(239\) | 17.4641 | 1.12966 | 0.564829 | − | 0.825208i | \(-0.308942\pi\) | ||||
0.564829 | + | 0.825208i | \(0.308942\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.8564 | −0.956985 | −0.478493 | − | 0.878092i | \(-0.658817\pi\) | ||||
−0.478493 | + | 0.878092i | \(0.658817\pi\) | |||||||
\(242\) | 8.57321 | + | 4.94975i | 0.551107 | + | 0.318182i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.00000 | + | 5.19615i | 0.192055 | + | 0.332650i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 29.1672 | + | 29.1672i | 1.85587 | + | 1.85587i | ||||
\(248\) | 0.757875 | 0.0481251 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 2.14359i | − | 0.135302i | −0.997709 | − | 0.0676512i | \(-0.978449\pi\) | ||
0.997709 | − | 0.0676512i | \(-0.0215505\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.757875 | + | 0.757875i | 0.0476472 | + | 0.0476472i | ||||
\(254\) | −1.07180 | − | 4.00000i | −0.0672505 | − | 0.250982i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | − | 13.8564i | −0.500000 | − | 0.866025i | ||||
\(257\) | −9.04008 | + | 9.04008i | −0.563905 | + | 0.563905i | −0.930414 | − | 0.366509i | \(-0.880553\pi\) |
0.366509 | + | 0.930414i | \(0.380553\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.21539 | −0.448343 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6.69213 | + | 11.5911i | −0.413441 | + | 0.716101i | ||||
\(263\) | 15.1774 | − | 15.1774i | 0.935879 | − | 0.935879i | −0.0621853 | − | 0.998065i | \(-0.519807\pi\) |
0.998065 | + | 0.0621853i | \(0.0198070\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −6.49038 | − | 24.2224i | −0.397951 | − | 1.48517i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6.45189 | − | 24.0788i | 0.394112 | − | 1.47085i | ||||
\(269\) | − | 1.60770i | − | 0.0980229i | −0.998798 | − | 0.0490115i | \(-0.984393\pi\) | ||
0.998798 | − | 0.0490115i | \(-0.0156071\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.2487i | 1.47300i | 0.676435 | + | 0.736502i | \(0.263524\pi\) | ||||
−0.676435 | + | 0.736502i | \(0.736476\pi\) | |||||||
\(272\) | −6.21166 | − | 23.1822i | −0.376637 | − | 1.40563i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11.6603 | − | 3.12436i | 0.704422 | − | 0.188749i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.845807 | − | 0.845807i | 0.0508196 | − | 0.0508196i | −0.681240 | − | 0.732060i | \(-0.738559\pi\) |
0.732060 | + | 0.681240i | \(0.238559\pi\) | |||||||
\(278\) | 23.8386 | + | 13.7632i | 1.42974 | + | 0.825462i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.3923 | 0.858573 | 0.429286 | − | 0.903168i | \(-0.358765\pi\) | ||||
0.429286 | + | 0.903168i | \(0.358765\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.1266 | + | 15.1266i | −0.899186 | + | 0.899186i | −0.995364 | − | 0.0961785i | \(-0.969338\pi\) |
0.0961785 | + | 0.995364i | \(0.469338\pi\) | |||||||
\(284\) | 16.3923 | − | 9.46410i | 0.972704 | − | 0.561591i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −15.6603 | + | 4.19615i | −0.926010 | + | 0.248124i | ||||
\(287\) | −9.52056 | − | 9.52056i | −0.561981 | − | 0.561981i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 19.0000i | − | 1.11765i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.07055 | − | 7.72741i | 0.121170 | − | 0.452212i | ||||
\(293\) | −8.86422 | − | 8.86422i | −0.517853 | − | 0.517853i | 0.399068 | − | 0.916921i | \(-0.369334\pi\) |
−0.916921 | + | 0.399068i | \(0.869334\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 5.85641 | + | 5.85641i | 0.340397 | + | 0.340397i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 11.2122 | − | 19.4201i | 0.649504 | − | 1.12497i | ||||
\(299\) | 3.07180 | 0.177647 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.07180 | −0.349973 | ||||||||
\(302\) | 3.01790 | − | 5.22715i | 0.173660 | − | 0.300789i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −14.3923 | + | 24.9282i | −0.825455 | + | 1.42973i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.46979 | + | 9.46979i | 0.540469 | + | 0.540469i | 0.923667 | − | 0.383197i | \(-0.125177\pi\) |
−0.383197 | + | 0.923667i | \(0.625177\pi\) | |||||||
\(308\) | 9.52056 | + | 2.55103i | 0.542484 | + | 0.145358i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 27.4641i | 1.55735i | 0.627430 | + | 0.778673i | \(0.284107\pi\) | ||||
−0.627430 | + | 0.778673i | \(0.715893\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.74479 | + | 5.74479i | 0.324715 | + | 0.324715i | 0.850572 | − | 0.525858i | \(-0.176256\pi\) |
−0.525858 | + | 0.850572i | \(0.676256\pi\) | |||||||
\(314\) | 13.2942 | − | 3.56218i | 0.750237 | − | 0.201025i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.535898 | + | 0.928203i | 0.0301466 | + | 0.0522155i | ||||
\(317\) | 4.89898 | − | 4.89898i | 0.275154 | − | 0.275154i | −0.556017 | − | 0.831171i | \(-0.687671\pi\) |
0.831171 | + | 0.556017i | \(0.187671\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −14.9282 | −0.835819 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.61729 | − | 0.933740i | −0.0901278 | − | 0.0520353i | ||||
\(323\) | −30.5307 | + | 30.5307i | −1.69877 | + | 1.69877i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 19.7583 | − | 5.29423i | 1.09431 | − | 0.293220i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 15.4548i | 0.853349i | ||||||||
\(329\) | 31.8564i | 1.75630i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 2.39230i | − | 0.131493i | −0.997836 | − | 0.0657465i | \(-0.979057\pi\) | ||
0.997836 | − | 0.0657465i | \(-0.0209429\pi\) | |||||||
\(332\) | 1.79315 | + | 0.480473i | 0.0984119 | + | 0.0263694i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.60770 | + | 6.00000i | 0.0879692 | + | 0.328305i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.01841 | − | 8.01841i | 0.436791 | − | 0.436791i | −0.454140 | − | 0.890930i | \(-0.650053\pi\) |
0.890930 | + | 0.454140i | \(0.150053\pi\) | |||||||
\(338\) | −14.0406 | + | 24.3190i | −0.763708 | + | 1.32278i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.535898 | 0.0290205 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.8140 | + | 13.8140i | −0.745884 | + | 0.745884i | ||||
\(344\) | 4.92820 | + | 4.92820i | 0.265711 | + | 0.265711i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.26795 | − | 12.1962i | −0.175686 | − | 0.655669i | ||||
\(347\) | 7.82894 | + | 7.82894i | 0.420280 | + | 0.420280i | 0.885300 | − | 0.465020i | \(-0.153953\pi\) |
−0.465020 | + | 0.885300i | \(0.653953\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.85641i | 0.206429i | 0.994659 | + | 0.103214i | \(0.0329128\pi\) | ||||
−0.994659 | + | 0.103214i | \(0.967087\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −5.65685 | − | 9.79796i | −0.301511 | − | 0.522233i | ||||
\(353\) | 11.2122 | + | 11.2122i | 0.596764 | + | 0.596764i | 0.939450 | − | 0.342686i | \(-0.111337\pi\) |
−0.342686 | + | 0.939450i | \(0.611337\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 12.0000 | − | 6.92820i | 0.635999 | − | 0.367194i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −31.0112 | − | 17.9043i | −1.63899 | − | 0.946272i | ||||
\(359\) | −24.3923 | −1.28738 | −0.643688 | − | 0.765288i | \(-0.722597\pi\) | ||||
−0.643688 | + | 0.765288i | \(0.722597\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 32.7846 | 1.72551 | ||||||||
\(362\) | −17.0585 | − | 9.84873i | −0.896575 | − | 0.517638i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 24.4641 | − | 14.1244i | 1.28227 | − | 0.740317i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.50077 | + | 7.50077i | 0.391537 | + | 0.391537i | 0.875235 | − | 0.483698i | \(-0.160707\pi\) |
−0.483698 | + | 0.875235i | \(0.660707\pi\) | |||||||
\(368\) | 0.554803 | + | 2.07055i | 0.0289211 | + | 0.107935i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.60770i | 0.187302i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.6753 | + | 13.6753i | 0.708078 | + | 0.708078i | 0.966131 | − | 0.258052i | \(-0.0830808\pi\) |
−0.258052 | + | 0.966131i | \(0.583081\pi\) | |||||||
\(374\) | −4.39230 | − | 16.3923i | −0.227121 | − | 0.847626i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 25.8564 | − | 25.8564i | 1.33344 | − | 1.33344i | ||||
\(377\) | −30.2533 | + | 30.2533i | −1.55812 | + | 1.55812i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.7321 | −0.808101 | −0.404051 | − | 0.914737i | \(-0.632398\pi\) | ||||
−0.404051 | + | 0.914737i | \(0.632398\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 11.9700 | − | 20.7327i | 0.612441 | − | 1.06078i | ||||
\(383\) | 11.8685 | − | 11.8685i | 0.606453 | − | 0.606453i | −0.335565 | − | 0.942017i | \(-0.608927\pi\) |
0.942017 | + | 0.335565i | \(0.108927\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.02628 | + | 18.7583i | 0.255831 | + | 0.954774i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −12.1087 | − | 3.24453i | −0.614729 | − | 0.164716i | ||||
\(389\) | − | 14.5359i | − | 0.736999i | −0.929628 | − | 0.368500i | \(-0.879872\pi\) | ||
0.929628 | − | 0.368500i | \(-0.120128\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.21539i | 0.162609i | ||||||||
\(392\) | 2.62536 | 0.132600 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 19.6603 | − | 5.26795i | 0.990469 | − | 0.265395i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.8511 | + | 13.8511i | −0.695168 | + | 0.695168i | −0.963364 | − | 0.268196i | \(-0.913573\pi\) |
0.268196 | + | 0.963364i | \(0.413573\pi\) | |||||||
\(398\) | −17.2987 | − | 9.98743i | −0.867107 | − | 0.500625i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 33.1769 | 1.65678 | 0.828388 | − | 0.560155i | \(-0.189258\pi\) | ||||
0.828388 | + | 0.560155i | \(0.189258\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.08604 | − | 1.08604i | 0.0540997 | − | 0.0540997i | ||||
\(404\) | 1.46410 | + | 2.53590i | 0.0728418 | + | 0.126166i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 25.1244 | − | 6.73205i | 1.24690 | − | 0.334106i | ||||
\(407\) | 4.14110 | + | 4.14110i | 0.205267 | + | 0.205267i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 27.7846i | − | 1.37386i | −0.726723 | − | 0.686930i | \(-0.758958\pi\) | ||
0.726723 | − | 0.686930i | \(-0.241042\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −13.3843 | − | 3.58630i | −0.659395 | − | 0.176684i | ||||
\(413\) | −7.90327 | − | 7.90327i | −0.388895 | − | 0.388895i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −31.3205 | − | 8.39230i | −1.53561 | − | 0.411467i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −10.1769 | + | 17.6269i | −0.497768 | + | 0.862160i | ||||
\(419\) | −26.5359 | −1.29636 | −0.648182 | − | 0.761486i | \(-0.724470\pi\) | ||||
−0.648182 | + | 0.761486i | \(0.724470\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.78461 | 0.330662 | 0.165331 | − | 0.986238i | \(-0.447131\pi\) | ||||
0.165331 | + | 0.986238i | \(0.447131\pi\) | |||||||
\(422\) | −5.08845 | + | 8.81345i | −0.247702 | + | 0.429032i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.92820 | − | 2.92820i | 0.142206 | − | 0.142206i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.22715 | − | 5.22715i | −0.252959 | − | 0.252959i | ||||
\(428\) | −3.38323 | + | 12.6264i | −0.163535 | + | 0.610319i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 25.7128i | − | 1.23854i | −0.785177 | − | 0.619271i | \(-0.787428\pi\) | ||
0.785177 | − | 0.619271i | \(-0.212572\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.11943 | − | 3.11943i | −0.149910 | − | 0.149910i | 0.628168 | − | 0.778078i | \(-0.283805\pi\) |
−0.778078 | + | 0.628168i | \(0.783805\pi\) | |||||||
\(434\) | −0.901924 | + | 0.241670i | −0.0432937 | + | 0.0116005i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −12.1244 | + | 7.00000i | −0.580651 | + | 0.335239i | ||||
\(437\) | 2.72689 | − | 2.72689i | 0.130445 | − | 0.130445i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −27.9808 | −1.33545 | −0.667724 | − | 0.744409i | \(-0.732732\pi\) | ||||
−0.667724 | + | 0.744409i | \(0.732732\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −42.1218 | − | 24.3190i | −2.00353 | − | 1.15674i | ||||
\(443\) | −9.04008 | + | 9.04008i | −0.429507 | + | 0.429507i | −0.888460 | − | 0.458953i | \(-0.848225\pi\) |
0.458953 | + | 0.888460i | \(0.348225\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 15.5622 | − | 4.16987i | 0.736890 | − | 0.197449i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 13.9391 | + | 13.9391i | 0.658559 | + | 0.658559i | ||||
\(449\) | − | 33.8564i | − | 1.59778i | −0.601475 | − | 0.798891i | \(-0.705420\pi\) | ||
0.601475 | − | 0.798891i | \(-0.294580\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.9282i | 0.514589i | ||||||||
\(452\) | −7.17260 | + | 26.7685i | −0.337371 | + | 1.25909i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4.53590 | + | 16.9282i | 0.212880 | + | 0.794480i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −25.2528 | + | 25.2528i | −1.18127 | + | 1.18127i | −0.201861 | + | 0.979414i | \(0.564699\pi\) |
−0.979414 | + | 0.201861i | \(0.935301\pi\) | |||||||
\(458\) | 17.5761 | − | 30.4428i | 0.821279 | − | 1.42250i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15.6077 | −0.726923 | −0.363461 | − | 0.931609i | \(-0.618405\pi\) | ||||
−0.363461 | + | 0.931609i | \(0.618405\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.24316 | − | 9.24316i | 0.429566 | − | 0.429566i | −0.458915 | − | 0.888480i | \(-0.651762\pi\) |
0.888480 | + | 0.458915i | \(0.151762\pi\) | |||||||
\(464\) | −25.8564 | − | 14.9282i | −1.20035 | − | 0.693024i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.53590 | − | 16.9282i | −0.210121 | − | 0.784184i | ||||
\(467\) | 2.44949 | + | 2.44949i | 0.113349 | + | 0.113349i | 0.761506 | − | 0.648157i | \(-0.224460\pi\) |
−0.648157 | + | 0.761506i | \(0.724460\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 30.7128i | 1.41819i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 12.8295i | 0.590524i | ||||||||
\(473\) | 3.48477 | + | 3.48477i | 0.160230 | + | 0.160230i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 14.7846 | + | 25.6077i | 0.677651 | + | 1.17373i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 21.3891 | + | 12.3490i | 0.978313 | + | 0.564829i | ||||
\(479\) | −13.3205 | −0.608630 | −0.304315 | − | 0.952572i | \(-0.598427\pi\) | ||||
−0.304315 | + | 0.952572i | \(0.598427\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.7846 | 0.765312 | ||||||||
\(482\) | −18.1953 | − | 10.5051i | −0.828774 | − | 0.478493i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7.00000 | + | 12.1244i | 0.318182 | + | 0.551107i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15.2282 | − | 15.2282i | −0.690055 | − | 0.690055i | 0.272189 | − | 0.962244i | \(-0.412252\pi\) |
−0.962244 | + | 0.272189i | \(0.912252\pi\) | |||||||
\(488\) | 8.48528i | 0.384111i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 34.6410i | 1.56333i | 0.623700 | + | 0.781664i | \(0.285629\pi\) | ||||
−0.623700 | + | 0.781664i | \(0.714371\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −31.6675 | − | 31.6675i | −1.42623 | − | 1.42623i | ||||
\(494\) | 15.0981 | + | 56.3468i | 0.679295 | + | 2.53516i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.928203 | + | 0.535898i | 0.0416776 | + | 0.0240625i | ||||
\(497\) | −16.4901 | + | 16.4901i | −0.739682 | + | 0.739682i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.87564 | 0.263030 | 0.131515 | − | 0.991314i | \(-0.458016\pi\) | ||||
0.131515 | + | 0.991314i | \(0.458016\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.51575 | − | 2.62536i | 0.0676512 | − | 0.117175i | ||||
\(503\) | −14.4195 | + | 14.4195i | −0.642935 | + | 0.642935i | −0.951276 | − | 0.308341i | \(-0.900226\pi\) |
0.308341 | + | 0.951276i | \(0.400226\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.392305 | + | 1.46410i | 0.0174401 | + | 0.0650873i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.51575 | − | 5.65685i | 0.0672505 | − | 0.250982i | ||||
\(509\) | 11.0718i | 0.490749i | 0.969428 | + | 0.245374i | \(0.0789109\pi\) | ||||
−0.969428 | + | 0.245374i | \(0.921089\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.85641i | 0.436022i | ||||||||
\(512\) | − | 22.6274i | − | 1.00000i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −17.4641 | + | 4.67949i | −0.770309 | + | 0.206404i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 18.2832 | − | 18.2832i | 0.804096 | − | 0.804096i | ||||
\(518\) | −8.83701 | − | 5.10205i | −0.388276 | − | 0.224171i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.6077 | 0.771407 | 0.385704 | − | 0.922623i | \(-0.373959\pi\) | ||||
0.385704 | + | 0.922623i | \(0.373959\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.7124 | + | 13.7124i | −0.599603 | + | 0.599603i | −0.940207 | − | 0.340604i | \(-0.889368\pi\) |
0.340604 | + | 0.940207i | \(0.389368\pi\) | |||||||
\(524\) | −16.3923 | + | 9.46410i | −0.716101 | + | 0.413441i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 29.3205 | − | 7.85641i | 1.27843 | − | 0.342556i | ||||
\(527\) | 1.13681 | + | 1.13681i | 0.0495203 | + | 0.0495203i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.7128i | 0.987514i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 9.17878 | − | 34.2557i | 0.397951 | − | 1.48517i | ||||
\(533\) | 22.1469 | + | 22.1469i | 0.959291 | + | 0.959291i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 24.9282 | − | 24.9282i | 1.07673 | − | 1.07673i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.13681 | − | 1.96902i | 0.0490115 | − | 0.0848903i | ||||
\(539\) | 1.85641 | 0.0799611 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −33.7846 | −1.45251 | −0.726257 | − | 0.687423i | \(-0.758742\pi\) | ||||
−0.726257 | + | 0.687423i | \(0.758742\pi\) | |||||||
\(542\) | −17.1464 | + | 29.6985i | −0.736502 | + | 1.27566i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 8.78461 | − | 32.7846i | 0.376637 | − | 1.40563i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.5254 | + | 17.5254i | 0.749331 | + | 0.749331i | 0.974353 | − | 0.225023i | \(-0.0722457\pi\) |
−0.225023 | + | 0.974353i | \(0.572246\pi\) | |||||||
\(548\) | 16.4901 | + | 4.41851i | 0.704422 | + | 0.188749i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 53.7128i | 2.28824i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.933740 | − | 0.933740i | −0.0397067 | − | 0.0397067i | ||||
\(554\) | 1.63397 | − | 0.437822i | 0.0694209 | − | 0.0186013i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 19.4641 | + | 33.7128i | 0.825462 | + | 1.42974i | ||||
\(557\) | 25.6317 | − | 25.6317i | 1.08605 | − | 1.08605i | 0.0901194 | − | 0.995931i | \(-0.471275\pi\) |
0.995931 | − | 0.0901194i | \(-0.0287249\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14.1244 | 0.597397 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 17.6269 | + | 10.1769i | 0.743546 | + | 0.429286i | ||||
\(563\) | 16.3886 | − | 16.3886i | 0.690695 | − | 0.690695i | −0.271690 | − | 0.962385i | \(-0.587582\pi\) |
0.962385 | + | 0.271690i | \(0.0875824\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −29.2224 | + | 7.83013i | −1.22831 | + | 0.329125i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 26.7685 | 1.12318 | ||||||||
\(569\) | − | 17.3205i | − | 0.726113i | −0.931767 | − | 0.363057i | \(-0.881733\pi\) | ||
0.931767 | − | 0.363057i | \(-0.118267\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 16.8038i | − | 0.703219i | −0.936147 | − | 0.351610i | \(-0.885634\pi\) | ||
0.936147 | − | 0.351610i | \(-0.114366\pi\) | |||||||
\(572\) | −22.1469 | − | 5.93426i | −0.926010 | − | 0.248124i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −4.92820 | − | 18.3923i | −0.205699 | − | 0.767680i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10.8468 | + | 10.8468i | −0.451560 | + | 0.451560i | −0.895872 | − | 0.444312i | \(-0.853448\pi\) |
0.444312 | + | 0.895872i | \(0.353448\pi\) | |||||||
\(578\) | 13.4350 | − | 23.2702i | 0.558824 | − | 0.967911i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.28719 | −0.0948885 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.07055 | − | 2.07055i | 0.0857535 | − | 0.0857535i | ||||
\(584\) | 8.00000 | − | 8.00000i | 0.331042 | − | 0.331042i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.58846 | − | 17.1244i | −0.189547 | − | 0.707401i | ||||
\(587\) | −13.6617 | − | 13.6617i | −0.563877 | − | 0.563877i | 0.366529 | − | 0.930406i | \(-0.380546\pi\) |
−0.930406 | + | 0.366529i | \(0.880546\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 1.92820i | − | 0.0794502i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.03150 | + | 11.3137i | 0.124594 | + | 0.464991i | ||||
\(593\) | 22.9048 | + | 22.9048i | 0.940588 | + | 0.940588i | 0.998331 | − | 0.0577433i | \(-0.0183905\pi\) |
−0.0577433 | + | 0.998331i | \(0.518390\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 27.4641 | − | 15.8564i | 1.12497 | − | 0.649504i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3.76217 | + | 2.17209i | 0.153846 | + | 0.0888233i | ||||
\(599\) | 46.6410 | 1.90570 | 0.952850 | − | 0.303441i | \(-0.0981356\pi\) | ||||
0.952850 | + | 0.303441i | \(0.0981356\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.7846 | −0.807031 | −0.403516 | − | 0.914973i | \(-0.632212\pi\) | ||||
−0.403516 | + | 0.914973i | \(0.632212\pi\) | |||||||
\(602\) | −7.43640 | − | 4.29341i | −0.303085 | − | 0.174986i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 7.39230 | − | 4.26795i | 0.300789 | − | 0.173660i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.9391 | + | 13.9391i | 0.565769 | + | 0.565769i | 0.930940 | − | 0.365171i | \(-0.118990\pi\) |
−0.365171 | + | 0.930940i | \(0.618990\pi\) | |||||||
\(608\) | −35.2538 | + | 20.3538i | −1.42973 | + | 0.825455i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 74.1051i | − | 2.99797i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(614\) | 4.90192 | + | 18.2942i | 0.197826 | + | 0.738295i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 9.85641 | + | 9.85641i | 0.397126 | + | 0.397126i | ||||
\(617\) | −10.0754 | + | 10.0754i | −0.405619 | + | 0.405619i | −0.880208 | − | 0.474589i | \(-0.842597\pi\) |
0.474589 | + | 0.880208i | \(0.342597\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −35.9808 | −1.44619 | −0.723094 | − | 0.690749i | \(-0.757281\pi\) | ||||
−0.723094 | + | 0.690749i | \(0.757281\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −19.4201 | + | 33.6365i | −0.778673 | + | 1.34870i | ||||
\(623\) | −12.0716 | + | 12.0716i | −0.483638 | + | 0.483638i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 2.97372 | + | 11.0981i | 0.118854 | + | 0.443568i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 18.8009 | + | 5.03768i | 0.750237 | + | 0.201025i | ||||
\(629\) | 17.5692i | 0.700531i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 1.58846i | − | 0.0632355i | −0.999500 | − | 0.0316177i | \(-0.989934\pi\) | ||
0.999500 | − | 0.0316177i | \(-0.0100659\pi\) | |||||||
\(632\) | 1.51575i | 0.0602933i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9.46410 | − | 2.53590i | 0.375867 | − | 0.100713i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.76217 | − | 3.76217i | 0.149062 | − | 0.149062i | ||||
\(638\) | −18.2832 | − | 10.5558i | −0.723840 | − | 0.417909i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.21539 | 0.127000 | 0.0635001 | − | 0.997982i | \(-0.479774\pi\) | ||||
0.0635001 | + | 0.997982i | \(0.479774\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.0716 | − | 12.0716i | 0.476057 | − | 0.476057i | −0.427811 | − | 0.903868i | \(-0.640715\pi\) |
0.903868 | + | 0.427811i | \(0.140715\pi\) | |||||||
\(644\) | −1.32051 | − | 2.28719i | −0.0520353 | − | 0.0901278i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −58.9808 | + | 15.8038i | −2.32057 | + | 0.621794i | ||||
\(647\) | 3.58630 | + | 3.58630i | 0.140992 | + | 0.140992i | 0.774080 | − | 0.633088i | \(-0.218213\pi\) |
−0.633088 | + | 0.774080i | \(0.718213\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.07180i | 0.356099i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 27.9425 | + | 7.48717i | 1.09431 | + | 0.293220i | ||||
\(653\) | −7.34847 | − | 7.34847i | −0.287568 | − | 0.287568i | 0.548550 | − | 0.836118i | \(-0.315180\pi\) |
−0.836118 | + | 0.548550i | \(0.815180\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −10.9282 | + | 18.9282i | −0.426675 | + | 0.739022i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −22.5259 | + | 39.0160i | −0.878150 | + | 1.52100i | ||||
\(659\) | 14.5359 | 0.566238 | 0.283119 | − | 0.959085i | \(-0.408631\pi\) | ||||
0.283119 | + | 0.959085i | \(0.408631\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.85641 | −0.305579 | −0.152789 | − | 0.988259i | \(-0.548826\pi\) | ||||
−0.152789 | + | 0.988259i | \(0.548826\pi\) | |||||||
\(662\) | 1.69161 | − | 2.92996i | 0.0657465 | − | 0.113876i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.85641 | + | 1.85641i | 0.0720425 | + | 0.0720425i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.82843 | + | 2.82843i | 0.109517 | + | 0.109517i | ||||
\(668\) | −2.27362 | + | 8.48528i | −0.0879692 | + | 0.328305i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.00000i | 0.231627i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.82843 | + | 2.82843i | 0.109028 | + | 0.109028i | 0.759516 | − | 0.650488i | \(-0.225436\pi\) |
−0.650488 | + | 0.759516i | \(0.725436\pi\) | |||||||
\(674\) | 15.4904 | − | 4.15064i | 0.596667 | − | 0.159876i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −34.3923 | + | 19.8564i | −1.32278 | + | 0.763708i | ||||
\(677\) | 25.9091 | − | 25.9091i | 0.995768 | − | 0.995768i | −0.00422306 | − | 0.999991i | \(-0.501344\pi\) |
0.999991 | + | 0.00422306i | \(0.00134424\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 15.4449 | 0.592719 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.656339 | + | 0.378937i | 0.0251325 | + | 0.0145103i | ||||
\(683\) | 3.58630 | − | 3.58630i | 0.137226 | − | 0.137226i | −0.635157 | − | 0.772383i | \(-0.719065\pi\) |
0.772383 | + | 0.635157i | \(0.219065\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −26.6865 | + | 7.15064i | −1.01890 | + | 0.273013i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.55103 | + | 9.52056i | 0.0972569 | + | 0.362968i | ||||
\(689\) | − | 8.39230i | − | 0.319721i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25.3205i | 0.963238i | 0.876381 | + | 0.481619i | \(0.159951\pi\) | ||||
−0.876381 | + | 0.481619i | \(0.840049\pi\) | |||||||
\(692\) | 4.62158 | − | 17.2480i | 0.175686 | − | 0.655669i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4.05256 | + | 15.1244i | 0.153833 | + | 0.574113i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −23.1822 | + | 23.1822i | −0.878089 | + | 0.878089i | ||||
\(698\) | −2.72689 | + | 4.72311i | −0.103214 | + | 0.178773i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15.4641 | 0.584071 | 0.292036 | − | 0.956407i | \(-0.405667\pi\) | ||||
0.292036 | + | 0.956407i | \(0.405667\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14.9000 | − | 14.9000i | 0.561965 | − | 0.561965i | ||||
\(704\) | − | 16.0000i | − | 0.603023i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 5.80385 | + | 21.6603i | 0.218431 | + | 0.815194i | ||||
\(707\) | −2.55103 | − | 2.55103i | −0.0959412 | − | 0.0959412i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 24.8564i | − | 0.933502i | −0.884389 | − | 0.466751i | \(-0.845424\pi\) | ||
0.884389 | − | 0.466751i | \(-0.154576\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 19.5959 | 0.734388 | ||||||||
\(713\) | −0.101536 | − | 0.101536i | −0.00380255 | − | 0.00380255i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −25.3205 | − | 43.8564i | −0.946272 | − | 1.63899i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −29.8744 | − | 17.2480i | −1.11490 | − | 0.643688i | ||||
\(719\) | −12.9282 | −0.482141 | −0.241070 | − | 0.970508i | \(-0.577498\pi\) | ||||
−0.241070 | + | 0.970508i | \(0.577498\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 17.0718 | 0.635787 | ||||||||
\(722\) | 40.1528 | + | 23.1822i | 1.49433 | + | 0.862753i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −13.9282 | − | 24.1244i | −0.517638 | − | 0.896575i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −33.3083 | − | 33.3083i | −1.23534 | − | 1.23534i | −0.961885 | − | 0.273453i | \(-0.911834\pi\) |
−0.273453 | − | 0.961885i | \(-0.588166\pi\) | |||||||
\(728\) | 39.9497 | 1.48063 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14.7846i | 0.546829i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.9391 | + | 13.9391i | 0.514851 | + | 0.514851i | 0.916009 | − | 0.401158i | \(-0.131392\pi\) |
−0.401158 | + | 0.916009i | \(0.631392\pi\) | |||||||
\(734\) | 3.88269 | + | 14.4904i | 0.143313 | + | 0.534850i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.784610 | + | 2.92820i | −0.0289211 | + | 0.107935i | ||||
\(737\) | 17.6269 | − | 17.6269i | 0.649295 | − | 0.649295i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.3923 | 0.529429 | 0.264715 | − | 0.964327i | \(-0.414722\pi\) | ||||
0.264715 | + | 0.964327i | \(0.414722\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.55103 | + | 4.41851i | −0.0936511 | + | 0.162208i | ||||
\(743\) | 21.8695 | − | 21.8695i | 0.802316 | − | 0.802316i | −0.181141 | − | 0.983457i | \(-0.557979\pi\) |
0.983457 | + | 0.181141i | \(0.0579792\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 7.07884 | + | 26.4186i | 0.259175 | + | 0.967253i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 6.21166 | − | 23.1822i | 0.227121 | − | 0.847626i | ||||
\(749\) | − | 16.1051i | − | 0.588468i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.4641i | 0.418331i | 0.977880 | + | 0.209166i | \(0.0670747\pi\) | ||||
−0.977880 | + | 0.209166i | \(0.932925\pi\) | |||||||
\(752\) | 49.9507 | − | 13.3843i | 1.82152 | − | 0.488074i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −58.4449 | + | 15.6603i | −2.12844 | + | 0.570313i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20.6448 | − | 20.6448i | 0.750348 | − | 0.750348i | −0.224196 | − | 0.974544i | \(-0.571976\pi\) |
0.974544 | + | 0.224196i | \(0.0719756\pi\) | |||||||
\(758\) | −19.2677 | − | 11.1242i | −0.699836 | − | 0.404051i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −46.6410 | −1.69074 | −0.845368 | − | 0.534185i | \(-0.820619\pi\) | ||||
−0.845368 | + | 0.534185i | \(0.820619\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.1967 | − | 12.1967i | 0.441549 | − | 0.441549i | ||||
\(764\) | 29.3205 | − | 16.9282i | 1.06078 | − | 0.612441i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 22.9282 | − | 6.14359i | 0.828430 | − | 0.221977i | ||||
\(767\) | 18.3848 | + | 18.3848i | 0.663836 | + | 0.663836i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 29.9282i | 1.07924i | 0.841909 | + | 0.539619i | \(0.181432\pi\) | ||||
−0.841909 | + | 0.539619i | \(0.818568\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −7.10823 | + | 26.5283i | −0.255831 | + | 0.954774i | ||||
\(773\) | −23.4596 | − | 23.4596i | −0.843784 | − | 0.843784i | 0.145565 | − | 0.989349i | \(-0.453500\pi\) |
−0.989349 | + | 0.145565i | \(0.953500\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −12.5359 | − | 12.5359i | −0.450013 | − | 0.450013i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 10.2784 | − | 17.8028i | 0.368500 | − | 0.638260i | ||||
\(779\) | 39.3205 | 1.40880 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18.9282 | 0.677304 | ||||||||
\(782\) | −2.27362 | + | 3.93803i | −0.0813046 | + | 0.140824i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.21539 | + | 1.85641i | 0.114835 | + | 0.0663002i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10.0246 | − | 10.0246i | −0.357338 | − | 0.357338i | 0.505493 | − | 0.862831i | \(-0.331311\pi\) |
−0.862831 | + | 0.505493i | \(0.831311\pi\) | |||||||
\(788\) | 27.8038 | + | 7.45001i | 0.990469 | + | 0.265395i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 34.1436i | − | 1.21401i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.1595 | + | 12.1595i | 0.431797 | + | 0.431797i | ||||
\(794\) | −26.7583 | + | 7.16987i | −0.949618 | + | 0.254449i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −14.1244 | − | 24.4641i | −0.500625 | − | 0.867107i | ||||
\(797\) | −9.79796 | + | 9.79796i | −0.347062 | + | 0.347062i | −0.859014 | − | 0.511952i | \(-0.828922\pi\) |
0.511952 | + | 0.859014i | \(0.328922\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 77.5692 | 2.74420 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 40.6333 | + | 23.4596i | 1.43481 | + | 0.828388i | ||||
\(803\) | 5.65685 | − | 5.65685i | 0.199626 | − | 0.199626i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.09808 | − | 0.562178i | 0.0739016 | − | 0.0198019i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4.14110i | 0.145684i | ||||||||
\(809\) | 49.1769i | 1.72897i | 0.502660 | + | 0.864484i | \(0.332355\pi\) | ||||
−0.502660 | + | 0.864484i | \(0.667645\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 26.1244i | − | 0.917350i | −0.888604 | − | 0.458675i | \(-0.848324\pi\) | ||
0.888604 | − | 0.458675i | \(-0.151676\pi\) | |||||||
\(812\) | 35.5312 | + | 9.52056i | 1.24690 | + | 0.334106i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.14359 | + | 8.00000i | 0.0751329 | + | 0.280400i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.5385 | − | 12.5385i | 0.438665 | − | 0.438665i | ||||
\(818\) | 19.6467 | − | 34.0291i | 0.686930 | − | 1.18980i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −55.5692 | −1.93938 | −0.969690 | − | 0.244340i | \(-0.921429\pi\) | ||||
−0.969690 | + | 0.244340i | \(0.921429\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −33.5114 | + | 33.5114i | −1.16813 | + | 1.16813i | −0.185488 | + | 0.982646i | \(0.559387\pi\) |
−0.982646 | + | 0.185488i | \(0.940613\pi\) | |||||||
\(824\) | −13.8564 | − | 13.8564i | −0.482711 | − | 0.482711i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.09103 | − | 15.2679i | −0.142345 | − | 0.531240i | ||||
\(827\) | −30.0774 | − | 30.0774i | −1.04589 | − | 1.04589i | −0.998895 | − | 0.0469995i | \(-0.985034\pi\) |
−0.0469995 | − | 0.998895i | \(-0.514966\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 17.7128i | − | 0.615191i | −0.951517 | − | 0.307596i | \(-0.900476\pi\) | ||
0.951517 | − | 0.307596i | \(-0.0995244\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −32.4254 | − | 32.4254i | −1.12415 | − | 1.12415i | ||||
\(833\) | 3.93803 | + | 3.93803i | 0.136445 | + | 0.136445i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −24.9282 | + | 14.3923i | −0.862160 | + | 0.497768i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −32.4997 | − | 18.7637i | −1.12268 | − | 0.648182i | ||||
\(839\) | −40.6410 | −1.40308 | −0.701542 | − | 0.712628i | \(-0.747505\pi\) | ||||
−0.701542 | + | 0.712628i | \(0.747505\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.7128 | −0.921131 | ||||||||
\(842\) | 8.30942 | + | 4.79744i | 0.286361 | + | 0.165331i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −12.4641 | + | 7.19615i | −0.429032 | + | 0.247702i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −12.1967 | − | 12.1967i | −0.419083 | − | 0.419083i | ||||
\(848\) | 5.65685 | − | 1.51575i | 0.194257 | − | 0.0520511i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 1.56922i | − | 0.0537921i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11.0227 | + | 11.0227i | 0.377410 | + | 0.377410i | 0.870167 | − | 0.492757i | \(-0.164011\pi\) |
−0.492757 | + | 0.870167i | \(0.664011\pi\) | |||||||
\(854\) | −2.70577 | − | 10.0981i | −0.0925896 | − | 0.345549i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −13.0718 | + | 13.0718i | −0.446785 | + | 0.446785i | ||||
\(857\) | −33.7381 | + | 33.7381i | −1.15247 | + | 1.15247i | −0.166414 | + | 0.986056i | \(0.553219\pi\) |
−0.986056 | + | 0.166414i | \(0.946781\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21.6077 | 0.737245 | 0.368623 | − | 0.929579i | \(-0.379830\pi\) | ||||
0.368623 | + | 0.929579i | \(0.379830\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 18.1817 | − | 31.4916i | 0.619271 | − | 1.07261i | ||||
\(863\) | −27.3233 | + | 27.3233i | −0.930097 | + | 0.930097i | −0.997712 | − | 0.0676147i | \(-0.978461\pi\) |
0.0676147 | + | 0.997712i | \(0.478461\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.61474 | − | 6.02628i | −0.0548710 | − | 0.204781i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.27551 | − | 0.341773i | −0.0432937 | − | 0.0116005i | ||||
\(869\) | 1.07180i | 0.0363582i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 71.4449i | − | 2.42082i | ||||||
\(872\) | −19.7990 | −0.670478 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 5.26795 | − | 1.41154i | 0.178191 | − | 0.0477461i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 22.5123 | − | 22.5123i | 0.760186 | − | 0.760186i | −0.216170 | − | 0.976356i | \(-0.569357\pi\) |
0.976356 | + | 0.216170i | \(0.0693566\pi\) | |||||||
\(878\) | −34.2693 | − | 19.7854i | −1.15653 | − | 0.667724i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 50.9282 | 1.71581 | 0.857907 | − | 0.513804i | \(-0.171764\pi\) | ||||
0.857907 | + | 0.513804i | \(0.171764\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.3383 | − | 21.3383i | 0.718091 | − | 0.718091i | −0.250123 | − | 0.968214i | \(-0.580471\pi\) |
0.968214 | + | 0.250123i | \(0.0804711\pi\) | |||||||
\(884\) | −34.3923 | − | 59.5692i | −1.15674 | − | 2.00353i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −17.4641 | + | 4.67949i | −0.586718 | + | 0.157211i | ||||
\(887\) | 5.55532 | + | 5.55532i | 0.186529 | + | 0.186529i | 0.794194 | − | 0.607665i | \(-0.207893\pi\) |
−0.607665 | + | 0.794194i | \(0.707893\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.21539i | 0.241996i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 22.0082 | + | 5.89709i | 0.736890 | + | 0.197449i | ||||
\(893\) | −65.7845 | − | 65.7845i | −2.20139 | − | 2.20139i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 7.21539 | + | 26.9282i | 0.241049 | + | 0.899608i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 23.9401 | − | 41.4655i | 0.798891 | − | 1.38372i | ||||
\(899\) | 2.00000 | 0.0667037 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.78461 | 0.292658 | ||||||||
\(902\) | −7.72741 | + | 13.3843i | −0.257294 | + | 0.445647i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −27.7128 | + | 27.7128i | −0.921714 | + | 0.921714i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.96953 | + | 6.96953i | 0.231420 | + | 0.231420i | 0.813285 | − | 0.581866i | \(-0.197677\pi\) |
−0.581866 | + | 0.813285i | \(0.697677\pi\) | |||||||
\(908\) | −6.41473 | + | 23.9401i | −0.212880 | + | 0.794480i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 26.3923i | − | 0.874416i | −0.899360 | − | 0.437208i | \(-0.855967\pi\) | ||
0.899360 | − | 0.437208i | \(-0.144033\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.31268 | + | 1.31268i | 0.0434433 | + | 0.0434433i | ||||
\(914\) | −48.7846 | + | 13.0718i | −1.61365 | + | 0.432377i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 43.0526 | − | 24.8564i | 1.42250 | − | 0.821279i | ||||
\(917\) | 16.4901 | − | 16.4901i | 0.544551 | − | 0.544551i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.33975 | 0.308090 | 0.154045 | − | 0.988064i | \(-0.450770\pi\) | ||||
0.154045 | + | 0.988064i | \(0.450770\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −19.1154 | − | 11.0363i | −0.629534 | − | 0.363461i | ||||
\(923\) | 38.3596 | − | 38.3596i | 1.26262 | − | 1.26262i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 17.8564 | − | 4.78461i | 0.586798 | − | 0.157232i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −21.1117 | − | 36.5665i | −0.693024 | − | 1.20035i | ||||
\(929\) | 7.46410i | 0.244889i | 0.992475 | + | 0.122445i | \(0.0390734\pi\) | ||||
−0.992475 | + | 0.122445i | \(0.960927\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 6.67949i | − | 0.218912i | ||||||
\(932\) | 6.41473 | − | 23.9401i | 0.210121 | − | 0.784184i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.26795 | + | 4.73205i | 0.0414886 | + | 0.154837i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 37.4123 | − | 37.4123i | 1.22221 | − | 1.22221i | 0.255360 | − | 0.966846i | \(-0.417806\pi\) |
0.966846 | − | 0.255360i | \(-0.0821940\pi\) | |||||||
\(938\) | −21.7172 | + | 37.6154i | −0.709093 | + | 1.22819i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24.9282 | −0.812636 | −0.406318 | − | 0.913732i | \(-0.633188\pi\) | ||||
−0.406318 | + | 0.913732i | \(0.633188\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.07055 | − | 2.07055i | 0.0674265 | − | 0.0674265i | ||||
\(944\) | −9.07180 | + | 15.7128i | −0.295262 | + | 0.511409i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.80385 | + | 6.73205i | 0.0586481 | + | 0.218878i | ||||
\(947\) | 11.4896 | + | 11.4896i | 0.373361 | + | 0.373361i | 0.868700 | − | 0.495339i | \(-0.164956\pi\) |
−0.495339 | + | 0.868700i | \(0.664956\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 22.9282i | − | 0.744281i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 41.8172i | 1.35530i | ||||||||
\(953\) | −11.1106 | − | 11.1106i | −0.359909 | − | 0.359909i | 0.503870 | − | 0.863779i | \(-0.331909\pi\) |
−0.863779 | + | 0.503870i | \(0.831909\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 17.4641 | + | 30.2487i | 0.564829 | + | 0.978313i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −16.3142 | − | 9.41902i | −0.527089 | − | 0.304315i | ||||
\(959\) | −21.0333 | −0.679201 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.9282 | 0.997684 | ||||||||
\(962\) | 20.5569 | + | 11.8685i | 0.662780 | + | 0.382656i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −14.8564 | − | 25.7321i | −0.478493 | − | 0.828774i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −33.9411 | − | 33.9411i | −1.09147 | − | 1.09147i | −0.995372 | − | 0.0961015i | \(-0.969363\pi\) |
−0.0961015 | − | 0.995372i | \(-0.530637\pi\) | |||||||
\(968\) | 19.7990i | 0.636364i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 19.1769i | − | 0.615416i | −0.951481 | − | 0.307708i | \(-0.900438\pi\) | ||
0.951481 | − | 0.307708i | \(-0.0995621\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −33.9139 | − | 33.9139i | −1.08723 | − | 1.08723i | ||||
\(974\) | −7.88269 | − | 29.4186i | −0.252578 | − | 0.942632i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.00000 | + | 10.3923i | −0.192055 | + | 0.332650i | ||||
\(977\) | 27.7023 | − | 27.7023i | 0.886274 | − | 0.886274i | −0.107889 | − | 0.994163i | \(-0.534409\pi\) |
0.994163 | + | 0.107889i | \(0.0344091\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 13.8564 | 0.442853 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −24.4949 | + | 42.4264i | −0.781664 | + | 1.35388i | ||||
\(983\) | 18.2832 | − | 18.2832i | 0.583145 | − | 0.583145i | −0.352621 | − | 0.935766i | \(-0.614710\pi\) |
0.935766 | + | 0.352621i | \(0.114710\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −16.3923 | − | 61.1769i | −0.522037 | − | 1.94827i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −21.3519 | + | 79.6864i | −0.679295 | + | 2.53516i | ||||
\(989\) | − | 1.32051i | − | 0.0419897i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 57.5885i | − | 1.82936i | −0.404181 | − | 0.914679i | \(-0.632444\pi\) | ||
0.404181 | − | 0.914679i | \(-0.367556\pi\) | |||||||
\(992\) | 0.757875 | + | 1.31268i | 0.0240625 | + | 0.0416776i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −31.8564 | + | 8.53590i | −1.01042 | + | 0.270742i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.5959 | − | 19.5959i | 0.620609 | − | 0.620609i | −0.325078 | − | 0.945687i | \(-0.605391\pi\) |
0.945687 | + | 0.325078i | \(0.105391\pi\) | |||||||
\(998\) | 7.19617 | + | 4.15471i | 0.227791 | + | 0.131515i | ||||
\(999\) | 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 | 900.2.k.l.343.4 | 8 | ||
3.2 | odd | 2 | 300.2.j.c.43.1 | yes | 8 | ||
4.3 | odd | 2 | 900.2.k.g.343.1 | 8 | |||
5.2 | odd | 4 | 900.2.k.g.307.2 | 8 | |||
5.3 | odd | 4 | 900.2.k.g.307.3 | 8 | |||
5.4 | even | 2 | inner | 900.2.k.l.343.1 | 8 | ||
12.11 | even | 2 | 300.2.j.a.43.4 | yes | 8 | ||
15.2 | even | 4 | 300.2.j.a.7.3 | yes | 8 | ||
15.8 | even | 4 | 300.2.j.a.7.2 | ✓ | 8 | ||
15.14 | odd | 2 | 300.2.j.c.43.4 | yes | 8 | ||
20.3 | even | 4 | inner | 900.2.k.l.307.2 | 8 | ||
20.7 | even | 4 | inner | 900.2.k.l.307.3 | 8 | ||
20.19 | odd | 2 | 900.2.k.g.343.4 | 8 | |||
60.23 | odd | 4 | 300.2.j.c.7.3 | yes | 8 | ||
60.47 | odd | 4 | 300.2.j.c.7.2 | yes | 8 | ||
60.59 | even | 2 | 300.2.j.a.43.1 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.2.j.a.7.2 | ✓ | 8 | 15.8 | even | 4 | ||
300.2.j.a.7.3 | yes | 8 | 15.2 | even | 4 | ||
300.2.j.a.43.1 | yes | 8 | 60.59 | even | 2 | ||
300.2.j.a.43.4 | yes | 8 | 12.11 | even | 2 | ||
300.2.j.c.7.2 | yes | 8 | 60.47 | odd | 4 | ||
300.2.j.c.7.3 | yes | 8 | 60.23 | odd | 4 | ||
300.2.j.c.43.1 | yes | 8 | 3.2 | odd | 2 | ||
300.2.j.c.43.4 | yes | 8 | 15.14 | odd | 2 | ||
900.2.k.g.307.2 | 8 | 5.2 | odd | 4 | |||
900.2.k.g.307.3 | 8 | 5.3 | odd | 4 | |||
900.2.k.g.343.1 | 8 | 4.3 | odd | 2 | |||
900.2.k.g.343.4 | 8 | 20.19 | odd | 2 | |||
900.2.k.l.307.2 | 8 | 20.3 | even | 4 | inner | ||
900.2.k.l.307.3 | 8 | 20.7 | even | 4 | inner | ||
900.2.k.l.343.1 | 8 | 5.4 | even | 2 | inner | ||
900.2.k.l.343.4 | 8 | 1.1 | even | 1 | trivial |