Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3150,2,Mod(1151,3150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3150, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 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("3150.1151");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3150.bf (of order \(6\), 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: | \(25.1528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
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: | \( 1 \) |
Twist minimal: | no (minimal twist has level 630) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1151.3 | ||
Root | \(-0.965926 + 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3150.1151 |
Dual form | 3150.2.bf.b.1601.3 |
$q$-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 \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(2801\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | − | 0.500000i | 0.612372 | − | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.189469 | − | 2.63896i | −0.0716124 | − | 0.997433i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.55171 | − | 1.47323i | −0.769370 | − | 0.444196i | 0.0632797 | − | 0.997996i | \(-0.479844\pi\) |
−0.832650 | + | 0.553800i | \(0.813177\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 3.93185i | − | 1.09050i | −0.838274 | − | 0.545250i | \(-0.816435\pi\) | ||
0.838274 | − | 0.545250i | \(-0.183565\pi\) | |||||||
\(14\) | −1.48356 | − | 2.19067i | −0.396499 | − | 0.585481i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −0.199801 | + | 0.346065i | −0.0484588 | + | 0.0839331i | −0.889237 | − | 0.457446i | \(-0.848764\pi\) |
0.840779 | + | 0.541379i | \(0.182098\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.0305501 | − | 0.0176381i | 0.00700867 | − | 0.00404646i | −0.496492 | − | 0.868042i | \(-0.665379\pi\) |
0.503500 | + | 0.863995i | \(0.332045\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.94646 | −0.628188 | ||||||||
\(23\) | 3.23205 | − | 1.86603i | 0.673929 | − | 0.389093i | −0.123635 | − | 0.992328i | \(-0.539455\pi\) |
0.797564 | + | 0.603235i | \(0.206122\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.96593 | − | 3.40508i | −0.385550 | − | 0.667792i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.38014 | − | 1.15539i | −0.449804 | − | 0.218349i | ||||
\(29\) | 8.89898i | 1.65250i | 0.563304 | + | 0.826250i | \(0.309530\pi\) | ||||
−0.563304 | + | 0.826250i | \(0.690470\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.717439 | + | 0.414214i | 0.128856 | + | 0.0743950i | 0.563042 | − | 0.826428i | \(-0.309631\pi\) |
−0.434187 | + | 0.900823i | \(0.642964\pi\) | |||||||
\(32\) | −0.866025 | − | 0.500000i | −0.153093 | − | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.399602i | 0.0685311i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.96593 | − | 6.86919i | −0.651994 | − | 1.12929i | −0.982638 | − | 0.185532i | \(-0.940599\pi\) |
0.330644 | − | 0.943756i | \(-0.392734\pi\) | |||||||
\(38\) | 0.0176381 | − | 0.0305501i | 0.00286128 | − | 0.00495588i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.31079 | −0.985580 | −0.492790 | − | 0.870148i | \(-0.664023\pi\) | ||||
−0.492790 | + | 0.870148i | \(0.664023\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.03528 | 0.462875 | 0.231438 | − | 0.972850i | \(-0.425657\pi\) | ||||
0.231438 | + | 0.972850i | \(0.425657\pi\) | |||||||
\(44\) | −2.55171 | + | 1.47323i | −0.384685 | + | 0.222098i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.86603 | − | 3.23205i | 0.275130 | − | 0.476540i | ||||
\(47\) | −2.90130 | − | 5.02520i | −0.423198 | − | 0.733001i | 0.573052 | − | 0.819519i | \(-0.305759\pi\) |
−0.996250 | + | 0.0865180i | \(0.972426\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.92820 | + | 1.00000i | −0.989743 | + | 0.142857i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.40508 | − | 1.96593i | −0.472200 | − | 0.272625i | ||||
\(53\) | −3.72268 | − | 2.14929i | −0.511349 | − | 0.295228i | 0.222039 | − | 0.975038i | \(-0.428729\pi\) |
−0.733388 | + | 0.679810i | \(0.762062\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.63896 | + | 0.189469i | −0.352646 | + | 0.0253188i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.44949 | + | 7.70674i | 0.584247 | + | 1.01194i | ||||
\(59\) | −2.78522 | + | 4.82415i | −0.362605 | + | 0.628050i | −0.988389 | − | 0.151946i | \(-0.951446\pi\) |
0.625784 | + | 0.779997i | \(0.284779\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.97710 | + | 5.76028i | −1.27744 | + | 0.737528i | −0.976376 | − | 0.216077i | \(-0.930674\pi\) |
−0.301060 | + | 0.953605i | \(0.597340\pi\) | |||||||
\(62\) | 0.828427 | 0.105210 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.25966 | + | 10.8420i | −0.764739 | + | 1.32457i | 0.175646 | + | 0.984453i | \(0.443799\pi\) |
−0.940385 | + | 0.340113i | \(0.889535\pi\) | |||||||
\(68\) | 0.199801 | + | 0.346065i | 0.0242294 | + | 0.0419666i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.93426i | 0.229554i | 0.993391 | + | 0.114777i | \(0.0366153\pi\) | ||||
−0.993391 | + | 0.114777i | \(0.963385\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.297173 | + | 0.171573i | 0.0347815 | + | 0.0200811i | 0.517290 | − | 0.855810i | \(-0.326941\pi\) |
−0.482508 | + | 0.875891i | \(0.660274\pi\) | |||||||
\(74\) | −6.86919 | − | 3.96593i | −0.798527 | − | 0.461030i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 0.0352762i | − | 0.00404646i | ||||||
\(77\) | −3.40433 | + | 7.01299i | −0.387959 | + | 0.799205i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.15331 | − | 7.19375i | −0.467284 | − | 0.809360i | 0.532017 | − | 0.846734i | \(-0.321434\pi\) |
−0.999301 | + | 0.0373736i | \(0.988101\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −5.46530 | + | 3.15539i | −0.603542 | + | 0.348455i | ||||
\(83\) | 10.3490 | 1.13595 | 0.567974 | − | 0.823046i | \(-0.307727\pi\) | ||||
0.567974 | + | 0.823046i | \(0.307727\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.62863 | − | 1.51764i | 0.283452 | − | 0.163651i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.47323 | + | 2.55171i | −0.157047 | + | 0.272013i | ||||
\(89\) | 3.08604 | + | 5.34519i | 0.327120 | + | 0.566589i | 0.981939 | − | 0.189197i | \(-0.0605885\pi\) |
−0.654819 | + | 0.755786i | \(0.727255\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.3760 | + | 0.744963i | −1.08770 | + | 0.0780933i | ||||
\(92\) | − | 3.73205i | − | 0.389093i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −5.02520 | − | 2.90130i | −0.518310 | − | 0.299246i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 15.6344i | − | 1.58744i | −0.608286 | − | 0.793718i | \(-0.708143\pi\) | ||
0.608286 | − | 0.793718i | \(-0.291857\pi\) | |||||||
\(98\) | −5.50000 | + | 4.33013i | −0.555584 | + | 0.437409i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.02458 | − | 15.6310i | 0.897979 | − | 1.55535i | 0.0679057 | − | 0.997692i | \(-0.478368\pi\) |
0.830074 | − | 0.557654i | \(-0.188298\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.37857 | − | 4.26002i | 0.727032 | − | 0.419752i | −0.0903031 | − | 0.995914i | \(-0.528784\pi\) |
0.817336 | + | 0.576162i | \(0.195450\pi\) | |||||||
\(104\) | −3.93185 | −0.385550 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.29858 | −0.417515 | ||||||||
\(107\) | −14.7702 | + | 8.52761i | −1.42789 | + | 0.824395i | −0.996954 | − | 0.0779862i | \(-0.975151\pi\) |
−0.430939 | + | 0.902381i | \(0.641818\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.84909 | − | 10.1309i | 0.560241 | − | 0.970366i | −0.437234 | − | 0.899348i | \(-0.644042\pi\) |
0.997475 | − | 0.0710185i | \(-0.0226249\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.19067 | + | 1.48356i | −0.206999 | + | 0.140184i | ||||
\(113\) | − | 13.5546i | − | 1.27511i | −0.770405 | − | 0.637554i | \(-0.779946\pi\) | ||
0.770405 | − | 0.637554i | \(-0.220054\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 7.70674 | + | 4.44949i | 0.715553 | + | 0.413125i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 5.57045i | 0.512801i | ||||||||
\(119\) | 0.951108 | + | 0.461698i | 0.0871879 | + | 0.0423237i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.15918 | − | 2.00775i | −0.105380 | − | 0.182523i | ||||
\(122\) | −5.76028 | + | 9.97710i | −0.521511 | + | 0.903284i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.717439 | − | 0.414214i | 0.0644279 | − | 0.0371975i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.95983 | −0.795056 | −0.397528 | − | 0.917590i | \(-0.630132\pi\) | ||||
−0.397528 | + | 0.917590i | \(0.630132\pi\) | |||||||
\(128\) | −0.866025 | + | 0.500000i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.39047 | + | 11.0686i | 0.558338 | + | 0.967070i | 0.997635 | + | 0.0687282i | \(0.0218941\pi\) |
−0.439297 | + | 0.898342i | \(0.644773\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.0523345 | − | 0.0772785i | −0.00453797 | − | 0.00670090i | ||||
\(134\) | 12.5193i | 1.08150i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.346065 | + | 0.199801i | 0.0296748 | + | 0.0171328i | ||||
\(137\) | −4.78094 | − | 2.76028i | −0.408464 | − | 0.235827i | 0.281666 | − | 0.959513i | \(-0.409113\pi\) |
−0.690129 | + | 0.723686i | \(0.742446\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 21.8471i | − | 1.85305i | −0.376235 | − | 0.926524i | \(-0.622782\pi\) | ||
0.376235 | − | 0.926524i | \(-0.377218\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.967128 | + | 1.67511i | 0.0811596 | + | 0.140572i | ||||
\(143\) | −5.79253 | + | 10.0330i | −0.484396 | + | 0.838998i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.343146 | 0.0283989 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7.93185 | −0.651994 | ||||||||
\(149\) | 18.6179 | − | 10.7491i | 1.52524 | − | 0.880598i | 0.525688 | − | 0.850677i | \(-0.323808\pi\) |
0.999552 | − | 0.0299204i | \(-0.00952537\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.47531 | + | 2.55532i | −0.120059 | + | 0.207949i | −0.919791 | − | 0.392409i | \(-0.871642\pi\) |
0.799732 | + | 0.600358i | \(0.204975\pi\) | |||||||
\(152\) | −0.0176381 | − | 0.0305501i | −0.00143064 | − | 0.00247794i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.558263 | + | 7.77559i | 0.0449861 | + | 0.626575i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −19.4823 | − | 11.2481i | −1.55486 | − | 0.897698i | −0.997735 | − | 0.0672682i | \(-0.978572\pi\) |
−0.557123 | − | 0.830430i | \(-0.688095\pi\) | |||||||
\(158\) | −7.19375 | − | 4.15331i | −0.572304 | − | 0.330420i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.53674 | − | 8.17569i | −0.436356 | − | 0.644335i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.4035 | + | 19.7515i | 0.893192 | + | 1.54705i | 0.836026 | + | 0.548690i | \(0.184873\pi\) |
0.0571664 | + | 0.998365i | \(0.481793\pi\) | |||||||
\(164\) | −3.15539 | + | 5.46530i | −0.246395 | + | 0.426769i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.96248 | − | 5.17449i | 0.695624 | − | 0.401618i | ||||
\(167\) | 8.84961 | 0.684803 | 0.342402 | − | 0.939554i | \(-0.388760\pi\) | ||||
0.342402 | + | 0.939554i | \(0.388760\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.45946 | −0.189189 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.51764 | − | 2.62863i | 0.115719 | − | 0.200431i | ||||
\(173\) | 3.86843 | + | 6.70032i | 0.294111 | + | 0.509416i | 0.974778 | − | 0.223178i | \(-0.0716430\pi\) |
−0.680667 | + | 0.732593i | \(0.738310\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.94646i | 0.222098i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 5.34519 | + | 3.08604i | 0.400639 | + | 0.231309i | ||||
\(179\) | 0.417291 | + | 0.240923i | 0.0311898 | + | 0.0180074i | 0.515514 | − | 0.856881i | \(-0.327601\pi\) |
−0.484324 | + | 0.874889i | \(0.660934\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 2.44876i | − | 0.182015i | −0.995850 | − | 0.0910075i | \(-0.970991\pi\) | ||
0.995850 | − | 0.0910075i | \(-0.0290087\pi\) | |||||||
\(182\) | −8.61339 | + | 5.83315i | −0.638467 | + | 0.432382i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.86603 | − | 3.23205i | −0.137565 | − | 0.238270i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.01967 | − | 0.588706i | 0.0745655 | − | 0.0430504i | ||||
\(188\) | −5.80260 | −0.423198 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.89241 | + | 2.24728i | −0.281645 | + | 0.162608i | −0.634168 | − | 0.773195i | \(-0.718657\pi\) |
0.352523 | + | 0.935803i | \(0.385324\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.28497 | + | 10.8859i | −0.452402 | + | 0.783583i | −0.998535 | − | 0.0541158i | \(-0.982766\pi\) |
0.546133 | + | 0.837698i | \(0.316099\pi\) | |||||||
\(194\) | −7.81722 | − | 13.5398i | −0.561243 | − | 0.972102i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.59808 | + | 6.50000i | −0.185577 | + | 0.464286i | ||||
\(197\) | 13.3748i | 0.952916i | 0.879197 | + | 0.476458i | \(0.158080\pi\) | ||||
−0.879197 | + | 0.476458i | \(0.841920\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −23.5169 | − | 13.5775i | −1.66707 | − | 0.962483i | −0.969206 | − | 0.246253i | \(-0.920801\pi\) |
−0.697864 | − | 0.716231i | \(-0.745866\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 18.0492i | − | 1.26993i | ||||||
\(203\) | 23.4840 | − | 1.68608i | 1.64826 | − | 0.118339i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 4.26002 | − | 7.37857i | 0.296810 | − | 0.514090i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.40508 | + | 1.96593i | −0.236100 | + | 0.136312i | ||||
\(209\) | −0.103940 | −0.00718968 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.4183 | 1.26797 | 0.633984 | − | 0.773346i | \(-0.281419\pi\) | ||||
0.633984 | + | 0.773346i | \(0.281419\pi\) | |||||||
\(212\) | −3.72268 | + | 2.14929i | −0.255675 | + | 0.147614i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −8.52761 | + | 14.7702i | −0.582935 | + | 1.00967i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.957160 | − | 1.97177i | 0.0649763 | − | 0.133853i | ||||
\(218\) | − | 11.6982i | − | 0.792301i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.36068 | + | 0.785587i | 0.0915290 | + | 0.0528443i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 17.8045i | − | 1.19228i | −0.802881 | − | 0.596140i | \(-0.796700\pi\) | ||
0.802881 | − | 0.596140i | \(-0.203300\pi\) | |||||||
\(224\) | −1.15539 | + | 2.38014i | −0.0771980 | + | 0.159030i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.77729 | − | 11.7386i | −0.450819 | − | 0.780841i | ||||
\(227\) | 0.856140 | − | 1.48288i | 0.0568240 | − | 0.0984220i | −0.836214 | − | 0.548403i | \(-0.815236\pi\) |
0.893038 | + | 0.449981i | \(0.148569\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.26142 | − | 3.03768i | 0.347684 | − | 0.200736i | −0.315981 | − | 0.948766i | \(-0.602333\pi\) |
0.663665 | + | 0.748030i | \(0.269000\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8.89898 | 0.584247 | ||||||||
\(233\) | −6.17109 | + | 3.56288i | −0.404282 | + | 0.233412i | −0.688330 | − | 0.725398i | \(-0.741656\pi\) |
0.284048 | + | 0.958810i | \(0.408322\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.78522 | + | 4.82415i | 0.181303 | + | 0.314025i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.05453 | − | 0.0757120i | 0.0683552 | − | 0.00490768i | ||||
\(239\) | 18.7194i | 1.21085i | 0.795900 | + | 0.605427i | \(0.206998\pi\) | ||||
−0.795900 | + | 0.605427i | \(0.793002\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.68036 | + | 4.43426i | 0.494735 | + | 0.285636i | 0.726537 | − | 0.687128i | \(-0.241129\pi\) |
−0.231802 | + | 0.972763i | \(0.574462\pi\) | |||||||
\(242\) | −2.00775 | − | 1.15918i | −0.129063 | − | 0.0745147i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 11.5206i | 0.737528i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.0693504 | − | 0.120118i | −0.00441266 | − | 0.00764295i | ||||
\(248\) | 0.414214 | − | 0.717439i | 0.0263026 | − | 0.0455574i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −22.1738 | −1.39960 | −0.699798 | − | 0.714341i | \(-0.746727\pi\) | ||||
−0.699798 | + | 0.714341i | \(0.746727\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −10.9964 | −0.691335 | ||||||||
\(254\) | −7.75944 | + | 4.47992i | −0.486871 | + | 0.281095i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −8.41662 | − | 14.5780i | −0.525014 | − | 0.909351i | −0.999576 | − | 0.0291289i | \(-0.990727\pi\) |
0.474561 | − | 0.880222i | \(-0.342607\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −17.3761 | + | 11.7674i | −1.07970 | + | 0.731191i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 11.0686 | + | 6.39047i | 0.683822 | + | 0.394805i | ||||
\(263\) | 19.1562 | + | 11.0599i | 1.18122 | + | 0.681980i | 0.956297 | − | 0.292396i | \(-0.0944525\pi\) |
0.224926 | + | 0.974376i | \(0.427786\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.0839622 | − | 0.0407579i | −0.00514805 | − | 0.00249903i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6.25966 | + | 10.8420i | 0.382369 | + | 0.662283i | ||||
\(269\) | −1.45049 | + | 2.51231i | −0.0884377 | + | 0.153179i | −0.906851 | − | 0.421452i | \(-0.861521\pi\) |
0.818413 | + | 0.574630i | \(0.194854\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.1244 | − | 8.73205i | 0.918739 | − | 0.530434i | 0.0355066 | − | 0.999369i | \(-0.488696\pi\) |
0.883233 | + | 0.468935i | \(0.155362\pi\) | |||||||
\(272\) | 0.399602 | 0.0242294 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.52056 | −0.333509 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.28825 | − | 3.96336i | 0.137488 | − | 0.238135i | −0.789057 | − | 0.614319i | \(-0.789431\pi\) |
0.926545 | + | 0.376184i | \(0.122764\pi\) | |||||||
\(278\) | −10.9236 | − | 18.9202i | −0.655152 | − | 1.13476i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.55948i | 0.570271i | 0.958487 | + | 0.285135i | \(0.0920386\pi\) | ||||
−0.958487 | + | 0.285135i | \(0.907961\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.46238 | − | 5.46311i | −0.562480 | − | 0.324748i | 0.191660 | − | 0.981461i | \(-0.438613\pi\) |
−0.754140 | + | 0.656713i | \(0.771946\pi\) | |||||||
\(284\) | 1.67511 | + | 0.967128i | 0.0993998 | + | 0.0573885i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 11.5851i | 0.685039i | ||||||||
\(287\) | 1.19570 | + | 16.6539i | 0.0705798 | + | 0.983049i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.42016 | + | 14.5841i | 0.495303 | + | 0.857891i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.297173 | − | 0.171573i | 0.0173907 | − | 0.0100405i | ||||
\(293\) | 16.2280 | 0.948052 | 0.474026 | − | 0.880511i | \(-0.342800\pi\) | ||||
0.474026 | + | 0.880511i | \(0.342800\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −6.86919 | + | 3.96593i | −0.399263 | + | 0.230515i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 10.7491 | − | 18.6179i | 0.622677 | − | 1.07851i | ||||
\(299\) | −7.33694 | − | 12.7079i | −0.424306 | − | 0.734919i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.575090 | − | 8.00997i | −0.0331476 | − | 0.461687i | ||||
\(302\) | 2.95063i | 0.169790i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.0305501 | − | 0.0176381i | −0.00175217 | − | 0.00101161i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 12.3782i | − | 0.706462i | −0.935536 | − | 0.353231i | \(-0.885083\pi\) | ||
0.935536 | − | 0.353231i | \(-0.114917\pi\) | |||||||
\(308\) | 4.37127 | + | 6.45473i | 0.249076 | + | 0.367792i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.4312 | + | 19.7995i | −0.648206 | + | 1.12272i | 0.335346 | + | 0.942095i | \(0.391147\pi\) |
−0.983551 | + | 0.180630i | \(0.942186\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 30.1399 | − | 17.4013i | 1.70361 | − | 0.983578i | 0.761563 | − | 0.648091i | \(-0.224432\pi\) |
0.942045 | − | 0.335487i | \(-0.108901\pi\) | |||||||
\(314\) | −22.4962 | −1.26954 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.30663 | −0.467284 | ||||||||
\(317\) | 5.87780 | − | 3.39355i | 0.330130 | − | 0.190601i | −0.325769 | − | 0.945449i | \(-0.605623\pi\) |
0.655899 | + | 0.754849i | \(0.272290\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 13.1103 | − | 22.7076i | 0.734034 | − | 1.27138i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −8.88280 | − | 4.31199i | −0.495019 | − | 0.240298i | ||||
\(323\) | 0.0140964i | 0.000784346i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 19.7515 | + | 11.4035i | 1.09393 | + | 0.631582i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6.31079i | 0.348455i | ||||||||
\(329\) | −12.7116 | + | 8.60853i | −0.700813 | + | 0.474604i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.56985 | − | 9.64726i | −0.306147 | − | 0.530261i | 0.671369 | − | 0.741123i | \(-0.265706\pi\) |
−0.977516 | + | 0.210862i | \(0.932373\pi\) | |||||||
\(332\) | 5.17449 | − | 8.96248i | 0.283987 | − | 0.491880i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 7.66398 | − | 4.42480i | 0.419355 | − | 0.242114i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.59111 | −0.0866733 | −0.0433366 | − | 0.999061i | \(-0.513799\pi\) | ||||
−0.0433366 | + | 0.999061i | \(0.513799\pi\) | |||||||
\(338\) | −2.12995 | + | 1.22973i | −0.115854 | + | 0.0668884i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.22047 | − | 2.11391i | −0.0660919 | − | 0.114475i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.95164 | + | 18.0938i | 0.213368 | + | 0.976972i | ||||
\(344\) | − | 3.03528i | − | 0.163651i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.70032 | + | 3.86843i | 0.360211 | + | 0.207968i | ||||
\(347\) | 13.3860 | + | 7.72840i | 0.718597 | + | 0.414882i | 0.814236 | − | 0.580534i | \(-0.197156\pi\) |
−0.0956388 | + | 0.995416i | \(0.530489\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 0.585057i | − | 0.0313174i | −0.999877 | − | 0.0156587i | \(-0.995015\pi\) | ||
0.999877 | − | 0.0156587i | \(-0.00498452\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.47323 | + | 2.55171i | 0.0785235 | + | 0.136007i | ||||
\(353\) | −1.83788 | + | 3.18330i | −0.0978204 | + | 0.169430i | −0.910782 | − | 0.412887i | \(-0.864520\pi\) |
0.812962 | + | 0.582317i | \(0.197854\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 6.17209 | 0.327120 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.481846 | 0.0254664 | ||||||||
\(359\) | 17.4069 | − | 10.0499i | 0.918702 | − | 0.530413i | 0.0354812 | − | 0.999370i | \(-0.488704\pi\) |
0.883221 | + | 0.468958i | \(0.155370\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.49938 | + | 16.4534i | −0.499967 | + | 0.865969i | ||||
\(362\) | −1.22438 | − | 2.12069i | −0.0643520 | − | 0.111461i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −4.54284 | + | 9.35835i | −0.238110 | + | 0.490511i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.2665 | + | 9.96885i | 0.901306 | + | 0.520369i | 0.877624 | − | 0.479350i | \(-0.159128\pi\) |
0.0236826 | + | 0.999720i | \(0.492461\pi\) | |||||||
\(368\) | −3.23205 | − | 1.86603i | −0.168482 | − | 0.0972733i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.96656 | + | 10.2312i | −0.257851 | + | 0.531179i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.9081 | − | 29.2856i | −0.875467 | − | 1.51635i | −0.856265 | − | 0.516537i | \(-0.827221\pi\) |
−0.0192016 | − | 0.999816i | \(-0.506112\pi\) | |||||||
\(374\) | 0.588706 | − | 1.01967i | 0.0304413 | − | 0.0527258i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.02520 | + | 2.90130i | −0.259155 | + | 0.149623i | ||||
\(377\) | 34.9895 | 1.80205 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.7614 | 1.37464 | 0.687321 | − | 0.726353i | \(-0.258786\pi\) | ||||
0.687321 | + | 0.726353i | \(0.258786\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.24728 | + | 3.89241i | −0.114981 | + | 0.199153i | ||||
\(383\) | −9.89060 | − | 17.1310i | −0.505386 | − | 0.875355i | −0.999981 | − | 0.00623078i | \(-0.998017\pi\) |
0.494594 | − | 0.869124i | \(-0.335317\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 12.5699i | 0.639793i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −13.5398 | − | 7.81722i | −0.687380 | − | 0.396859i | ||||
\(389\) | −4.49181 | − | 2.59335i | −0.227744 | − | 0.131488i | 0.381787 | − | 0.924250i | \(-0.375309\pi\) |
−0.609531 | + | 0.792762i | \(0.708642\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.49133i | 0.0754200i | ||||||||
\(392\) | 1.00000 | + | 6.92820i | 0.0505076 | + | 0.349927i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6.68740 | + | 11.5829i | 0.336907 | + | 0.583539i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.99280 | + | 2.88259i | −0.250581 | + | 0.144673i | −0.620030 | − | 0.784578i | \(-0.712880\pi\) |
0.369449 | + | 0.929251i | \(0.379546\pi\) | |||||||
\(398\) | −27.1550 | −1.36116 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.4361 | − | 8.91202i | 0.770841 | − | 0.445045i | −0.0623335 | − | 0.998055i | \(-0.519854\pi\) |
0.833175 | + | 0.553010i | \(0.186521\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.62863 | − | 2.82086i | 0.0811277 | − | 0.140517i | ||||
\(404\) | −9.02458 | − | 15.6310i | −0.448990 | − | 0.777673i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 19.4947 | − | 13.2022i | 0.967507 | − | 0.655214i | ||||
\(407\) | 23.3709i | 1.15845i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −28.5617 | − | 16.4901i | −1.41228 | − | 0.815382i | −0.416681 | − | 0.909053i | \(-0.636807\pi\) |
−0.995603 | + | 0.0936705i | \(0.970140\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 8.52004i | − | 0.419752i | ||||||
\(413\) | 13.2584 | + | 6.43606i | 0.652405 | + | 0.316698i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.96593 | + | 3.40508i | −0.0963874 | + | 0.166948i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.0900147 | + | 0.0519700i | −0.00440276 | + | 0.00254194i | ||||
\(419\) | 15.2287 | 0.743969 | 0.371985 | − | 0.928239i | \(-0.378677\pi\) | ||||
0.371985 | + | 0.928239i | \(0.378677\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.9939 | 0.828234 | 0.414117 | − | 0.910224i | \(-0.364090\pi\) | ||||
0.414117 | + | 0.910224i | \(0.364090\pi\) | |||||||
\(422\) | 15.9507 | − | 9.20915i | 0.776468 | − | 0.448294i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.14929 | + | 3.72268i | −0.104379 | + | 0.180789i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 17.0915 | + | 25.2377i | 0.827115 | + | 1.22134i | ||||
\(428\) | 17.0552i | 0.824395i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.4818 | − | 8.93842i | −0.745732 | − | 0.430549i | 0.0784178 | − | 0.996921i | \(-0.475013\pi\) |
−0.824150 | + | 0.566372i | \(0.808347\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 5.56388i | − | 0.267383i | −0.991023 | − | 0.133691i | \(-0.957317\pi\) | ||
0.991023 | − | 0.133691i | \(-0.0426831\pi\) | |||||||
\(434\) | −0.156961 | − | 2.18618i | −0.00753437 | − | 0.104940i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.84909 | − | 10.1309i | −0.280121 | − | 0.485183i | ||||
\(437\) | 0.0658262 | − | 0.114014i | 0.00314890 | − | 0.00545405i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.53568 | − | 5.50543i | 0.455113 | − | 0.262760i | −0.254874 | − | 0.966974i | \(-0.582034\pi\) |
0.709987 | + | 0.704214i | \(0.248701\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.57117 | 0.0747332 | ||||||||
\(443\) | 14.7091 | − | 8.49233i | 0.698853 | − | 0.403483i | −0.108067 | − | 0.994144i | \(-0.534466\pi\) |
0.806920 | + | 0.590661i | \(0.201133\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −8.90226 | − | 15.4192i | −0.421534 | − | 0.730119i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.189469 | + | 2.63896i | 0.00895155 | + | 0.124679i | ||||
\(449\) | 12.5892i | 0.594122i | 0.954858 | + | 0.297061i | \(0.0960065\pi\) | ||||
−0.954858 | + | 0.297061i | \(0.903994\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.1033 | + | 9.29725i | 0.758276 | + | 0.437791i | ||||
\(452\) | −11.7386 | − | 6.77729i | −0.552138 | − | 0.318777i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 1.71228i | − | 0.0803612i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.08417 | − | 1.87783i | −0.0507153 | − | 0.0878414i | 0.839553 | − | 0.543277i | \(-0.182817\pi\) |
−0.890269 | + | 0.455436i | \(0.849483\pi\) | |||||||
\(458\) | 3.03768 | − | 5.26142i | 0.141941 | − | 0.245850i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 34.3032 | 1.59766 | 0.798829 | − | 0.601558i | \(-0.205453\pi\) | ||||
0.798829 | + | 0.601558i | \(0.205453\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −28.2133 | −1.31118 | −0.655592 | − | 0.755115i | \(-0.727581\pi\) | ||||
−0.655592 | + | 0.755115i | \(0.727581\pi\) | |||||||
\(464\) | 7.70674 | − | 4.44949i | 0.357777 | − | 0.206562i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.56288 | + | 6.17109i | −0.165047 | + | 0.285870i | ||||
\(467\) | 2.10342 | + | 3.64324i | 0.0973349 | + | 0.168589i | 0.910581 | − | 0.413331i | \(-0.135635\pi\) |
−0.813246 | + | 0.581920i | \(0.802302\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 29.7977 | + | 14.4647i | 1.37593 | + | 0.667920i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.82415 | + | 2.78522i | 0.222049 | + | 0.128200i | ||||
\(473\) | −7.74515 | − | 4.47167i | −0.356122 | − | 0.205607i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.875396 | − | 0.592835i | 0.0401237 | − | 0.0271725i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 9.35968 | + | 16.2114i | 0.428102 | + | 0.741494i | ||||
\(479\) | 7.35968 | − | 12.7473i | 0.336272 | − | 0.582441i | −0.647456 | − | 0.762103i | \(-0.724167\pi\) |
0.983728 | + | 0.179662i | \(0.0575004\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −27.0086 | + | 15.5934i | −1.23149 | + | 0.710999i | ||||
\(482\) | 8.86851 | 0.403950 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.31835 | −0.105380 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.938784 | + | 1.62602i | −0.0425404 | + | 0.0736821i | −0.886512 | − | 0.462706i | \(-0.846878\pi\) |
0.843971 | + | 0.536388i | \(0.180212\pi\) | |||||||
\(488\) | 5.76028 | + | 9.97710i | 0.260756 | + | 0.451642i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.4281i | 0.470613i | 0.971921 | + | 0.235307i | \(0.0756095\pi\) | ||||
−0.971921 | + | 0.235307i | \(0.924391\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.07963 | − | 1.77802i | −0.138699 | − | 0.0800782i | ||||
\(494\) | −0.120118 | − | 0.0693504i | −0.00540438 | − | 0.00312022i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 0.828427i | − | 0.0371975i | ||||||
\(497\) | 5.10442 | − | 0.366481i | 0.228965 | − | 0.0164389i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.8822 | + | 32.7050i | 0.845285 | + | 1.46408i | 0.885374 | + | 0.464880i | \(0.153903\pi\) |
−0.0400890 | + | 0.999196i | \(0.512764\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −19.2030 | + | 11.0869i | −0.857074 | + | 0.494832i | ||||
\(503\) | −35.8895 | −1.60023 | −0.800116 | − | 0.599845i | \(-0.795229\pi\) | ||||
−0.800116 | + | 0.599845i | \(0.795229\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −9.52312 | + | 5.49818i | −0.423354 | + | 0.244424i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.47992 | + | 7.75944i | −0.198764 | + | 0.344270i | ||||
\(509\) | −8.58746 | − | 14.8739i | −0.380633 | − | 0.659275i | 0.610520 | − | 0.792001i | \(-0.290960\pi\) |
−0.991153 | + | 0.132726i | \(0.957627\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.396469 | − | 0.816735i | 0.0175387 | − | 0.0361302i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −14.5780 | − | 8.41662i | −0.643008 | − | 0.371241i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 17.0972i | 0.751932i | ||||||||
\(518\) | −9.16442 | + | 18.8789i | −0.402661 | + | 0.829492i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.26539 | + | 3.92377i | −0.0992484 | + | 0.171903i | −0.911374 | − | 0.411580i | \(-0.864977\pi\) |
0.812125 | + | 0.583483i | \(0.198311\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 22.9267 | − | 13.2368i | 1.00252 | − | 0.578803i | 0.0935241 | − | 0.995617i | \(-0.470187\pi\) |
0.908992 | + | 0.416814i | \(0.136853\pi\) | |||||||
\(524\) | 12.7809 | 0.558338 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 22.1197 | 0.964465 | ||||||||
\(527\) | −0.286690 | + | 0.165520i | −0.0124884 | + | 0.00721018i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.53590 | + | 7.85641i | −0.197213 | + | 0.341583i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.0930924 | + | 0.00668373i | −0.00403607 | + | 0.000289777i | ||||
\(533\) | 24.8131i | 1.07477i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 10.8420 | + | 6.25966i | 0.468305 | + | 0.270376i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 2.90097i | 0.125070i | ||||||||
\(539\) | 19.1520 | + | 7.65514i | 0.824936 | + | 0.329730i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.16504 | − | 5.48201i | −0.136076 | − | 0.235690i | 0.789932 | − | 0.613194i | \(-0.210116\pi\) |
−0.926008 | + | 0.377504i | \(0.876782\pi\) | |||||||
\(542\) | 8.73205 | − | 15.1244i | 0.375074 | − | 0.649647i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.346065 | − | 0.199801i | 0.0148374 | − | 0.00856639i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 38.5271 | 1.64730 | 0.823651 | − | 0.567097i | \(-0.191934\pi\) | ||||
0.823651 | + | 0.567097i | \(0.191934\pi\) | |||||||
\(548\) | −4.78094 | + | 2.76028i | −0.204232 | + | 0.117913i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.156961 | + | 0.271864i | 0.00668676 | + | 0.0115818i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −18.1971 | + | 12.3234i | −0.773819 | + | 0.524045i | ||||
\(554\) | − | 4.57650i | − | 0.194437i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −18.9202 | − | 10.9236i | −0.802393 | − | 0.463262i | ||||
\(557\) | −8.00456 | − | 4.62144i | −0.339164 | − | 0.195817i | 0.320738 | − | 0.947168i | \(-0.396069\pi\) |
−0.659902 | + | 0.751351i | \(0.729402\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 11.9343i | − | 0.504765i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4.77974 | + | 8.27875i | 0.201621 | + | 0.349218i | ||||
\(563\) | −13.3871 | + | 23.1872i | −0.564201 | + | 0.977225i | 0.432923 | + | 0.901431i | \(0.357482\pi\) |
−0.997124 | + | 0.0757935i | \(0.975851\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −10.9262 | −0.459263 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.93426 | 0.0811596 | ||||||||
\(569\) | 39.6604 | − | 22.8979i | 1.66265 | − | 0.959931i | 0.691207 | − | 0.722657i | \(-0.257079\pi\) |
0.971443 | − | 0.237274i | \(-0.0762539\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.390149 | + | 0.675759i | −0.0163272 | + | 0.0282796i | −0.874074 | − | 0.485794i | \(-0.838531\pi\) |
0.857746 | + | 0.514073i | \(0.171864\pi\) | |||||||
\(572\) | 5.79253 | + | 10.0330i | 0.242198 | + | 0.419499i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 9.36246 | + | 13.8249i | 0.390781 | + | 0.577039i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.74401 | + | 5.62571i | 0.405648 | + | 0.234201i | 0.688918 | − | 0.724839i | \(-0.258086\pi\) |
−0.283270 | + | 0.959040i | \(0.591419\pi\) | |||||||
\(578\) | 14.5841 | + | 8.42016i | 0.606620 | + | 0.350232i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.96081 | − | 27.3105i | −0.0813480 | − | 1.13303i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.33281 | + | 10.9687i | 0.262278 | + | 0.454279i | ||||
\(584\) | 0.171573 | − | 0.297173i | 0.00709974 | − | 0.0122971i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 14.0539 | − | 8.11401i | 0.580561 | − | 0.335187i | ||||
\(587\) | −40.1593 | −1.65755 | −0.828775 | − | 0.559582i | \(-0.810962\pi\) | ||||
−0.828775 | + | 0.559582i | \(0.810962\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.0292237 | 0.00120414 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.96593 | + | 6.86919i | −0.162999 | + | 0.282322i | ||||
\(593\) | −9.54170 | − | 16.5267i | −0.391831 | − | 0.678671i | 0.600860 | − | 0.799354i | \(-0.294825\pi\) |
−0.992691 | + | 0.120683i | \(0.961491\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 21.4981i | − | 0.880598i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −12.7079 | − | 7.33694i | −0.519666 | − | 0.300030i | ||||
\(599\) | 24.6424 | + | 14.2273i | 1.00686 | + | 0.581312i | 0.910271 | − | 0.414013i | \(-0.135873\pi\) |
0.0965902 | + | 0.995324i | \(0.469206\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 29.2553i | − | 1.19335i | −0.802484 | − | 0.596673i | \(-0.796489\pi\) | ||
0.802484 | − | 0.596673i | \(-0.203511\pi\) | |||||||
\(602\) | −4.50303 | − | 6.64929i | −0.183530 | − | 0.271005i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.47531 | + | 2.55532i | 0.0600297 | + | 0.103974i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22.3712 | − | 12.9160i | 0.908020 | − | 0.524246i | 0.0282267 | − | 0.999602i | \(-0.491014\pi\) |
0.879794 | + | 0.475356i | \(0.157681\pi\) | |||||||
\(608\) | −0.0352762 | −0.00143064 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −19.7583 | + | 11.4075i | −0.799337 | + | 0.461498i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.12216 | − | 14.0680i | 0.328051 | − | 0.568201i | −0.654074 | − | 0.756430i | \(-0.726942\pi\) |
0.982125 | + | 0.188230i | \(0.0602749\pi\) | |||||||
\(614\) | −6.18910 | − | 10.7198i | −0.249772 | − | 0.432618i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7.01299 | + | 3.40433i | 0.282562 | + | 0.137164i | ||||
\(617\) | − | 31.8398i | − | 1.28182i | −0.767615 | − | 0.640911i | \(-0.778557\pi\) | ||
0.767615 | − | 0.640911i | \(-0.221443\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.01055 | + | 4.62490i | 0.321971 | + | 0.185890i | 0.652271 | − | 0.757986i | \(-0.273816\pi\) |
−0.330300 | + | 0.943876i | \(0.607150\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 22.8625i | 0.916701i | ||||||||
\(623\) | 13.5210 | − | 9.15669i | 0.541708 | − | 0.366855i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 17.4013 | − | 30.1399i | 0.695495 | − | 1.20463i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −19.4823 | + | 11.2481i | −0.777429 | + | 0.448849i | ||||
\(629\) | 3.16958 | 0.126379 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.3096 | −0.410421 | −0.205210 | − | 0.978718i | \(-0.565788\pi\) | ||||
−0.205210 | + | 0.978718i | \(0.565788\pi\) | |||||||
\(632\) | −7.19375 | + | 4.15331i | −0.286152 | + | 0.165210i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 3.39355 | − | 5.87780i | 0.134775 | − | 0.233437i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.93185 | + | 27.2407i | 0.155786 | + | 1.07931i | ||||
\(638\) | − | 26.2205i | − | 1.03808i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.1181 | + | 6.41906i | 0.439140 | + | 0.253538i | 0.703233 | − | 0.710960i | \(-0.251739\pi\) |
−0.264093 | + | 0.964497i | \(0.585072\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 8.96224i | − | 0.353436i | −0.984262 | − | 0.176718i | \(-0.943452\pi\) | ||
0.984262 | − | 0.176718i | \(-0.0565481\pi\) | |||||||
\(644\) | −9.84873 | + | 0.707107i | −0.388094 | + | 0.0278639i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.00704821 | + | 0.0122079i | 0.000277308 | + | 0.000480312i | ||||
\(647\) | 22.6852 | − | 39.2919i | 0.891846 | − | 1.54472i | 0.0541854 | − | 0.998531i | \(-0.482744\pi\) |
0.837660 | − | 0.546191i | \(-0.183923\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14.2142 | − | 8.20656i | 0.557955 | − | 0.322136i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 22.8070 | 0.893192 | ||||||||
\(653\) | 28.4051 | − | 16.3997i | 1.11158 | − | 0.641769i | 0.172340 | − | 0.985038i | \(-0.444867\pi\) |
0.939237 | + | 0.343268i | \(0.111534\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.15539 | + | 5.46530i | 0.123197 | + | 0.213384i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −6.70430 | + | 13.8110i | −0.261361 | + | 0.538409i | ||||
\(659\) | − | 18.7103i | − | 0.728850i | −0.931233 | − | 0.364425i | \(-0.881266\pi\) | ||
0.931233 | − | 0.364425i | \(-0.118734\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.41761 | + | 4.28256i | 0.288512 | + | 0.166572i | 0.637270 | − | 0.770640i | \(-0.280063\pi\) |
−0.348759 | + | 0.937213i | \(0.613397\pi\) | |||||||
\(662\) | −9.64726 | − | 5.56985i | −0.374951 | − | 0.216478i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 10.3490i | − | 0.401618i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 16.6057 | + | 28.7620i | 0.642976 | + | 1.11367i | ||||
\(668\) | 4.42480 | − | 7.66398i | 0.171201 | − | 0.296528i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 33.9449 | 1.31043 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.179617 | 0.00692372 | 0.00346186 | − | 0.999994i | \(-0.498898\pi\) | ||||
0.00346186 | + | 0.999994i | \(0.498898\pi\) | |||||||
\(674\) | −1.37794 | + | 0.795555i | −0.0530763 | + | 0.0306436i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.22973 | + | 2.12995i | −0.0472973 | + | 0.0819213i | ||||
\(677\) | −20.7051 | − | 35.8623i | −0.795763 | − | 1.37830i | −0.922354 | − | 0.386346i | \(-0.873737\pi\) |
0.126591 | − | 0.991955i | \(-0.459596\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −41.2586 | + | 2.96224i | −1.58336 | + | 0.113680i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.11391 | − | 1.22047i | −0.0809457 | − | 0.0467340i | ||||
\(683\) | −37.5900 | − | 21.7026i | −1.43834 | − | 0.830427i | −0.440608 | − | 0.897700i | \(-0.645237\pi\) |
−0.997735 | + | 0.0672723i | \(0.978570\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 12.4691 | + | 13.6938i | 0.476073 | + | 0.522834i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.51764 | − | 2.62863i | −0.0578594 | − | 0.100215i | ||||
\(689\) | −8.45069 | + | 14.6370i | −0.321946 | + | 0.557626i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.8728 | + | 9.74150i | −0.641871 | + | 0.370584i | −0.785335 | − | 0.619071i | \(-0.787509\pi\) |
0.143464 | + | 0.989656i | \(0.454176\pi\) | |||||||
\(692\) | 7.73686 | 0.294111 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 15.4568 | 0.586732 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.26090 | − | 2.18394i | 0.0477600 | − | 0.0827228i | ||||
\(698\) | −0.292529 | − | 0.506675i | −0.0110724 | − | 0.0191779i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 47.0245i | − | 1.77609i | −0.459755 | − | 0.888046i | \(-0.652063\pi\) | ||
0.459755 | − | 0.888046i | \(-0.347937\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.242319 | − | 0.139903i | −0.00913922 | − | 0.00527653i | ||||
\(704\) | 2.55171 | + | 1.47323i | 0.0961713 | + | 0.0555245i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.67576i | 0.138339i | ||||||||
\(707\) | −42.9595 | − | 20.8539i | −1.61566 | − | 0.784292i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 24.2227 | + | 41.9549i | 0.909701 | + | 1.57565i | 0.814480 | + | 0.580192i | \(0.197023\pi\) |
0.0952213 | + | 0.995456i | \(0.469644\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 5.34519 | − | 3.08604i | 0.200319 | − | 0.115654i | ||||
\(713\) | 3.09173 | 0.115786 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.417291 | − | 0.240923i | 0.0155949 | − | 0.00900372i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 10.0499 | − | 17.4069i | 0.375058 | − | 0.649620i | ||||
\(719\) | −20.6632 | − | 35.7897i | −0.770606 | − | 1.33473i | −0.937231 | − | 0.348709i | \(-0.886620\pi\) |
0.166625 | − | 0.986020i | \(-0.446713\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.6400 | − | 18.6646i | −0.470739 | − | 0.695106i | ||||
\(722\) | 18.9988i | 0.707060i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.12069 | − | 1.22438i | −0.0788148 | − | 0.0455037i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 16.7905i | − | 0.622726i | −0.950291 | − | 0.311363i | \(-0.899214\pi\) | ||
0.950291 | − | 0.311363i | \(-0.100786\pi\) | |||||||
\(728\) | 0.744963 | + | 10.3760i | 0.0276102 | + | 0.384560i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.606451 | + | 1.05040i | −0.0224304 | + | 0.0388506i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 26.6043 | − | 15.3600i | 0.982652 | − | 0.567335i | 0.0795826 | − | 0.996828i | \(-0.474641\pi\) |
0.903070 | + | 0.429494i | \(0.141308\pi\) | |||||||
\(734\) | 19.9377 | 0.735914 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.73205 | −0.137565 | ||||||||
\(737\) | 31.9457 | − | 18.4438i | 1.17673 | − | 0.679388i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15.3876 | + | 26.6521i | −0.566041 | + | 0.980412i | 0.430911 | + | 0.902395i | \(0.358192\pi\) |
−0.996952 | + | 0.0780176i | \(0.975141\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.814447 | + | 11.3438i | 0.0298993 | + | 0.416443i | ||||
\(743\) | 33.3616i | 1.22392i | 0.790889 | + | 0.611960i | \(0.209619\pi\) | ||||
−0.790889 | + | 0.611960i | \(0.790381\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −29.2856 | − | 16.9081i | −1.07222 | − | 0.619048i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 1.17741i | − | 0.0430504i | ||||||
\(749\) | 25.3025 | + | 37.3624i | 0.924533 | + | 1.36519i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.9452 | + | 27.6179i | 0.581849 | + | 1.00779i | 0.995260 | + | 0.0972480i | \(0.0310040\pi\) |
−0.413411 | + | 0.910545i | \(0.635663\pi\) | |||||||
\(752\) | −2.90130 | + | 5.02520i | −0.105800 | + | 0.183250i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 30.3018 | − | 17.4947i | 1.10353 | − | 0.637121i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.9065 | 0.396404 | 0.198202 | − | 0.980161i | \(-0.436490\pi\) | ||||
0.198202 | + | 0.980161i | \(0.436490\pi\) | |||||||
\(758\) | 23.1761 | − | 13.3807i | 0.841793 | − | 0.486010i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12.2097 | + | 21.1479i | 0.442602 | + | 0.766610i | 0.997882 | − | 0.0650543i | \(-0.0207220\pi\) |
−0.555280 | + | 0.831664i | \(0.687389\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −27.8433 | − | 13.5160i | −1.00800 | − | 0.489313i | ||||
\(764\) | 4.49457i | 0.162608i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −17.1310 | − | 9.89060i | −0.618969 | − | 0.357362i | ||||
\(767\) | 18.9678 | + | 10.9511i | 0.684889 | + | 0.395421i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 22.9416i | − | 0.827294i | −0.910437 | − | 0.413647i | \(-0.864255\pi\) | ||
0.910437 | − | 0.413647i | \(-0.135745\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 6.28497 | + | 10.8859i | 0.226201 | + | 0.391791i | ||||
\(773\) | −22.6837 | + | 39.2894i | −0.815877 | + | 1.41314i | 0.0928193 | + | 0.995683i | \(0.470412\pi\) |
−0.908696 | + | 0.417458i | \(0.862921\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −15.6344 | −0.561243 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −5.18670 | −0.185952 | ||||||||
\(779\) | −0.192795 | + | 0.111310i | −0.00690760 | + | 0.00398810i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.84961 | − | 4.93566i | 0.101967 | − | 0.176612i | ||||
\(782\) | 0.745667 | + | 1.29153i | 0.0266650 | + | 0.0461851i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 4.33013 | + | 5.50000i | 0.154647 | + | 0.196429i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.89834 | − | 1.67335i | −0.103314 | − | 0.0596487i | 0.447452 | − | 0.894308i | \(-0.352331\pi\) |
−0.550767 | + | 0.834659i | \(0.685665\pi\) | |||||||
\(788\) | 11.5829 | + | 6.68740i | 0.412625 | + | 0.238229i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −35.7700 | + | 2.56817i | −1.27183 | + | 0.0913136i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 22.6486 | + | 39.2285i | 0.804274 | + | 1.39304i | ||||
\(794\) | −2.88259 | + | 4.99280i | −0.102299 | + | 0.177188i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −23.5169 | + | 13.5775i | −0.833535 | + | 0.481242i | ||||
\(797\) | 36.5402 | 1.29432 | 0.647160 | − | 0.762354i | \(-0.275956\pi\) | ||||
0.647160 | + | 0.762354i | \(0.275956\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.31873 | 0.0820308 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 8.91202 | − | 15.4361i | 0.314695 | − | 0.545067i | ||||
\(803\) | −0.505533 | − | 0.875609i | −0.0178399 | − | 0.0308996i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 3.25725i | − | 0.114732i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −15.6310 | − | 9.02458i | −0.549898 | − | 0.317484i | ||||
\(809\) | −41.5179 | − | 23.9704i | −1.45969 | − | 0.842753i | −0.460696 | − | 0.887558i | \(-0.652400\pi\) |
−0.998996 | + | 0.0448048i | \(0.985733\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 49.6994i | 1.74518i | 0.488452 | + | 0.872591i | \(0.337562\pi\) | ||||
−0.488452 | + | 0.872591i | \(0.662438\pi\) | |||||||
\(812\) | 10.2818 | − | 21.1808i | 0.360822 | − | 0.743301i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 11.6855 | + | 20.2398i | 0.409575 | + | 0.709405i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.0927279 | − | 0.0535365i | 0.00324414 | − | 0.00187300i | ||||
\(818\) | −32.9802 | −1.15312 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19.6520 | − | 11.3461i | 0.685858 | − | 0.395980i | −0.116200 | − | 0.993226i | \(-0.537071\pi\) |
0.802059 | + | 0.597245i | \(0.203738\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.59711 | + | 2.76628i | −0.0556719 | + | 0.0964266i | −0.892518 | − | 0.451011i | \(-0.851063\pi\) |
0.836846 | + | 0.547438i | \(0.184397\pi\) | |||||||
\(824\) | −4.26002 | − | 7.37857i | −0.148405 | − | 0.257045i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 14.7002 | − | 1.05543i | 0.511484 | − | 0.0367229i | ||||
\(827\) | 29.7259i | 1.03367i | 0.856084 | + | 0.516836i | \(0.172890\pi\) | ||||
−0.856084 | + | 0.516836i | \(0.827110\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 26.8588 | + | 15.5069i | 0.932845 | + | 0.538578i | 0.887710 | − | 0.460403i | \(-0.152295\pi\) |
0.0451348 | + | 0.998981i | \(0.485628\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.93185i | 0.136312i | ||||||||
\(833\) | 1.03820 | − | 2.59741i | 0.0359713 | − | 0.0899950i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.0519700 | + | 0.0900147i | −0.00179742 | + | 0.00311322i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 13.1884 | − | 7.61434i | 0.455586 | − | 0.263033i | ||||
\(839\) | 35.8462 | 1.23755 | 0.618773 | − | 0.785570i | \(-0.287630\pi\) | ||||
0.618773 | + | 0.785570i | \(0.287630\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −50.1918 | −1.73075 | ||||||||
\(842\) | 14.7172 | − | 8.49697i | 0.507188 | − | 0.292825i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 9.20915 | − | 15.9507i | 0.316992 | − | 0.549046i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.07875 | + | 3.43942i | −0.174508 | + | 0.118180i | ||||
\(848\) | 4.29858i | 0.147614i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −25.6361 | − | 14.8010i | −0.878796 | − | 0.507373i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.8818i | 0.783456i | 0.920081 | + | 0.391728i | \(0.128123\pi\) | ||||
−0.920081 | + | 0.391728i | \(0.871877\pi\) | |||||||
\(854\) | 27.4205 | + | 13.3108i | 0.938311 | + | 0.455486i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8.52761 | + | 14.7702i | 0.291468 | + | 0.504837i | ||||
\(857\) | 16.8593 | − | 29.2012i | 0.575904 | − | 0.997494i | −0.420039 | − | 0.907506i | \(-0.637984\pi\) |
0.995943 | − | 0.0899883i | \(-0.0286830\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.3926 | − | 9.46427i | 0.559308 | − | 0.322917i | −0.193560 | − | 0.981088i | \(-0.562003\pi\) |
0.752868 | + | 0.658172i | \(0.228670\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −17.8768 | −0.608888 | ||||||||
\(863\) | 4.55277 | − | 2.62854i | 0.154978 | − | 0.0894767i | −0.420505 | − | 0.907290i | \(-0.638147\pi\) |
0.575484 | + | 0.817813i | \(0.304814\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −2.78194 | − | 4.81846i | −0.0945341 | − | 0.163738i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.22902 | − | 1.81481i | −0.0417158 | − | 0.0615987i | ||||
\(869\) | 24.4752i | 0.830263i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 42.6293 | + | 24.6120i | 1.44444 | + | 0.833947i | ||||
\(872\) | −10.1309 | − | 5.84909i | −0.343076 | − | 0.198075i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 0.131652i | − | 0.00445321i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.3326 | − | 35.2170i | −0.686582 | − | 1.18919i | −0.972937 | − | 0.231071i | \(-0.925777\pi\) |
0.286355 | − | 0.958124i | \(-0.407556\pi\) | |||||||
\(878\) | 5.50543 | − | 9.53568i | 0.185799 | − | 0.321814i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.01828 | 0.0343067 | 0.0171533 | − | 0.999853i | \(-0.494540\pi\) | ||||
0.0171533 | + | 0.999853i | \(0.494540\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11.0436 | −0.371647 | −0.185823 | − | 0.982583i | \(-0.559495\pi\) | ||||
−0.185823 | + | 0.982583i | \(0.559495\pi\) | |||||||
\(884\) | 1.36068 | − | 0.785587i | 0.0457645 | − | 0.0264222i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 8.49233 | − | 14.7091i | 0.285305 | − | 0.494163i | ||||
\(887\) | −12.0492 | − | 20.8698i | −0.404571 | − | 0.700738i | 0.589700 | − | 0.807622i | \(-0.299246\pi\) |
−0.994271 | + | 0.106884i | \(0.965913\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.69761 | + | 23.6446i | 0.0569359 | + | 0.793015i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −15.4192 | − | 8.90226i | −0.516272 | − | 0.298070i | ||||
\(893\) | −0.177270 | − | 0.102347i | −0.00593211 | − | 0.00342491i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.48356 | + | 2.19067i | 0.0495624 | + | 0.0731852i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 6.29461 | + | 10.9026i | 0.210054 | + | 0.363824i | ||||
\(899\) | −3.68608 | + | 6.38447i | −0.122938 | + | 0.212934i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.48759 | − | 0.858860i | 0.0495588 | − | 0.0286128i | ||||
\(902\) | 18.5945 | 0.619129 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −13.5546 | −0.450819 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.10243 | + | 14.0338i | −0.269037 | + | 0.465985i | −0.968613 | − | 0.248572i | \(-0.920039\pi\) |
0.699577 | + | 0.714558i | \(0.253372\pi\) | |||||||
\(908\) | −0.856140 | − | 1.48288i | −0.0284120 | − | 0.0492110i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 21.4586i | − | 0.710955i | −0.934685 | − | 0.355477i | \(-0.884318\pi\) | ||
0.934685 | − | 0.355477i | \(-0.115682\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −26.4076 | − | 15.2465i | −0.873965 | − | 0.504584i | ||||
\(914\) | −1.87783 | − | 1.08417i | −0.0621133 | − | 0.0358611i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 6.07536i | − | 0.200736i | ||||||
\(917\) | 27.9988 | − | 18.9613i | 0.924603 | − | 0.626159i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 29.5164 | + | 51.1240i | 0.973657 | + | 1.68642i | 0.684297 | + | 0.729203i | \(0.260109\pi\) |
0.289360 | + | 0.957220i | \(0.406558\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 29.7074 | − | 17.1516i | 0.978362 | − | 0.564857i | ||||
\(923\) | 7.60521 | 0.250328 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −24.4335 | + | 14.1067i | −0.802933 | + | 0.463574i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.44949 | − | 7.70674i | 0.146062 | − | 0.252986i | ||||
\(929\) | −12.3197 | − | 21.3383i | −0.404195 | − | 0.700087i | 0.590032 | − | 0.807380i | \(-0.299115\pi\) |
−0.994227 | + | 0.107293i | \(0.965782\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.194019 | + | 0.152750i | −0.00635872 | + | 0.00500619i | ||||
\(932\) | 7.12576i | 0.233412i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 3.64324 | + | 2.10342i | 0.119210 | + | 0.0688262i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 52.5496i | 1.71672i | 0.513048 | + | 0.858360i | \(0.328516\pi\) | ||||
−0.513048 | + | 0.858360i | \(0.671484\pi\) | |||||||
\(938\) | 33.0379 | − | 2.37202i | 1.07873 | − | 0.0774491i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.752551 | − | 1.30346i | 0.0245325 | − | 0.0424915i | −0.853499 | − | 0.521095i | \(-0.825524\pi\) |
0.878031 | + | 0.478604i | \(0.158857\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −20.3968 | + | 11.7761i | −0.664211 | + | 0.383482i | ||||
\(944\) | 5.57045 | 0.181303 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.94333 | −0.290773 | ||||||||
\(947\) | 9.84136 | − | 5.68191i | 0.319801 | − | 0.184637i | −0.331503 | − | 0.943454i | \(-0.607556\pi\) |
0.651304 | + | 0.758817i | \(0.274222\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.674599 | − | 1.16844i | 0.0218984 | − | 0.0379292i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.461698 | − | 0.951108i | 0.0149637 | − | 0.0308256i | ||||
\(953\) | − | 21.9184i | − | 0.710006i | −0.934865 | − | 0.355003i | \(-0.884480\pi\) | ||
0.934865 | − | 0.355003i | \(-0.115520\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 16.2114 | + | 9.35968i | 0.524316 | + | 0.302714i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 14.7194i | − | 0.475561i | ||||||
\(959\) | −6.37842 | + | 13.1397i | −0.205970 | + | 0.424303i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.1569 | − | 26.2524i | −0.488931 | − | 0.846853i | ||||
\(962\) | −15.5934 | + | 27.0086i | −0.502752 | + | 0.870793i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 7.68036 | − | 4.43426i | 0.247368 | − | 0.142818i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −21.6634 | −0.696649 | −0.348324 | − | 0.937374i | \(-0.613249\pi\) | ||||
−0.348324 | + | 0.937374i | \(0.613249\pi\) | |||||||
\(968\) | −2.00775 | + | 1.15918i | −0.0645316 | + | 0.0372573i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.0858379 | + | 0.148676i | 0.00275467 | + | 0.00477123i | 0.867399 | − | 0.497612i | \(-0.165790\pi\) |
−0.864645 | + | 0.502384i | \(0.832456\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −57.6536 | + | 4.13934i | −1.84829 | + | 0.132701i | ||||
\(974\) | 1.87757i | 0.0601612i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 9.97710 | + | 5.76028i | 0.319359 | + | 0.184382i | ||||
\(977\) | 9.72792 | + | 5.61642i | 0.311224 | + | 0.179685i | 0.647474 | − | 0.762088i | \(-0.275825\pi\) |
−0.336250 | + | 0.941773i | \(0.609159\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 18.1858i | − | 0.581222i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 5.21405 | + | 9.03100i | 0.166387 | + | 0.288191i | ||||
\(983\) | −13.3960 | + | 23.2026i | −0.427267 | + | 0.740048i | −0.996629 | − | 0.0820385i | \(-0.973857\pi\) |
0.569362 | + | 0.822087i | \(0.307190\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −3.55605 | −0.113248 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.138701 | −0.00441266 | ||||||||
\(989\) | 9.81017 | − | 5.66390i | 0.311945 | − | 0.180102i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.99635 | + | 12.1180i | −0.222246 | + | 0.384942i | −0.955490 | − | 0.295024i | \(-0.904672\pi\) |
0.733243 | + | 0.679966i | \(0.238006\pi\) | |||||||
\(992\) | −0.414214 | − | 0.717439i | −0.0131513 | − | 0.0227787i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 4.23732 | − | 2.86959i | 0.134400 | − | 0.0910179i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −34.2497 | − | 19.7740i | −1.08470 | − | 0.626250i | −0.152538 | − | 0.988298i | \(-0.548745\pi\) |
−0.932160 | + | 0.362047i | \(0.882078\pi\) | |||||||
\(998\) | 32.7050 | + | 18.8822i | 1.03526 | + | 0.597707i | ||||
\(999\) | 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 | 3150.2.bf.b.1151.3 | 8 | ||
3.2 | odd | 2 | 3150.2.bf.c.1151.1 | 8 | |||
5.2 | odd | 4 | 3150.2.bp.d.899.4 | 8 | |||
5.3 | odd | 4 | 3150.2.bp.a.899.1 | 8 | |||
5.4 | even | 2 | 630.2.be.a.521.2 | yes | 8 | ||
7.5 | odd | 6 | 3150.2.bf.c.1601.1 | 8 | |||
15.2 | even | 4 | 3150.2.bp.c.899.4 | 8 | |||
15.8 | even | 4 | 3150.2.bp.f.899.1 | 8 | |||
15.14 | odd | 2 | 630.2.be.b.521.4 | yes | 8 | ||
21.5 | even | 6 | inner | 3150.2.bf.b.1601.3 | 8 | ||
35.4 | even | 6 | 4410.2.b.e.881.3 | 8 | |||
35.12 | even | 12 | 3150.2.bp.f.1349.1 | 8 | |||
35.19 | odd | 6 | 630.2.be.b.341.4 | yes | 8 | ||
35.24 | odd | 6 | 4410.2.b.b.881.3 | 8 | |||
35.33 | even | 12 | 3150.2.bp.c.1349.4 | 8 | |||
105.47 | odd | 12 | 3150.2.bp.a.1349.1 | 8 | |||
105.59 | even | 6 | 4410.2.b.e.881.6 | 8 | |||
105.68 | odd | 12 | 3150.2.bp.d.1349.4 | 8 | |||
105.74 | odd | 6 | 4410.2.b.b.881.6 | 8 | |||
105.89 | even | 6 | 630.2.be.a.341.2 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.be.a.341.2 | ✓ | 8 | 105.89 | even | 6 | ||
630.2.be.a.521.2 | yes | 8 | 5.4 | even | 2 | ||
630.2.be.b.341.4 | yes | 8 | 35.19 | odd | 6 | ||
630.2.be.b.521.4 | yes | 8 | 15.14 | odd | 2 | ||
3150.2.bf.b.1151.3 | 8 | 1.1 | even | 1 | trivial | ||
3150.2.bf.b.1601.3 | 8 | 21.5 | even | 6 | inner | ||
3150.2.bf.c.1151.1 | 8 | 3.2 | odd | 2 | |||
3150.2.bf.c.1601.1 | 8 | 7.5 | odd | 6 | |||
3150.2.bp.a.899.1 | 8 | 5.3 | odd | 4 | |||
3150.2.bp.a.1349.1 | 8 | 105.47 | odd | 12 | |||
3150.2.bp.c.899.4 | 8 | 15.2 | even | 4 | |||
3150.2.bp.c.1349.4 | 8 | 35.33 | even | 12 | |||
3150.2.bp.d.899.4 | 8 | 5.2 | odd | 4 | |||
3150.2.bp.d.1349.4 | 8 | 105.68 | odd | 12 | |||
3150.2.bp.f.899.1 | 8 | 15.8 | even | 4 | |||
3150.2.bp.f.1349.1 | 8 | 35.12 | even | 12 | |||
4410.2.b.b.881.3 | 8 | 35.24 | odd | 6 | |||
4410.2.b.b.881.6 | 8 | 105.74 | odd | 6 | |||
4410.2.b.e.881.3 | 8 | 35.4 | even | 6 | |||
4410.2.b.e.881.6 | 8 | 105.59 | even | 6 |